Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 150001/16149702. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 150002/16149720. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 150003/16149729. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 150004/16149783. ------ 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 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 150005/16149837. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.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. ------ 150006/16149864. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 150007/16149927. ------ 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. ------ 150008/16149954. ------ 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)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^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. ------ 150009/16149981. ------ 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. ------ 150010/16150008. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) 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. ------ 150011/16150035. ------ 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 (^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 150012/16150062. ------ 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. ------ 150013/16150593. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(c (^x.(^y.y)))) REDUCED to normal form. ------ 150014/16150620. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b (^x.a))) REDUCED to normal form. ------ 150015/16150665. ------ 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. ------ 150016/16150692. ------ 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.(^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. ------ 150017/16150728. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 150018/16150746. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.(z1 z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.(y1 y1)))) REDUCED to normal form. ------ 150019/16150755. ------ 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. ------ 150020/16150827. ------ 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 (((a a) a) a)) REDUCED to normal form. ------ 150021/16150836. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 150022/16150863. ------ 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.(^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. ------ 150023/16150944. ------ 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.(^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. ------ 150024/16150971. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b (^x.a))(^z.a)) 6. ==[ alpha ]==> ((b (^x.a))(^y.a)) REDUCED to normal form. ------ 150025/16151061. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 150026/16151088. ------ 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. ------ 150027/16151115. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 150028/16151223. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c d)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c d)) 3. ==[ beta ]==> (((a b)(a a))(c d)) REDUCED to normal form. ------ 150029/16151358. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c ((^z.z) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(c ((^z.z) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c ((^y.y) a))) 5. ==[ beta ]==> ((b a)(c ((^y.y) a))) 6. ==[ alpha ]==> ((b a)(c ((^x.x) a))) 7. ==[ beta ]==> ((b a)(c a)) REDUCED to normal form. ------ 150030/16151385. ------ 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. ------ 150031/16151439. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (a a))(a a))) 2. ==[ alpha ]==> ((a ((^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. ------ 150032/16151610. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))(^b.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. ------ 150033/16151718. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150034/16151835. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^b.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. ------ 150035/16151880. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 150036/16151934. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^b.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. ------ 150037/16151943. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 150038/16151970. ------ 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)(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150039/16152015. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a) c)) 3. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 150040/16152024. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 150041/16152051. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (^z.z))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 150042/16152078. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 150043/16152123. ------ 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 (^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150044/16152132. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(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. ------ 150045/16152159. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 150046/16152186. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^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. ------ 150047/16152240. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 150048/16152258. ------ 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 (^y.y)))) b) REDUCED to normal form. ------ 150049/16152276. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b a)) 3. ==[ beta ]==> (((a a)(^y.y))(b a)) 4. ==[ alpha ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 150050/16152303. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a b)) REDUCED to normal form. ------ 150051/16152330. ------ 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. ------ 150052/16152357. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a a)) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 150053/16155528. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^z.(^x1.(a a)))(^z.(^x1.(a a))))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.(a a)))(^z.(^x1.(a a))))(^y1.y1)) 5. ==[ beta ]==> ((^y.(a a))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 150054/16157724. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150055/16159038. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.(^z3.z3))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.(^z3.z3))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150056/16160118. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(a z))) 3. ==[ eta ]==> ((^x.(b (^y.y))) a) 4. ==[ beta ]==> (b (^y.y)) 5. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150057/16162200. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b)) b) 2. ==[ alpha ]==> (((a (a a))((^x.x) b)) b) 3. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 150058/16162224. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150059/16162269. ------ 1. ==[ start ]==> ((^a.b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(c (^y.(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 150060/16162305. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150061/16162326. ------ 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. ------ 150062/16162539. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^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. ------ 150063/16162731. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 150064/16164105. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((^y.(a a))(^z.b)) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.b)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 150065/16164306. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((a b)(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((a b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 150066/16164492. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)(a b))) 3. ==[ beta ]==> (^y.(((a b)(a b))((a b)(a b)))) 4. ==[ alpha ]==> (^x.(((a b)(a b))((a b)(a b)))) REDUCED to normal form. ------ 150067/16165017. ------ 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. ------ 150068/16165377. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 150069/16166052. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a b)((^x.x) 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. ------ 150070/16166679. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 150071/16166700. ------ 1. ==[ start ]==> (((a a)(b a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 150072/16166967. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 150073/16167303. ------ 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)(^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)))) REDUCED to normal form. ------ 150074/16167570. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150075/16167573. ------ 1. ==[ start ]==> ((a (^b.b))(^c.(b a))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(b a))) REDUCED to normal form. ------ 150076/16167591. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 150077/16167852. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 150078/16167861. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(z a))) REDUCED to normal form. ------ 150079/16168383. ------ 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)))) REDUCED to normal form. ------ 150080/16168644. ------ 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)))) REDUCED to normal form. ------ 150081/16168887. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 150082/16169778. ------ 1. ==[ start ]==> (((a b)(a b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 150083/16169964. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150084/16169967. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a y))) 3. ==[ eta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 150085/16170966. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 150086/16171218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(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))) REDUCED to normal form. ------ 150087/16171632. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 150088/16171713. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 150089/16171848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 150090/16171944. ------ 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. ------ 150091/16171965. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 150092/16171992. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(a a))) REDUCED to normal form. ------ 150093/16172019. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^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. ------ 150094/16172046. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^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. ------ 150095/16172076. ------ 1. ==[ start ]==> ((a (^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (^x.x))((a (a a)) b)) REDUCED to normal form. ------ 150096/16172103. ------ 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 ]==> (((^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. ------ 150097/16172121. ------ 1. ==[ start ]==> ((a b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((a b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 150098/16172130. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(b (^a.a)))) 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. ------ 150099/16172157. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.(^x1.x1)) 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. ------ 150100/16172175. ------ 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. ------ 150101/16172193. ------ 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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150102/16172220. ------ 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. ------ 150103/16172247. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 150104/16172274. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 150105/16172301. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 150106/16172355. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((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. ------ 150107/16172391. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 150108/16172463. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 150109/16172490. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(^y.y))) REDUCED to normal form. ------ 150110/16172580. ------ 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) 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. ------ 150111/16172904. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^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. ------ 150112/16172931. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 150113/16173021. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 150114/16173048. ------ 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))(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. ------ 150115/16173102. ------ 1. ==[ start ]==> (((^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)))(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. ------ 150116/16173156. ------ 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))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((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. ------ 150117/16173183. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a 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. ------ 150118/16173237. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 150119/16173570. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.b))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 7. ==[ beta ]==> (b ((a a)(^y.b))) 8. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 150120/16173597. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 150121/16173678. ------ 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))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 150122/16173705. ------ 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. ------ 150123/16173849. ------ 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. ------ 150124/16173876. ------ 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. ------ 150125/16173957. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.b))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 150126/16174128. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 150127/16174155. ------ 1. ==[ start ]==> (((^a.a)(a b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(a (b (^y.y)))) 3. ==[ beta ]==> ((a b)(a (b (^y.y)))) 4. ==[ alpha ]==> ((a b)(a (b (^x.x)))) REDUCED to normal form. ------ 150128/16174182. ------ 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))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 150129/16174218. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) c)) 5. ==[ beta ]==> ((a (^x.(^y.y))) c) REDUCED to normal form. ------ 150130/16174236. ------ 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. ------ 150131/16174317. ------ 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 (((^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. ------ 150132/16174344. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)(a b))) REDUCED to normal form. ------ 150133/16174497. ------ 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. ------ 150134/16174731. ------ 1. ==[ start ]==> (((a b) b)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 150135/16174812. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 150136/16174866. ------ 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. ------ 150137/16174893. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a)) a)) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a)) a)) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a)) a)) 7. ==[ beta ]==> ((((a a)(a a)) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 150138/16174920. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b b)) REDUCED to normal form. ------ 150139/16174947. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1))) c)) REDUCED to normal form. ------ 150140/16175037. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 150141/16175064. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.b)(^z.b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.b)(^y.b))) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 150142/16175118. ------ 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. ------ 150143/16175172. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 150144/16175199. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.a))(^b.b))) 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))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 150145/16175262. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 150146/16175397. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 150147/16175478. ------ 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. ------ 150148/16175505. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 150149/16175559. ------ 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)((^y.y) b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)((^x.x) b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a) b)) REDUCED to normal form. ------ 150150/16175595. ------ 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. ------ 150151/16175622. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 150152/16175649. ------ 1. ==[ start ]==> (((a b)(^b.a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 150153/16175676. ------ 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.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 150154/16175703. ------ 1. ==[ start ]==> ((((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))(^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. ------ 150155/16175739. ------ 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. ------ 150156/16175793. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 150157/16175820. ------ 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. ------ 150158/16175847. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(b a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(b a))) 7. ==[ beta ]==> ((^y.y)((^z.a)(b a))) 8. ==[ alpha ]==> ((^x.x)((^y.a)(b a))) 9. ==[ beta ]==> ((^y.a)(b a)) 10. ==[ alpha ]==> ((^x.a)(b a)) 11. ==[ beta ]==> a REDUCED to normal form. ------ 150159/16175874. ------ 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. ------ 150160/16175901. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a b) a)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a b) a)((^x.x)((^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. ------ 150161/16175928. ------ 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. ------ 150162/16175955. ------ 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.(^z1.z1)))) 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. ------ 150163/16176261. ------ 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. ------ 150164/16176288. ------ 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 (^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. ------ 150165/16176324. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z)) d)) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 150166/16176342. ------ 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. ------ 150167/16176423. ------ 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. ------ 150168/16176531. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 150169/16176549. ------ 1. ==[ start ]==> (((a a)(b a))(a (^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(a (^x.x))) REDUCED to normal form. ------ 150170/16176576. ------ 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.(^x1.(^y1.y1)))(a 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. ------ 150171/16176630. ------ 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. ------ 150172/16176657. ------ 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. ------ 150173/16176684. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 150174/16176711. ------ 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. ------ 150175/16176738. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(a b))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a b))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a b))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 150176/16176765. ------ 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 z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(a a))) REDUCED to normal form. ------ 150177/16176819. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 150178/16177125. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (b a))) REDUCED to normal form. ------ 150179/16177152. ------ 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)(a (a (^z.(^x1.x1))))) 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. ------ 150180/16177206. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(a (^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 150181/16177215. ------ 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. ------ 150182/16177287. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((a a) a)((^x1.x1)(^y1.y1)))) 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. ------ 150183/16177395. ------ 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))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150184/16177422. ------ 1. ==[ start ]==> ((a (^b.b))((a a)(b a))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(b a))) REDUCED to normal form. ------ 150185/16177440. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 150186/16177521. ------ 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. ------ 150187/16177548. ------ 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. ------ 150188/16177602. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(^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. ------ 150189/16177629. ------ 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. ------ 150190/16177656. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 150191/16177710. ------ 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. ------ 150192/16177908. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(d (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(d (a b))) 3. ==[ beta ]==> (b (d (a b))) REDUCED to normal form. ------ 150193/16178016. ------ 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.z1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1))(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. ------ 150194/16178025. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^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. ------ 150195/16178052. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a)) c)) 3. ==[ beta ]==> ((b a)((^y.(a a)) c)) 4. ==[ alpha ]==> ((b a)((^x.(a a)) c)) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 150196/16178070. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b)((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)((a b)((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)((a b)((^y.y) a))) 5. ==[ beta ]==> (b ((a b)((^y.y) a))) 6. ==[ alpha ]==> (b ((a b)((^x.x) a))) 7. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 150197/16178097. ------ 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. ------ 150198/16178151. ------ 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. ------ 150199/16178232. ------ 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. ------ 150200/16178268. ------ 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.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. ------ 150201/16178295. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 150202/16178349. ------ 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.(y1 y1)))) REDUCED to normal form. ------ 150203/16178376. ------ 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. ------ 150204/16178412. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))((a a) a))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))((a a) a))) 5. ==[ beta ]==> (((a a) b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 150205/16178439. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 150206/16178466. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 150207/16178493. ------ 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. ------ 150208/16178547. ------ 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. ------ 150209/16178574. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 150210/16178628. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 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. ------ 150211/16178682. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 150212/16178709. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 150213/16178772. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 150214/16178907. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 150215/16179051. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)(^y.a))) 3. ==[ beta ]==> ((b b)(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((b b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 150216/16179078. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^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. ------ 150217/16179132. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 150218/16179159. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 150219/16179240. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b) b)) REDUCED to normal form. ------ 150220/16179267. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a) c)) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a) c)) REDUCED to normal form. ------ 150221/16179429. ------ 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 a)) REDUCED to normal form. ------ 150222/16179600. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(b (^y.b))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (^y.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b (^x.b))) REDUCED to normal form. ------ 150223/16179627. ------ 1. ==[ start ]==> (((a b)(a b))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 150224/16179654. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)(a a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(a a))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 150225/16179735. ------ 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. ------ 150226/16179762. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 150227/16179789. ------ 1. ==[ start ]==> ((((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))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 150228/16179816. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(a b))) 3. ==[ beta ]==> ((a (b (^x.x)))(a b)) REDUCED to normal form. ------ 150229/16179987. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 150230/16180095. ------ 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. ------ 150231/16180266. ------ 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. ------ 150232/16180293. ------ 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.(y1 y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 150233/16180374. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a) a)) REDUCED to normal form. ------ 150234/16180401. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 150235/16180653. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 150236/16180707. ------ 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)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 150237/16180734. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 150238/16180761. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.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. ------ 150239/16180788. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^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. ------ 150240/16180815. ------ 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))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^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. ------ 150241/16180869. ------ 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))(^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. ------ 150242/16180896. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.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. ------ 150243/16180923. ------ 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))(^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. ------ 150244/16181067. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 150245/16181148. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c c)) 3. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 150246/16181256. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c (a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150247/16181391. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((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. ------ 150248/16181472. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b c)) 5. ==[ beta ]==> ((b ((^y.y) b))(b c)) 6. ==[ alpha ]==> ((b ((^x.x) b))(b c)) 7. ==[ beta ]==> ((b b)(b c)) REDUCED to normal form. ------ 150249/16181481. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 150250/16181508. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150251/16181553. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b (a (^z.z)))) 3. ==[ beta ]==> (b (b (a (^z.z)))) 4. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 150252/16181562. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a) c)) REDUCED to normal form. ------ 150253/16181589. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a) a)) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 150254/16181616. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 150255/16181670. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) REDUCED to normal form. ------ 150256/16181697. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 150257/16181724. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y)) a)) REDUCED to normal form. ------ 150258/16181778. ------ 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)(^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. ------ 150259/16181796. ------ 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. ------ 150260/16181814. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 150261/16181841. ------ 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 (^y.y)))(a a)) REDUCED to normal form. ------ 150262/16181868. ------ 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))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 150263/16181895. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (^y.y))) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 150264/16183626. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 150265/16189665. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150266/16191747. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b)) c) 2. ==[ alpha ]==> (((a (a a))((^x.x) b)) c) 3. ==[ beta ]==> (((a (a a)) b) c) REDUCED to normal form. ------ 150267/16191873. ------ 1. ==[ start ]==> (((^a.a) b)(^c.((^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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 150268/16191906. ------ 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)) a)(^y1.y1))(^y.y)) 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. ------ 150269/16192023. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 150270/16192095. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ eta ]==> ((^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. ------ 150271/16192266. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 150272/16192590. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150273/16193148. ------ 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. ------ 150274/16193481. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 150275/16193484. ------ 1. ==[ start ]==> ((a (^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 150276/16193871. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 150277/16194222. ------ 1. ==[ start ]==> (((^a.b) b)(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^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. ------ 150278/16194255. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> ((^y.y)((((a a)(a a))(^z.z))(((a a)(a a))(^z.z)))) 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))) REDUCED to normal form. ------ 150279/16195608. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^c.(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.z))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 150280/16195686. ------ 1. ==[ start ]==> ((^a.(b a))((b a) c)) 2. ==[ alpha ]==> ((^x.(b x))((b a) c)) 3. ==[ eta ]==> (b ((b a) c)) REDUCED to normal form. ------ 150281/16196235. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 150282/16196859. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 150283/16197441. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a) a)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a) a)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 150284/16197948. ------ 1. ==[ start ]==> (((a b)(^c.a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 150285/16199136. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^y.(y y))) REDUCED to normal form. ------ 150286/16199520. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a a)(^z.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150287/16199523. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 150288/16199910. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 150289/16200072. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (b (^z.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 150290/16200243. ------ 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. ------ 150291/16200681. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1)) a)) 3. ==[ eta ]==> ((^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. ------ 150292/16201125. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 150293/16201269. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 150294/16201296. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.(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. ------ 150295/16201368. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.(^b.a))) 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. ------ 150296/16201431. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.c)) REDUCED to normal form. ------ 150297/16201485. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^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))) REDUCED to normal form. ------ 150298/16201500. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (^x1.x1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150299/16201521. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 150300/16201548. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 150301/16201602. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.a)) 3. ==[ beta ]==> (((a (a a)) b)(^y.a)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.a)) REDUCED to normal form. ------ 150302/16201650. ------ 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))) 5. ==[ beta ]==> (a ((a (a a)) b)) REDUCED to normal form. ------ 150303/16201677. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 150304/16201704. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 150305/16201731. ------ 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))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 150306/16201767. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(^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. ------ 150307/16201857. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 150308/16201884. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 150309/16201902. ------ 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. ------ 150310/16201929. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 150311/16201956. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 150312/16201965. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 150313/16201992. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 150314/16202046. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(^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)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 150315/16202073. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^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. ------ 150316/16202127. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 150317/16202172. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^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. ------ 150318/16202199. ------ 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. ------ 150319/16202262. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 150320/16202370. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 150321/16202451. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 150322/16202541. ------ 1. ==[ start ]==> (((^a.(a a)) b)(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(b (b (^y.y)))) 3. ==[ beta ]==> ((b b)(b (b (^y.y)))) 4. ==[ alpha ]==> ((b b)(b (b (^x.x)))) REDUCED to normal form. ------ 150323/16202676. ------ 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. ------ 150324/16202703. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (a ((b a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (a ((b a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (a ((b a)(^y.y))) 8. ==[ alpha ]==> (a ((b a)(^x.x))) REDUCED to normal form. ------ 150325/16202730. ------ 1. ==[ start ]==> (((a a)(^b.(^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. ------ 150326/16202757. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)(a b))) REDUCED to normal form. ------ 150327/16202784. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.a))((a b)(a a))) REDUCED to normal form. ------ 150328/16202811. ------ 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. ------ 150329/16202838. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(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. ------ 150330/16202982. ------ 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. ------ 150331/16203009. ------ 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. ------ 150332/16203045. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)((^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 ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 150333/16203180. ------ 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. ------ 150334/16203261. ------ 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 z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.(y y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(a (^y.(^z.z))))) 9. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 10. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 150335/16203342. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.b))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.y))) REDUCED to normal form. ------ 150336/16203360. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x)) a)) REDUCED to normal form. ------ 150337/16203387. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a)) b)) REDUCED to normal form. ------ 150338/16203414. ------ 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. ------ 150339/16203531. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 150340/16203675. ------ 1. ==[ start ]==> ((((a a) a) b)(c ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)(c ((^x.x) b))) 3. ==[ beta ]==> ((((a a) a) b)(c b)) REDUCED to normal form. ------ 150341/16203693. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 150342/16203702. ------ 1. ==[ start ]==> (((a b) a)(b ((a a)(a a)))) REDUCED to normal form. ------ 150343/16203729. ------ 1. ==[ start ]==> (((a a)(^a.b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(a (b (^y.y)))) REDUCED to normal form. ------ 150344/16203783. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 150345/16203810. ------ 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. ------ 150346/16203837. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(a (a a)))) 5. ==[ beta ]==> ((^y.a)((b a)(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((b a)(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 150347/16203864. ------ 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 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. ------ 150348/16203891. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 150349/16204080. ------ 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 a)))) REDUCED to normal form. ------ 150350/16204116. ------ 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))) 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. ------ 150351/16204125. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 150352/16204152. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 150353/16204287. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> (b ((^x1.b)(a b))) 4. ==[ alpha ]==> (b ((^x.b)(a b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 150354/16204341. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 150355/16204368. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(z z))(b a))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(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. ------ 150356/16204422. ------ 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.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) 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. ------ 150357/16204503. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 150358/16204728. ------ 1. ==[ start ]==> (((^a.b) c)(d (b a))) 2. ==[ alpha ]==> (((^x.b) c)(d (b a))) 3. ==[ beta ]==> (b (d (b a))) REDUCED to normal form. ------ 150359/16204971. ------ 1. ==[ start ]==> (((a b) c)((a b)((a a) a))) REDUCED to normal form. ------ 150360/16204998. ------ 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. ------ 150361/16205025. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 150362/16205079. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a (b a))) REDUCED to normal form. ------ 150363/16205106. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 150364/16205124. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(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. ------ 150365/16205205. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 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. ------ 150366/16205304. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a b)(^y.a))) REDUCED to normal form. ------ 150367/16205331. ------ 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)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(^y.b))) REDUCED to normal form. ------ 150368/16205358. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a (a b))((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> ((a (a b))((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((a (a b))(^y.(a a))) 8. ==[ alpha ]==> ((a (a b))(^x.(a a))) REDUCED to normal form. ------ 150369/16205439. ------ 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. ------ 150370/16205466. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a a)(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 150371/16205493. ------ 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. ------ 150372/16205520. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 150373/16205547. ------ 1. ==[ start ]==> ((a (b a))((b a) c)) REDUCED to normal form. ------ 150374/16205637. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(^x1.a))) 5. ==[ beta ]==> (b ((^z.b)(^x1.a))) 6. ==[ alpha ]==> (b ((^x.b)(^y.a))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 150375/16205718. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 150376/16205781. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 150377/16205889. ------ 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)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 150378/16205916. ------ 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. ------ 150379/16205970. ------ 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. ------ 150380/16205997. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)(a b))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(a b))) 5. ==[ beta ]==> (((a b)(^x.(x x)))(a b)) REDUCED to normal form. ------ 150381/16206024. ------ 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. ------ 150382/16206051. ------ 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 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. ------ 150383/16206096. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 150384/16206141. ------ 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 (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 150385/16206168. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 150386/16206195. ------ 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. ------ 150387/16206222. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.(z z)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a 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. ------ 150388/16206249. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 150389/16206276. ------ 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. ------ 150390/16206303. ------ 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.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(^x1.b))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.b))) 7. ==[ beta ]==> (((a a) a)((^y.y)(^z.b))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(^y.b))) 9. ==[ beta ]==> (((a a) a)(^y.b)) 10. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 150391/16206330. ------ 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. ------ 150392/16206393. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150393/16206555. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.b)(^b.(^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. ------ 150394/16206663. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 150395/16206699. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (b a))) REDUCED to normal form. ------ 150396/16206717. ------ 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)((^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. ------ 150397/16206780. ------ 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. ------ 150398/16206807. ------ 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)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))((^z.z) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 150399/16206861. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 150400/16206888. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((a a) a))) 7. ==[ beta ]==> (((a a)(^x.(x x)))((a a) a)) REDUCED to normal form. ------ 150401/16206915. ------ 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. ------ 150402/16206969. ------ 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)))) REDUCED to normal form. ------ 150403/16207032. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a)(^y.y))) REDUCED to normal form. ------ 150404/16207059. ------ 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.(^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. ------ 150405/16207086. ------ 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. ------ 150406/16207113. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a b)(^y.(y y)))) 5. ==[ beta ]==> ((a b)((a b)(^y.(y y)))) 6. ==[ alpha ]==> ((a b)((a b)(^x.(x x)))) REDUCED to normal form. ------ 150407/16207140. ------ 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. ------ 150408/16207167. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.a))) 7. ==[ beta ]==> (((a b)(^x.x))(^z.a)) 8. ==[ alpha ]==> (((a b)(^x.x))(^y.a)) REDUCED to normal form. ------ 150409/16207194. ------ 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. ------ 150410/16207221. ------ 1. ==[ start ]==> ((((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)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a (^z.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (^y.(a a)))) REDUCED to normal form. ------ 150411/16207302. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a) a)) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a) a)) 3. ==[ beta ]==> ((a b)((b a) a)) REDUCED to normal form. ------ 150412/16207473. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 150413/16207590. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 150414/16207617. ------ 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. ------ 150415/16207644. ------ 1. ==[ start ]==> (((a a)(^b.b))((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. ------ 150416/16207671. ------ 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. ------ 150417/16207752. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(a b))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(a b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 150418/16207779. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a (^y.y))(a a))) REDUCED to normal form. ------ 150419/16207797. ------ 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 (b (^y.(^z.z)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 150420/16207806. ------ 1. ==[ start ]==> (((a b)(^c.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 150421/16207905. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 150422/16207977. ------ 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. ------ 150423/16208004. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^x1.b))) REDUCED to normal form. ------ 150424/16208031. ------ 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. ------ 150425/16208085. ------ 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)) REDUCED to normal form. ------ 150426/16208112. ------ 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. ------ 150427/16208139. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b) c)) REDUCED to normal form. ------ 150428/16208580. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(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. ------ 150429/16208661. ------ 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. ------ 150430/16208688. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 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. ------ 150431/16208742. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 150432/16208823. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 150433/16208931. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.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. ------ 150434/16208940. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c ((a a) a))) REDUCED to normal form. ------ 150435/16208967. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (a b))) REDUCED to normal form. ------ 150436/16208994. ------ 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)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a (a a))) REDUCED to normal form. ------ 150437/16209030. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b) b)) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 150438/16209057. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a) c)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a) c)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a) c)) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 150439/16209219. ------ 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. ------ 150440/16209246. ------ 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.(^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. ------ 150441/16209300. ------ 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. ------ 150442/16209327. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 150443/16209381. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 150444/16209471. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.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. ------ 150445/16209552. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^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. ------ 150446/16209696. ------ 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. ------ 150447/16209723. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 150448/16209768. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(a (^z.b))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.b))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.b))) REDUCED to normal form. ------ 150449/16209849. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^z1.z1) a)((^z1.z1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((^z1.z1) a))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((^y1.y1) a))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 150450/16209930. ------ 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. ------ 150451/16210038. ------ 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.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150452/16210074. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.a))(b (^z.z))) 6. ==[ alpha ]==> ((b (^x.a))(b (^y.y))) REDUCED to normal form. ------ 150453/16210101. ------ 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. ------ 150454/16210164. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y)) c)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(c c)) REDUCED to normal form. ------ 150455/16210272. ------ 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))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^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. ------ 150456/16210299. ------ 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. ------ 150457/16210326. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)(^b.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. ------ 150458/16210353. ------ 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))(^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. ------ 150459/16210380. ------ 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.(^z.z)))) REDUCED to normal form. ------ 150460/16210434. ------ 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. ------ 150461/16210461. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a) c)) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a) c)) 5. ==[ beta ]==> ((b a)(((^y.y) a) c)) 6. ==[ alpha ]==> ((b a)(((^x.x) a) c)) 7. ==[ beta ]==> ((b a)(a c)) REDUCED to normal form. ------ 150462/16210542. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((a ((^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. ------ 150463/16210632. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.(z z)))) 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. ------ 150464/16210713. ------ 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) REDUCED to normal form. ------ 150465/16210821. ------ 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)(^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. ------ 150466/16210938. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))(a (^x1.x1)))) 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. ------ 150467/16210956. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^b.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. ------ 150468/16210983. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 5. ==[ beta ]==> (a (^y.(y y))) 6. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 150469/16211037. ------ 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 (^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. ------ 150470/16211046. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b c)) REDUCED to normal form. ------ 150471/16211118. ------ 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))(^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. ------ 150472/16211127. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 150473/16211154. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 150474/16211181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(a a))) REDUCED to normal form. ------ 150475/16211226. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(a (^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150476/16211235. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c a)) REDUCED to normal form. ------ 150477/16211262. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b b)) 3. ==[ beta ]==> ((b (^y.(y y)))(b b)) 4. ==[ alpha ]==> ((b (^x.(x x)))(b b)) REDUCED to normal form. ------ 150478/16211289. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a c)) REDUCED to normal form. ------ 150479/16211343. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 150480/16211361. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.z))) REDUCED to normal form. ------ 150481/16211379. ------ 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)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 150482/16211406. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 150483/16211433. ------ 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. ------ 150484/16211460. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y) 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. ------ 150485/16211486. ------ 1. ==[ start ]==> (^a.(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(((^y.y)(^z.z))(x (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.((^z.z)(x (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((^y.y)(x (^z.(^x1.x1))))) 5. ==[ beta ]==> (^x.(x (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(x (^y.(^z.z)))) REDUCED to normal form. ------ 150486/16211487. ------ 1. ==[ start ]==> (a (((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (a ((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (a ((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (a (a (^y.(^z.z)))) 6. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 150487/16212435. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((^x.((^y.y)(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150488/16213200. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 150489/16220400. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 150490/16221348. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a)))) a) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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) REDUCED to normal form. ------ 150491/16221354. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(^a.a))(a (^a.(^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. ------ 150492/16221381. ------ 1. ==[ start ]==> ((^a.(a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x x))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((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))) 5. ==[ beta ]==> (((a (a a)) b)((a (a a))((^y.y) b))) 6. ==[ alpha ]==> (((a (a a)) b)((a (a a))((^x.x) b))) 7. ==[ beta ]==> (((a (a a)) b)((a (a a)) b)) REDUCED to normal form. ------ 150493/16221408. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 150494/16221483. ------ 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)))) REDUCED to normal form. ------ 150495/16221606. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((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)))) REDUCED to normal form. ------ 150496/16222299. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(a ((^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. ------ 150497/16222302. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((a ((^x.x)(^y.y)))(^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))) REDUCED to normal form. ------ 150498/16223067. ------ 1. ==[ start ]==> ((a (^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 150499/16223814. ------ 1. ==[ start ]==> (((a b)(a a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 150500/16224183. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))(^z.((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.((a a)(a a)))) 7. ==[ beta ]==> ((^y.((a a)(a a)))(^y.((a a)(a a)))) 8. ==[ alpha ]==> ((^x.((a a)(a a)))(^y.((a a)(a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 150501/16224513. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((b ((^z.z) b))(b ((^z.z) b)))(^y.y)) 4. ==[ alpha ]==> (((b ((^x.x) b))(b ((^y.y) b)))(^z.z)) 5. ==[ beta ]==> (((b b)(b ((^y.y) b)))(^z.z)) 6. ==[ alpha ]==> (((b b)(b ((^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. ------ 150502/16224885. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150503/16225839. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 150504/16227531. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 150505/16228023. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((b ((^y.y)(a a)))(b ((^y.y)(a a))))((b ((^y.y)(a a)))(b ((^y.y)(a a))))) 4. ==[ alpha ]==> (((b ((^x.x)(a a)))(b ((^y.y)(a a))))((b ((^z.z)(a a)))(b ((^x1.x1)(a a))))) 5. ==[ beta ]==> (((b (a a))(b ((^y.y)(a a))))((b ((^z.z)(a a)))(b ((^x1.x1)(a a))))) 6. ==[ alpha ]==> (((b (a a))(b ((^x.x)(a a))))((b ((^y.y)(a a)))(b ((^z.z)(a a))))) 7. ==[ beta ]==> (((b (a a))(b (a a)))((b ((^y.y)(a a)))(b ((^z.z)(a a))))) 8. ==[ alpha ]==> (((b (a a))(b (a a)))((b ((^x.x)(a a)))(b ((^y.y)(a a))))) 9. ==[ beta ]==> (((b (a a))(b (a a)))((b (a a))(b ((^y.y)(a a))))) 10. ==[ alpha ]==> (((b (a a))(b (a a)))((b (a a))(b ((^x.x)(a a))))) 11. ==[ beta ]==> (((b (a a))(b (a a)))((b (a a))(b (a a)))) REDUCED to normal form. ------ 150506/16228719. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 150507/16228917. ------ 1. ==[ start ]==> (((a b)(a b))(^c.(a b))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(a b))) REDUCED to normal form. ------ 150508/16229655. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 150509/16229664. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 150510/16229826. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 150511/16230264. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a ((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 150512/16230267. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 150513/16230798. ------ 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.((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150514/16230879. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(^b.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. ------ 150515/16230951. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.c)) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.c)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150516/16230960. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.y1))) REDUCED to normal form. ------ 150517/16231014. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 150518/16231068. ------ 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. ------ 150519/16231083. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150520/16231158. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.b)) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.b)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.b)) REDUCED to normal form. ------ 150521/16231185. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^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. ------ 150522/16231212. ------ 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 ]==> (((^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. ------ 150523/16231224. ------ 1. ==[ start ]==> ((a a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(((^x.x)(^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))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 150524/16231251. ------ 1. ==[ start ]==> ((a (a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a a))((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((a (a a))((a (a a)) b)) REDUCED to normal form. ------ 150525/16231278. ------ 1. ==[ start ]==> ((a b)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((a b)(a ((a a)(a a)))) REDUCED to normal form. ------ 150526/16231332. ------ 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. ------ 150527/16231350. ------ 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. ------ 150528/16231368. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^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. ------ 150529/16231395. ------ 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)((b (^x1.x1))(^y1.(^z1.z1)))) 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. ------ 150530/16231422. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 150531/16231449. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 150532/16231458. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.b)(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. ------ 150533/16231476. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 150534/16231557. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 150535/16231584. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 150536/16231593. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 150537/16231638. ------ 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.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 150538/16231647. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^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)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 150539/16231665. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 150540/16231674. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 150541/16231701. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 150542/16231890. ------ 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. ------ 150543/16231971. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 150544/16231998. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 150545/16232142. ------ 1. ==[ start ]==> (((a (a a))(a a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(b (b (^x.x)))) REDUCED to normal form. ------ 150546/16232169. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 150547/16232466. ------ 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)(^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. ------ 150548/16232493. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a ((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(a b)) REDUCED to normal form. ------ 150549/16232520. ------ 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)))) REDUCED to normal form. ------ 150550/16232547. ------ 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. ------ 150551/16232637. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.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. ------ 150552/16232691. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 150553/16232727. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^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)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150554/16232754. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 150555/16232772. ------ 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. ------ 150556/16232808. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 150557/16232835. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 150558/16232853. ------ 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))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((a (a a))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 150559/16232862. ------ 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. ------ 150560/16232889. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 150561/16232916. ------ 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. ------ 150562/16233105. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.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. ------ 150563/16233267. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.y))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 150564/16233294. ------ 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. ------ 150565/16233393. ------ 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. ------ 150566/16233519. ------ 1. ==[ start ]==> (((a a)(a b))((a b)(a b))) REDUCED to normal form. ------ 150567/16233546. ------ 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. ------ 150568/16233573. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((a a)(^z.z)))) 9. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 10. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 150569/16233600. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))(b a))) REDUCED to normal form. ------ 150570/16233627. ------ 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.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a (((^y.y) a)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (a (((^x.x) a)(a (^y.(^z.z))))) 9. ==[ beta ]==> (a (a (a (^y.(^z.z))))) 10. ==[ alpha ]==> (a (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 150571/16233654. ------ 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. ------ 150572/16233672. ------ 1. ==[ start ]==> (((^a.b) b)(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(b (^y.(a a)))) 3. ==[ beta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 150573/16233681. ------ 1. ==[ start ]==> (((a b)(a a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 150574/16233717. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a))(^y.y))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 150575/16233744. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 150576/16233798. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((b a)(^y1.(y1 y1)))) 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. ------ 150577/16233879. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.b))) 3. ==[ beta ]==> (b ((a b)(^x1.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 150578/16233888. ------ 1. ==[ start ]==> (((a b) b)((^a.b)(a b))) 2. ==[ alpha ]==> (((a b) b)((^x.b)(a b))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 150579/16233942. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 150580/16233969. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((b a)(b a))) REDUCED to normal form. ------ 150581/16234014. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 11. ==[ beta ]==> ((a (^y.y))(^z.z)) 12. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 150582/16234023. ------ 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. ------ 150583/16234050. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)((a a)(a a)))((^y.y)((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.y)((a a)(a a)))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)((a a)(a a)))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)((a a)(a a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 150584/16234077. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 150585/16234095. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 150586/16234104. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 150587/16234131. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 150588/16234320. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(a a))(^d.a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(y y))(^z.a))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.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. ------ 150589/16234383. ------ 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)(^x.x)))(b b)) REDUCED to normal form. ------ 150590/16234419. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 150591/16234698. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.b))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 150592/16234752. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a (^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150593/16234779. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 150594/16234797. ------ 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.(^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. ------ 150595/16234806. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 150596/16235373. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 150597/16235418. ------ 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. ------ 150598/16235445. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1))) 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. ------ 150599/16235499. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z)) d)) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y)) d)) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 150600/16235706. ------ 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. ------ 150601/16235967. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150602/16236066. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((b a) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((b a) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((b a) b)) 5. ==[ beta ]==> ((a a)((b a) b)) REDUCED to normal form. ------ 150603/16236264. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 150604/16236597. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(b a))) REDUCED to normal form. ------ 150605/16236858. ------ 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 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. ------ 150606/16236903. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 150607/16236930. ------ 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)(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1)) 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. ------ 150608/16237227. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a)) c)) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a)) c)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a)) c)) 5. ==[ beta ]==> (b ((^y.(a a)) c)) 6. ==[ alpha ]==> (b ((^x.(a a)) c)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 150609/16237371. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c (^y.(a a)))) REDUCED to normal form. ------ 150610/16237398. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 150611/16237497. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 150612/16237506. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 150613/16237533. ------ 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. ------ 150614/16237866. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(c (a b))) 3. ==[ beta ]==> ((b (a a))(c (a b))) REDUCED to normal form. ------ 150615/16237893. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(b ((^x.x)(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 150616/16237929. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 150617/16238172. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^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. ------ 150618/16238208. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((b b)((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> ((b b)((^x.b)(a (^y.y)))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 150619/16238253. ------ 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))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^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. ------ 150620/16238280. ------ 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. ------ 150621/16238289. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 10. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 150622/16238316. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 150623/16238334. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))(^z.b))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))(^z.b))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))(^y.b))) REDUCED to normal form. ------ 150624/16238397. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 150625/16238415. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b) b)) 2. ==[ alpha ]==> (((^x.b)(a b))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 150626/16238424. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 150627/16238478. ------ 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))(^z1.(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. ------ 150628/16238532. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 150629/16238559. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 150630/16238586. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(a a))) REDUCED to normal form. ------ 150631/16238622. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b)(a a))) REDUCED to normal form. ------ 150632/16238649. ------ 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. ------ 150633/16238676. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z) a)) 9. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 150634/16238703. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 150635/16238730. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 10. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 150636/16238757. ------ 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. ------ 150637/16238784. ------ 1. ==[ start ]==> (((a b)(a b))((a a)(a b))) REDUCED to normal form. ------ 150638/16239252. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^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. ------ 150639/16239288. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d (^y.(y y)))) 3. ==[ beta ]==> ((b c)(d (^y.(y y)))) 4. ==[ alpha ]==> ((b c)(d (^x.(x x)))) REDUCED to normal form. ------ 150640/16239315. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 150641/16239387. ------ 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. ------ 150642/16239423. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 150643/16239441. ------ 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. ------ 150644/16239450. ------ 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.y1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(((^y1.y1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((^y1.y1) a))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((^x1.x1) a))) 7. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 150645/16239522. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.a))) 3. ==[ beta ]==> (b ((a a)(^z.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 150646/16239531. ------ 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. ------ 150647/16239558. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 150648/16239639. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 150649/16239666. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^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. ------ 150650/16239756. ------ 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. ------ 150651/16239783. ------ 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)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 150652/16239810. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^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)))) REDUCED to normal form. ------ 150653/16239837. ------ 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)(^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. ------ 150654/16239945. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c d)) 3. ==[ beta ]==> (((a a)(a b))(c d)) REDUCED to normal form. ------ 150655/16240134. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 150656/16240305. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(^a.(^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. ------ 150657/16240413. ------ 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. ------ 150658/16240629. ------ 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))(^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. ------ 150659/16240638. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 150660/16240665. ------ 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)((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150661/16240710. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z)) b)) 3. ==[ beta ]==> (b ((a (^z.z)) b)) 4. ==[ alpha ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 150662/16240719. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 150663/16240746. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 150664/16240773. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.z))) REDUCED to normal form. ------ 150665/16240827. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.a))) REDUCED to normal form. ------ 150666/16240854. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 150667/16240881. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.y))) REDUCED to normal form. ------ 150668/16240935. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 150669/16240953. ------ 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 (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 150670/16240971. ------ 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. ------ 150671/16240998. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b a)) REDUCED to normal form. ------ 150672/16241025. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(a b)) 3. ==[ beta ]==> ((a ((a a)(a a)))(a b)) REDUCED to normal form. ------ 150673/16241052. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (a a))) 3. ==[ beta ]==> (((a (a a)) b)(a (a a))) REDUCED to normal form. ------ 150674/16241079. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(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. ------ 150675/16241226. ------ 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 (^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.x1)) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150676/16246761. ------ 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. ------ 150677/16250001. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 150678/16250820. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150679/16250949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(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. ------ 150680/16250973. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150681/16251054. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150682/16251099. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^z.(z (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 150683/16251102. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 150684/16251507. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 150685/16251921. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.x)(^y.(^z.z)))(^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. ------ 150686/16252695. ------ 1. ==[ start ]==> (((a a)((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 150687/16252854. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.a)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.a)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 150688/16253082. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^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. ------ 150689/16253241. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))((a a) a))(((^z.z)(a a))((a a) a)))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))((a a) a))(((^z.z)(a a))((a a) a)))) 5. ==[ beta ]==> (^x.(((a a)((a a) a))(((^z.z)(a a))((a a) a)))) 6. ==[ alpha ]==> (^x.(((a a)((a a) a))(((^y.y)(a a))((a a) a)))) 7. ==[ beta ]==> (^x.(((a a)((a a) a))((a a)((a a) a)))) REDUCED to normal form. ------ 150690/16254123. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.a))(^b.b))) 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. ------ 150691/16254162. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.((x1 x1)(x1 x1)))) 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. ------ 150692/16254828. ------ 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. ------ 150693/16254879. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ eta ]==> (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. ------ 150694/16255161. ------ 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. ------ 150695/16255428. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(b a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 150696/16255476. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 150697/16255716. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^x1.a)((a a)(^y1.y1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.a)((a a)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (a (^z.(^x1.x1))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 150698/16256319. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150699/16256367. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 150700/16256634. ------ 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. ------ 150701/16256637. ------ 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))) REDUCED to normal form. ------ 150702/16256916. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(b z1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 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. ------ 150703/16257420. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 150704/16257633. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.(a a)))((^y.(^z.z))(^x1.(a a))))(((^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))))(((^x2.(^y2.y2))(^z2.(a a)))((^x3.(^y3.y3))(^z3.(a a))))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(^z1.(a a))))(((^x2.(^y2.y2))(^z2.(a a)))((^x3.(^y3.y3))(^z3.(a a))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(a a))))(((^y1.(^z1.z1))(^x2.(a a)))((^y2.(^z2.z2))(^x3.(a a))))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(a a)))(((^y1.(^z1.z1))(^x2.(a a)))((^y2.(^z2.z2))(^x3.(a a))))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.(^y1.y1))(^z1.(a a)))((^x2.(^y2.y2))(^z2.(a a))))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.(a a)))((^x2.(^y2.y2))(^z2.(a a))))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(a a)))((^y1.(^z1.z1))(^x2.(a a))))) 11. ==[ beta ]==> (((^y.(^z.z))(^x1.(a a)))((^y1.(^z1.z1))(^x2.(a a)))) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 15. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150705/16257672. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 150706/16258554. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 150707/16258713. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150708/16259103. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((a a) a))) 3. ==[ beta ]==> ((b (^y.y))(^z.((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 150709/16259274. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 150710/16259607. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.y))) 5. ==[ beta ]==> ((b a)(^y.(^z.y))) 6. ==[ alpha ]==> ((b a)(^x.(^y.x))) REDUCED to normal form. ------ 150711/16259874. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 150712/16259877. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 150713/16260318. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1) 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. ------ 150714/16260489. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.c)) 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. ------ 150715/16260570. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.c)) REDUCED to normal form. ------ 150716/16260624. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 150717/16260693. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (a (^x1.x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150718/16260696. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 150719/16260741. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 150720/16260768. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(a a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(a a))) REDUCED to normal form. ------ 150721/16260795. ------ 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. ------ 150722/16260822. ------ 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))) REDUCED to normal form. ------ 150723/16260852. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(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))))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 150724/16260879. ------ 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 ]==> ((^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. ------ 150725/16260906. ------ 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)))) 5. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 150726/16260933. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 150727/16260978. ------ 1. ==[ start ]==> ((a (a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 150728/16260996. ------ 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. ------ 150729/16261023. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 150730/16261050. ------ 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))) REDUCED to normal form. ------ 150731/16261077. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(z z)))) REDUCED to normal form. ------ 150732/16261113. ------ 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. ------ 150733/16261131. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 150734/16261212. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 150735/16261266. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 150736/16261293. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 150737/16261356. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 150738/16261383. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^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. ------ 150739/16261428. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x)) a)((b (^y.y)) b)) 3. ==[ beta ]==> ((a a)((b (^y.y)) b)) 4. ==[ alpha ]==> ((a a)((b (^x.x)) b)) REDUCED to normal form. ------ 150740/16261680. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 150741/16261707. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^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. ------ 150742/16261734. ------ 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. ------ 150743/16261797. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150744/16261824. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((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. ------ 150745/16261878. ------ 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)((^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. ------ 150746/16261932. ------ 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))) 9. ==[ beta ]==> ((b a)(^y.y)) 10. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 150747/16261959. ------ 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)(^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. ------ 150748/16262013. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a b)(a a))) REDUCED to normal form. ------ 150749/16262346. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(^a.a))(^c.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. ------ 150750/16262373. ------ 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. ------ 150751/16262427. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 150752/16262481. ------ 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. ------ 150753/16262508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 150754/16262571. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(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. ------ 150755/16262652. ------ 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. ------ 150756/16262679. ------ 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.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 150757/16262733. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 150758/16262904. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 150759/16262931. ------ 1. ==[ start ]==> (((^a.a)(a b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a b)(b ((a a)(a a)))) REDUCED to normal form. ------ 150760/16262958. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(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. ------ 150761/16262994. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) b)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 150762/16263012. ------ 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. ------ 150763/16263021. ------ 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. ------ 150764/16263093. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 150765/16263120. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 150766/16263300. ------ 1. ==[ start ]==> (((a b)(a a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(b (^x.(a a)))) REDUCED to normal form. ------ 150767/16263507. ------ 1. ==[ start ]==> (((a b) b)((a b)(^a.b))) 2. ==[ alpha ]==> (((a b) b)((a b)(^x.b))) REDUCED to normal form. ------ 150768/16263534. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((a 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. ------ 150769/16263561. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 150770/16263642. ------ 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. ------ 150771/16263696. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 150772/16263723. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 150773/16263813. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 150774/16263840. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(a a))(^c.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. ------ 150775/16263867. ------ 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. ------ 150776/16263921. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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)))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 150777/16263975. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 150778/16264002. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^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. ------ 150779/16264038. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 150780/16264173. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1)(^y1.y1)))) 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. ------ 150781/16264254. ------ 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.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 150782/16264281. ------ 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 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. ------ 150783/16264335. ------ 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 (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 150784/16264398. ------ 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. ------ 150785/16264425. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 150786/16264452. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 150787/16264479. ------ 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)))) REDUCED to normal form. ------ 150788/16264515. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 150789/16264542. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 150790/16264569. ------ 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) REDUCED to normal form. ------ 150791/16264596. ------ 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. ------ 150792/16264623. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(^z.z)))) 9. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 10. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 11. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 12. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 150793/16264650. ------ 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. ------ 150794/16264677. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 150795/16264704. ------ 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. ------ 150796/16264731. ------ 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)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 150797/16264758. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a)))(^a.(^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. ------ 150798/16265037. ------ 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. ------ 150799/16265064. ------ 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.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(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. ------ 150800/16265118. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a b)(a b))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 150801/16265127. ------ 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. ------ 150802/16265199. ------ 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. ------ 150803/16265307. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(b a))) REDUCED to normal form. ------ 150804/16265325. ------ 1. ==[ start ]==> (((a a)(b a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 150805/16265352. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 150806/16265379. ------ 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.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 150807/16265460. ------ 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. ------ 150808/16265487. ------ 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. ------ 150809/16265541. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))(a 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. ------ 150810/16265595. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 150811/16265928. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(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. ------ 150812/16265982. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((b a)(a a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a)(a a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a)(a a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a)(a a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((b a)(a a))) REDUCED to normal form. ------ 150813/16266018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) c)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 150814/16266063. ------ 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. ------ 150815/16266171. ------ 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) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1)(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. ------ 150816/16266198. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 150817/16266243. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 150818/16266324. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((a b)((^y.(a a))((^z.z) a))) 6. ==[ alpha ]==> ((a b)((^x.(a a))((^y.y) a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 150819/16266351. ------ 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. ------ 150820/16266378. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 150821/16266405. ------ 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. ------ 150822/16266432. ------ 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 z))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(z z))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(a b))) REDUCED to normal form. ------ 150823/16266477. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 150824/16266486. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 150825/16266513. ------ 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. ------ 150826/16266792. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^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. ------ 150827/16266828. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^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)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 150828/16266846. ------ 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. ------ 150829/16266855. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 150830/16266873. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a b)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((a b)((^y1.y1) 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. ------ 150831/16266927. ------ 1. ==[ start ]==> (((^a.(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)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 150832/16267008. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 150833/16267071. ------ 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.z))(^x1.x1))) REDUCED to normal form. ------ 150834/16267125. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^y1.a))) REDUCED to normal form. ------ 150835/16267152. ------ 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. ------ 150836/16267188. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 150837/16267215. ------ 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 x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 150838/16267242. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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) REDUCED to normal form. ------ 150839/16267269. ------ 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.(^z.z))((^x1.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. ------ 150840/16267296. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)((a a)(^x1.x1)))) 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. ------ 150841/16267323. ------ 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. ------ 150842/16267350. ------ 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 a)) REDUCED to normal form. ------ 150843/16267377. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 150844/16267485. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.b))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.b))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.b))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 150845/16267512. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 150846/16267548. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 150847/16267683. ------ 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. ------ 150848/16267827. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b b)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 150849/16267854. ------ 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. ------ 150850/16267908. ------ 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. ------ 150851/16268016. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 150852/16268043. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b) b)) 2. ==[ alpha ]==> (((a b)(^x.b))((a b) b)) REDUCED to normal form. ------ 150853/16268403. ------ 1. ==[ start ]==> (((a b)(a b))(b (^a.b))) 2. ==[ alpha ]==> (((a b)(a b))(b (^x.b))) REDUCED to normal form. ------ 150854/16268430. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) 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. ------ 150855/16268457. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 150856/16268511. ------ 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))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 150857/16268538. ------ 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. ------ 150858/16268565. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 150859/16268592. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 150860/16268763. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(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. ------ 150861/16268871. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150862/16268907. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a)) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y)) d)) 3. ==[ beta ]==> ((b c)((^y.(y y)) d)) 4. ==[ alpha ]==> ((b c)((^x.(x x)) d)) 5. ==[ beta ]==> ((b c)(d d)) REDUCED to normal form. ------ 150863/16268979. ------ 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 ]==> ((b (^y.y))((a a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 150864/16269042. ------ 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.(^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. ------ 150865/16269069. ------ 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. ------ 150866/16269150. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 150867/16269177. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a) a)) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a) a)) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a) a)) REDUCED to normal form. ------ 150868/16269429. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c (^z.(z z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(c (^z.(z z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c (^y.(y y)))) 5. ==[ beta ]==> ((a b)(c (^y.(y y)))) 6. ==[ alpha ]==> ((a b)(c (^x.(x x)))) REDUCED to normal form. ------ 150869/16269456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 150870/16269483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 150871/16269510. ------ 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)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 150872/16269537. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (((a b)(a a))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 150873/16269564. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.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. ------ 150874/16269591. ------ 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)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 150875/16269645. ------ 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))(^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. ------ 150876/16269672. ------ 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))(^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. ------ 150877/16269699. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)(^b.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. ------ 150878/16269753. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 150879/16269843. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))((^x1.x1) 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. ------ 150880/16269924. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d b)) 3. ==[ beta ]==> (b (d b)) REDUCED to normal form. ------ 150881/16270149. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a) b)) 3. ==[ beta ]==> (((^y.y) a)((^z.a) b)) 4. ==[ alpha ]==> (((^x.x) a)((^y.a) b)) 5. ==[ beta ]==> (a ((^y.a) b)) 6. ==[ alpha ]==> (a ((^x.a) b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 150882/16270167. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((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. ------ 150883/16270194. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 150884/16270248. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c b)) 5. ==[ beta ]==> ((b ((^y.y) b))(c b)) 6. ==[ alpha ]==> ((b ((^x.x) b))(c b)) 7. ==[ beta ]==> ((b b)(c b)) REDUCED to normal form. ------ 150885/16270257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 150886/16270284. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a a)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150887/16270329. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (a a))) 3. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 150888/16270338. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 150889/16270365. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a a) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a) c)) REDUCED to normal form. ------ 150890/16270392. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 150891/16270437. ------ 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. ------ 150892/16270446. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) c) REDUCED to normal form. ------ 150893/16270473. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 150894/16270500. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 150895/16270554. ------ 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. ------ 150896/16270572. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 150897/16270590. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 150898/16270617. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 150899/16270644. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.a)(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. ------ 150900/16270671. ------ 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. ------ 150901/16270698. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 150902/16276389. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 150903/16280448. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150904/16280748. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^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. ------ 150905/16280853. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(a (a a)))) 3. ==[ beta ]==> (^y.((^z.z)(a (a a)))) 4. ==[ alpha ]==> (^x.((^y.y)(a (a a)))) 5. ==[ beta ]==> (^x.(a (a a))) REDUCED to normal form. ------ 150906/16280925. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(^z.z))(^x1.b))) 3. ==[ eta ]==> ((^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. ------ 150907/16281096. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 150908/16281195. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(x (x x)))((b (^y.y)) b)) 3. ==[ beta ]==> (((b (^y.y)) b)(((b (^y.y)) b)((b (^y.y)) b))) 4. ==[ alpha ]==> (((b (^x.x)) b)(((b (^y.y)) b)((b (^z.z)) b))) REDUCED to normal form. ------ 150909/16281420. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150910/16281978. ------ 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. ------ 150911/16282311. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 150912/16283799. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 150913/16284132. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 150914/16284516. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z))) b)) 3. ==[ eta ]==> (b ((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 150915/16284798. ------ 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. ------ 150916/16285956. ------ 1. ==[ start ]==> ((^a.(^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150917/16286274. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.a))) 3. ==[ beta ]==> ((a b)(^y.(^z.a))) 4. ==[ alpha ]==> ((a b)(^x.(^y.a))) REDUCED to normal form. ------ 150918/16286283. ------ 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)) REDUCED to normal form. ------ 150919/16286562. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(b z))) 3. ==[ eta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 150920/16286805. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 150921/16287309. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^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. ------ 150922/16287552. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 150923/16288350. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 150924/16288767. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 150925/16290153. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 150926/16290207. ------ 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)))) REDUCED to normal form. ------ 150927/16290330. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 150928/16290333. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 150929/16290378. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 150930/16290432. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.a)) 3. ==[ beta ]==> (((a (a a)) b)(^y.a)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.a)) REDUCED to normal form. ------ 150931/16290459. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 150932/16290507. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^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 ((^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. ------ 150933/16290534. ------ 1. ==[ start ]==> (((a a) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a) a)((a (a a))((^x.x) b))) 3. ==[ beta ]==> (((a a) a)((a (a a)) b)) REDUCED to normal form. ------ 150934/16290561. ------ 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. ------ 150935/16290588. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((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. ------ 150936/16290615. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a a)((^a.(^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. ------ 150937/16290633. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150938/16290741. ------ 1. ==[ start ]==> ((a (^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (^x.a))(a (a a))) REDUCED to normal form. ------ 150939/16290759. ------ 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. ------ 150940/16290786. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.a))) REDUCED to normal form. ------ 150941/16290813. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 150942/16290822. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 150943/16290849. ------ 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))((^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. ------ 150944/16290930. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150945/16290984. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 150946/16291056. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(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. ------ 150947/16291083. ------ 1. ==[ start ]==> ((a (a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (a (a a)))((b (^x.x)) b)) REDUCED to normal form. ------ 150948/16291119. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 150949/16291173. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 150950/16291281. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 150951/16291308. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 150952/16291398. ------ 1. ==[ start ]==> (((^a.(a a)) b)(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(c ((a a)(a a)))) 3. ==[ beta ]==> ((b b)(c ((a a)(a a)))) REDUCED to normal form. ------ 150953/16291533. ------ 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. ------ 150954/16291560. ------ 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. ------ 150955/16291587. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 150956/16291614. ------ 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)(^z.z))((a a) a))) REDUCED to normal form. ------ 150957/16291641. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> ((a (^x.a))((a a)(a b))) REDUCED to normal form. ------ 150958/16291668. ------ 1. ==[ start ]==> (((a (a a))(^a.(^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. ------ 150959/16291695. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^z.z)))) 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. ------ 150960/16291866. ------ 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. ------ 150961/16291902. ------ 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))(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 a) REDUCED to normal form. ------ 150962/16291956. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))(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. ------ 150963/16292037. ------ 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. ------ 150964/16292064. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)((^z1.z1)(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. ------ 150965/16292118. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a ((^x.x) 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. ------ 150966/16292199. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 150967/16292244. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((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)) REDUCED to normal form. ------ 150968/16292271. ------ 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. ------ 150969/16292298. ------ 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. ------ 150970/16292388. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 150971/16292550. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 150972/16292559. ------ 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. ------ 150973/16292577. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))(^c.(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. ------ 150974/16292586. ------ 1. ==[ start ]==> (((a a)(^a.b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(b ((a a)(a a)))) REDUCED to normal form. ------ 150975/16292640. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 150976/16292667. ------ 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. ------ 150977/16292694. ------ 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)))((^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 REDUCED to normal form. ------ 150978/16292721. ------ 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. ------ 150979/16292748. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 150980/16292937. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)((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. ------ 150981/16293009. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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 a) REDUCED to normal form. ------ 150982/16293063. ------ 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)))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 150983/16293144. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> (b ((^x1.(a a))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 150984/16293225. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150985/16293279. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 11. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 12. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 13. ==[ beta ]==> a REDUCED to normal form. ------ 150986/16293360. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(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 a)) REDUCED to normal form. ------ 150987/16293684. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 150988/16293828. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) c)((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a b) c)((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a b) c)((a a)(^y.y))) 6. ==[ alpha ]==> (((a b) c)((a a)(^x.x))) REDUCED to normal form. ------ 150989/16293855. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a b)((a a) a))) 3. ==[ beta ]==> (((a a) b)((a b)((a a) a))) REDUCED to normal form. ------ 150990/16293882. ------ 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. ------ 150991/16293936. ------ 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 a)(^z.z)))) REDUCED to normal form. ------ 150992/16293963. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((a (^x.b))(a (b a))) REDUCED to normal form. ------ 150993/16294017. ------ 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)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 150994/16294062. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z)(a a))) 3. ==[ beta ]==> (b ((^z.z)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 150995/16294161. ------ 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.(^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. ------ 150996/16294188. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a b)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a b)(^y.a))) REDUCED to normal form. ------ 150997/16294215. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a) a)(^y.b))) 3. ==[ beta ]==> ((a (a b))(((a a) a)(^y.b))) 4. ==[ alpha ]==> ((a (a b))(((a a) a)(^x.b))) REDUCED to normal form. ------ 150998/16294242. ------ 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. ------ 150999/16294323. ------ 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.(^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))))) REDUCED to normal form. ------ 151000/16294350. ------ 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. ------ 151001/16294377. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b a)) REDUCED to normal form. ------ 151002/16294404. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 151003/16294494. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 151004/16294575. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(^a.a))(^b.(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. ------ 151005/16294638. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (b a))) REDUCED to normal form. ------ 151006/16294683. ------ 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. ------ 151007/16294746. ------ 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. ------ 151008/16294773. ------ 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. ------ 151009/16294827. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 151010/16294854. ------ 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. ------ 151011/16294881. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)(a b))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a b))) 7. ==[ beta ]==> (((a a)(^x.a))(a b)) REDUCED to normal form. ------ 151012/16294908. ------ 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. ------ 151013/16295025. ------ 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 (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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))) REDUCED to normal form. ------ 151014/16295052. ------ 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. ------ 151015/16295079. ------ 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 a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.a))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 151016/16295106. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 151017/16295133. ------ 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. ------ 151018/16295187. ------ 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.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.b)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.b)) REDUCED to normal form. ------ 151019/16295250. ------ 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 a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151020/16295331. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 151021/16295412. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 151022/16295520. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 151023/16295547. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 151024/16295637. ------ 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. ------ 151025/16295664. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 151026/16295718. ------ 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. ------ 151027/16295745. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(((a a) a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 151028/16295772. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a) a)) REDUCED to normal form. ------ 151029/16295826. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (a a))) REDUCED to normal form. ------ 151030/16295844. ------ 1. ==[ start ]==> ((a (^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 151031/16295916. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(^y.y))) REDUCED to normal form. ------ 151032/16295943. ------ 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. ------ 151033/16295970. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.a))) 7. ==[ beta ]==> ((a b)((a a)(^y.a))) 8. ==[ alpha ]==> ((a b)((a a)(^x.a))) REDUCED to normal form. ------ 151034/16295997. ------ 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. ------ 151035/16296024. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a) a)(^b.(^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. ------ 151036/16296078. ------ 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. ------ 151037/16296168. ------ 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. ------ 151038/16296330. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^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. ------ 151039/16296447. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(a (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (b a))) REDUCED to normal form. ------ 151040/16296474. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) 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))) REDUCED to normal form. ------ 151041/16296501. ------ 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. ------ 151042/16296528. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b) a)) REDUCED to normal form. ------ 151043/16296609. ------ 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. ------ 151044/16296636. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a (a b))) REDUCED to normal form. ------ 151045/16296654. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 151046/16296663. ------ 1. ==[ start ]==> (((a b)(^c.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 (^y.y))(a a))) REDUCED to normal form. ------ 151047/16296690. ------ 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)(^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. ------ 151048/16296762. ------ 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. ------ 151049/16296834. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^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)))) 7. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 151050/16296888. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((a (b a))(a (^y.b))) 6. ==[ alpha ]==> ((a (b a))(a (^x.b))) REDUCED to normal form. ------ 151051/16296915. ------ 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 (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 151052/16296969. ------ 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. ------ 151053/16296996. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(a a)) b)) 3. ==[ beta ]==> (((a b)((a a) a))((a a) b)) REDUCED to normal form. ------ 151054/16297023. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a b) c)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b) c)) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b) c)) 5. ==[ beta ]==> (((a a)(^y.y))((a b) c)) 6. ==[ alpha ]==> (((a a)(^x.x))((a b) c)) REDUCED to normal form. ------ 151055/16297194. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)(^c.(^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))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151056/16297437. ------ 1. ==[ start ]==> (((^a.(^a.(^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))(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. ------ 151057/16297545. ------ 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. ------ 151058/16297599. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)((a a) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)((a a) a))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 151059/16297680. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 151060/16297788. ------ 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 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151061/16297824. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c ((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c ((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c ((a a) a))) REDUCED to normal form. ------ 151062/16297851. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b (a b))) REDUCED to normal form. ------ 151063/16297887. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a)) a)) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 151064/16297914. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b) b)) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 151065/16298103. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(^z.z))) REDUCED to normal form. ------ 151066/16298157. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.a))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.a)) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.a)) REDUCED to normal form. ------ 151067/16298184. ------ 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. ------ 151068/16298211. ------ 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.(^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. ------ 151069/16298238. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 151070/16298409. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 151071/16298553. ------ 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. ------ 151072/16298580. ------ 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. ------ 151073/16298625. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b (^z.a))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.a))) REDUCED to normal form. ------ 151074/16298652. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(a (^z.b))) 3. ==[ beta ]==> ((^y.y)(a (^z.b))) 4. ==[ alpha ]==> ((^x.x)(a (^y.b))) 5. ==[ beta ]==> (a (^y.b)) 6. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 151075/16298706. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 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. ------ 151076/16298787. ------ 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)(^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. ------ 151077/16298895. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151078/16298931. ------ 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. ------ 151079/16298958. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 151080/16299021. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 151081/16299156. ------ 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))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(^z.z))) 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. ------ 151082/16299183. ------ 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.(^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. ------ 151083/16299210. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a) a)(^b.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. ------ 151084/16299237. ------ 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))(^z.(z z)))) REDUCED to normal form. ------ 151085/16299291. ------ 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. ------ 151086/16299318. ------ 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. ------ 151087/16299489. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c (^b.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. ------ 151088/16299570. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 151089/16299678. ------ 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 z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151090/16299795. ------ 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))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 151091/16299840. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b (^b.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. ------ 151092/16299894. ------ 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) REDUCED to normal form. ------ 151093/16299903. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c b)) REDUCED to normal form. ------ 151094/16299930. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b c)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b c)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b c)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151095/16299975. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.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. ------ 151096/16299984. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 151097/16300011. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (a (^y.y)))) REDUCED to normal form. ------ 151098/16300038. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 151099/16300083. ------ 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 (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151100/16300092. ------ 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. ------ 151101/16300119. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c a)) 3. ==[ beta ]==> ((b (^y.(y y)))(c a)) 4. ==[ alpha ]==> ((b (^x.(x x)))(c a)) REDUCED to normal form. ------ 151102/16300146. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b b)) REDUCED to normal form. ------ 151103/16300200. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 151104/16300218. ------ 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 (^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 151105/16300236. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 151106/16300263. ------ 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 (^y.y))) b) REDUCED to normal form. ------ 151107/16300290. ------ 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. ------ 151108/16300317. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a) a)) 3. ==[ beta ]==> (((a (a a)) b)((a a) a)) REDUCED to normal form. ------ 151109/16300344. ------ 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) 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 (^x.(^y.y))) a) REDUCED to normal form. ------ 151110/16300370. ------ 1. ==[ start ]==> (^a.(((a a) a)(b a))) 2. ==[ alpha ]==> (^x.(((x x) x)(b x))) REDUCED to normal form. ------ 151111/16300371. ------ 1. ==[ start ]==> (a (((a a) a)(b a))) REDUCED to normal form. ------ 151112/16310259. ------ 1. ==[ start ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 151113/16310265. ------ 1. ==[ start ]==> ((^a.a)(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 3. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 151114/16310292. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 5. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 6. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 9. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 11. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 12. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 151115/16310319. ------ 1. ==[ start ]==> ((^a.b)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.b)((a (a a))((^y.y) b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 151116/16310400. ------ 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)((^z.(^x1.x1)) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 151117/16310421. ------ 1. ==[ start ]==> (((a a) b)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 151118/16310517. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (^x.(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (^x.(b (^z.(z z)))) 6. ==[ alpha ]==> (^x.(b (^y.(y y)))) REDUCED to normal form. ------ 151119/16311210. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(b (b (^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. ------ 151120/16311975. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 151121/16312749. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)((a a)(a a)))((a a)((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((a a)((a a)(a a)))((a a)((a a)(a a))))) 5. ==[ beta ]==> (((a a)((a a)(a a)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 151122/16313121. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 151123/16315668. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^c.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(b a))) REDUCED to normal form. ------ 151124/16315947. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 151125/16317441. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 151126/16317666. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^x.(x x))) REDUCED to normal form. ------ 151127/16318602. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((a a) a))) REDUCED to normal form. ------ 151128/16318908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.((^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)))) 7. ==[ beta ]==> ((b a)(^x.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 151129/16319175. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (a (a a)))) 3. ==[ eta ]==> ((^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. ------ 151130/16319817. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.a))) REDUCED to normal form. ------ 151131/16319898. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^b.a))) 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. ------ 151132/16319994. ------ 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. ------ 151133/16320015. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 151134/16320042. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(a a))) REDUCED to normal form. ------ 151135/16320096. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.b)) 3. ==[ beta ]==> (((a (a a)) b)(^y.b)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.b)) REDUCED to normal form. ------ 151136/16320123. ------ 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 ]==> (((^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. ------ 151137/16320150. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 151138/16320162. ------ 1. ==[ start ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 151139/16320189. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(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. ------ 151140/16320216. ------ 1. ==[ start ]==> ((a b)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a b)((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((a b)((a (a a)) b)) REDUCED to normal form. ------ 151141/16320261. ------ 1. ==[ start ]==> (((^a.a) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 151142/16320270. ------ 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. ------ 151143/16320297. ------ 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. ------ 151144/16320315. ------ 1. ==[ start ]==> (((a a) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 151145/16320333. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.(^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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151146/16320360. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b (^a.a))(^a.(^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)))) REDUCED to normal form. ------ 151147/16320387. ------ 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))(^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. ------ 151148/16320414. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.a))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.(y y)))) REDUCED to normal form. ------ 151149/16320450. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 151150/16320495. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 151151/16320522. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 151152/16320531. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 151153/16320558. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 151154/16320585. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(b a))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 151155/16320603. ------ 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)(^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. ------ 151156/16320612. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 151157/16320639. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 151158/16320765. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z)) b)) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z)) b)) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) b)) 5. ==[ beta ]==> (((b (^y.y)) b)((b (^y.y)) b)) 6. ==[ alpha ]==> (((b (^x.x)) b)((b (^y.y)) b)) REDUCED to normal form. ------ 151159/16320792. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((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. ------ 151160/16320828. ------ 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. ------ 151161/16320855. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))(^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. ------ 151162/16320909. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 151163/16320936. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 151164/16320963. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 151165/16321071. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 151166/16321107. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(b (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 151167/16321404. ------ 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)(^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. ------ 151168/16321431. ------ 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.(^z.z))))) REDUCED to normal form. ------ 151169/16321458. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 151170/16321485. ------ 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. ------ 151171/16321512. ------ 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. ------ 151172/16321575. ------ 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.(^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. ------ 151173/16321629. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (a ((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 151174/16321710. ------ 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. ------ 151175/16321737. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(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. ------ 151176/16321746. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 151177/16321800. ------ 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. ------ 151178/16321827. ------ 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 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. ------ 151179/16321854. ------ 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. ------ 151180/16321872. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 151181/16322205. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) b)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((a a) a) b)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 151182/16322232. ------ 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. ------ 151183/16322259. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 151184/16322457. ------ 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. ------ 151185/16322484. ------ 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. ------ 151186/16322511. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 151187/16322538. ------ 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. ------ 151188/16322565. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))(b a))) 5. ==[ beta ]==> (((^y.y) a)((a (a a))(b a))) 6. ==[ alpha ]==> (((^x.x) a)((a (a a))(b a))) 7. ==[ beta ]==> (a ((a (a a))(b a))) REDUCED to normal form. ------ 151189/16322592. ------ 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. ------ 151190/16322610. ------ 1. ==[ start ]==> (((^a.b) b)(c (^b.b))) 2. ==[ alpha ]==> (((^x.b) b)(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 151191/16322619. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a))((a (^x.x)) b)) REDUCED to normal form. ------ 151192/16322646. ------ 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. ------ 151193/16322682. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((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. ------ 151194/16322736. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 151195/16322817. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.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. ------ 151196/16322826. ------ 1. ==[ start ]==> (((a b) b)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 151197/16322853. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.b)(a b))) 3. ==[ beta ]==> (((a a) a)((^y.b)(a b))) 4. ==[ alpha ]==> (((a a) a)((^x.b)(a b))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 151198/16322871. ------ 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)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a 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. ------ 151199/16322880. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 151200/16322898. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 151201/16322907. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 151202/16322952. ------ 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) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 11. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.y1)))) 12. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1)))) 13. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 14. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 151203/16322961. ------ 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. ------ 151204/16322988. ------ 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.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) b))((^y.(^z.z))((^x1.x1) 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. ------ 151205/16323015. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 151206/16323033. ------ 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 (((a a)(a a)) a)) REDUCED to normal form. ------ 151207/16323042. ------ 1. ==[ start ]==> (((a b)(^a.(^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 a)) REDUCED to normal form. ------ 151208/16323069. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.b)(^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)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 151209/16323258. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 151210/16323690. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 151211/16323735. ------ 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. ------ 151212/16323744. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(a a))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 151213/16323771. ------ 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)))(a (^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a (^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. ------ 151214/16324383. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^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) 7. ==[ beta ]==> a REDUCED to normal form. ------ 151215/16324644. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(b a))) REDUCED to normal form. ------ 151216/16324671. ------ 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 (^z.(^x1.x1))))) REDUCED to normal form. ------ 151217/16324905. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(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. ------ 151218/16325004. ------ 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 a))(^y.(a a)))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.(a 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)) REDUCED to normal form. ------ 151219/16325202. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 151220/16325229. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 151221/16325301. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1))) a)) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1))) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z))) a)) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 151222/16325535. ------ 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 a)(^x1.x1)))) REDUCED to normal form. ------ 151223/16325562. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a a)(b a))) REDUCED to normal form. ------ 151224/16325796. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1)(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. ------ 151225/16325868. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((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. ------ 151226/16326165. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^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 (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151227/16326192. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a)) c)) 3. ==[ beta ]==> ((^y.y)((^y1.(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. ------ 151228/16326336. ------ 1. ==[ start ]==> (((a b)(^c.a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.(a a)))) REDUCED to normal form. ------ 151229/16326363. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 151230/16326435. ------ 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.(^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. ------ 151231/16326444. ------ 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 a)) REDUCED to normal form. ------ 151232/16326471. ------ 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. ------ 151233/16327146. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a))(a a))) 3. ==[ beta ]==> ((b b)((^y.(a a))(a a))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(a a))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 151234/16327173. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 151235/16327191. ------ 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. ------ 151236/16327218. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 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. ------ 151237/16327227. ------ 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. ------ 151238/16327254. ------ 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 y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(^x2.x2)))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 9. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 10. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 11. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 12. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 151239/16327272. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((b a)(b a))(a (^y.a))) 6. ==[ alpha ]==> (((b a)(b a))(a (^x.a))) REDUCED to normal form. ------ 151240/16327335. ------ 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.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 151241/16327353. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a b))(((^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. ------ 151242/16327362. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 151243/16327416. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 151244/16327470. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 151245/16327497. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)(^c.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. ------ 151246/16327524. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z))(^x1.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. ------ 151247/16327560. ------ 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. ------ 151248/16327587. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(a a))) REDUCED to normal form. ------ 151249/16327614. ------ 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. ------ 151250/16327641. ------ 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.z) a))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)((^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. ------ 151251/16327668. ------ 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. ------ 151252/16327695. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) 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))(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. ------ 151253/16327722. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 151254/16327749. ------ 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. ------ 151255/16328001. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a) a) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a) b)) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a) b)) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151256/16328361. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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) REDUCED to normal form. ------ 151257/16328379. ------ 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.(^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. ------ 151258/16328388. ------ 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 (^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. ------ 151259/16328460. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 151260/16328469. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 151261/16328496. ------ 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. ------ 151262/16328577. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 151263/16328604. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.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. ------ 151264/16328631. ------ 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.(^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. ------ 151265/16328694. ------ 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. ------ 151266/16328721. ------ 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. ------ 151267/16328748. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((a b)(a ((^y.y) a))) 8. ==[ alpha ]==> ((a b)(a ((^x.x) a))) 9. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 151268/16328775. ------ 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. ------ 151269/16328802. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)((^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. ------ 151270/16329072. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (a (a a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 151271/16329162. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.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. ------ 151272/16329243. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (b ((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 151273/16329351. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 151274/16329486. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a) b)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a) b)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 151275/16329513. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^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. ------ 151276/16329567. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(^z.z))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(^z.z))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.y))) 9. ==[ beta ]==> ((b b)(a (^y.y))) 10. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 151277/16329576. ------ 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) REDUCED to normal form. ------ 151278/16329603. ------ 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 (^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. ------ 151279/16329648. ------ 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 (((^z.z) a) a)) 4. ==[ alpha ]==> (b (((^x.x) a) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 151280/16329657. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.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. ------ 151281/16329684. ------ 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))(^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. ------ 151282/16329711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^b.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. ------ 151283/16329756. ------ 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.(^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. ------ 151284/16329765. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) REDUCED to normal form. ------ 151285/16329792. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.a))) REDUCED to normal form. ------ 151286/16329819. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(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. ------ 151287/16329873. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 151288/16329891. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a) b)) REDUCED to normal form. ------ 151289/16329909. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 151290/16329936. ------ 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. ------ 151291/16329963. ------ 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. ------ 151292/16329990. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a b)) 3. ==[ beta ]==> (((a (a a)) b)(a b)) REDUCED to normal form. ------ 151293/16330017. ------ 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. ------ 151294/16330044. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 151295/16339941. ------ 1. ==[ start ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 151296/16339965. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151297/16340046. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151298/16340526. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(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. ------ 151299/16340940. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.(z z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 151300/16341714. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^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. ------ 151301/16342233. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.((((a a)(^z.z))((^x1.x1)(^y1.y1)))(((a a)(^z.z))((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> (^x.((((a a)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> (^x.((((a a)(^y.y))(^x1.x1))(((a a)(^y1.y1))((^z1.z1)(^x2.x2))))) 6. ==[ alpha ]==> (^x.((((a a)(^y.y))(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1))))) 7. ==[ beta ]==> (^x.((((a a)(^y.y))(^z.z))(((a a)(^x1.x1))(^z1.z1)))) 8. ==[ alpha ]==> (^x.((((a a)(^y.y))(^z.z))(((a a)(^x1.x1))(^y1.y1)))) REDUCED to normal form. ------ 151302/16342440. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((b (^z.(a a)))(b (^z.(a a))))) 4. ==[ alpha ]==> ((^x.x)((b (^y.(a a)))(b (^z.(a a))))) 5. ==[ beta ]==> ((b (^y.(a a)))(b (^z.(a a)))) 6. ==[ alpha ]==> ((b (^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 151303/16342452. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 151304/16342812. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 151305/16343115. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^z.a)(^x1.(^y1.(^z1.z1))))((^z.a)(^x1.(^y1.(^z1.z1)))))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 5. ==[ beta ]==> ((a ((^y1.a)(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 6. ==[ alpha ]==> ((a ((^x.a)(^y.(^z.(^x1.x1)))))(^y1.y1)) 7. ==[ beta ]==> ((a a)(^y1.y1)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 151306/16343847. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^b.((^a.a) b))) 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. ------ 151307/16343871. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(^z.z))) 3. ==[ eta ]==> (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. ------ 151308/16344180. ------ 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)(^x1.((^y1.y1) 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. ------ 151309/16344420. ------ 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 a)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 151310/16344495. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.(^b.b))) 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))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 151311/16344708. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^x1.(x1 x1))((^y1.y1)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.x1))) 7. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^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. ------ 151312/16345098. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(z (^x1.(^y1.y1))))) 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))))) 7. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 151313/16345311. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151314/16345386. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 151315/16345626. ------ 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) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 151316/16346439. ------ 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. ------ 151317/16346625. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((^y.a)(^z.b))((^y.a)(^z.b)))(((^y.a)(^z.b))((^y.a)(^z.b)))) 4. ==[ alpha ]==> ((((^x.a)(^y.b))((^z.a)(^x1.b)))(((^y1.a)(^z1.b))((^x2.a)(^y2.b)))) 5. ==[ beta ]==> ((a ((^z.a)(^x1.b)))(((^y1.a)(^z1.b))((^x2.a)(^y2.b)))) 6. ==[ alpha ]==> ((a ((^x.a)(^y.b)))(((^z.a)(^x1.b))((^y1.a)(^z1.b)))) 7. ==[ beta ]==> ((a a)(((^z.a)(^x1.b))((^y1.a)(^z1.b)))) 8. ==[ alpha ]==> ((a a)(((^x.a)(^y.b))((^z.a)(^x1.b)))) 9. ==[ beta ]==> ((a a)(a ((^z.a)(^x1.b)))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)(^y.b)))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 151318/16346907. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151319/16347132. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 151320/16347357. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(^y.(a a)))) REDUCED to normal form. ------ 151321/16347573. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 151322/16347705. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151323/16348293. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 151324/16348761. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 151325/16348866. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^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. ------ 151326/16349508. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 151327/16349589. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.c)) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.c)) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.c)) REDUCED to normal form. ------ 151328/16349685. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 151329/16349706. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 151330/16349760. ------ 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. ------ 151331/16349787. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(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))) REDUCED to normal form. ------ 151332/16349814. ------ 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 ]==> (((^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. ------ 151333/16349841. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 151334/16349871. ------ 1. ==[ start ]==> ((a (^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 151335/16349898. ------ 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 ]==> (((^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. ------ 151336/16349925. ------ 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))) 5. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 151337/16349952. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 151338/16350006. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151339/16350042. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(^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. ------ 151340/16350069. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 151341/16350096. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 151342/16350132. ------ 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. ------ 151343/16350150. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 151344/16350159. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 151345/16350231. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(a a)))) REDUCED to normal form. ------ 151346/16350258. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a 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. ------ 151347/16350312. ------ 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)(^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. ------ 151348/16350339. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a a))(^b.b))) 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. ------ 151349/16350375. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 151350/16350402. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 151351/16350429. ------ 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))((^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. ------ 151352/16350447. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> ((a a)((^y.y) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 151353/16350726. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 151354/16350753. ------ 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. ------ 151355/16350780. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.a)(^c.(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. ------ 151356/16350816. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (b (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151357/16350843. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 151358/16350897. ------ 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))(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. ------ 151359/16350906. ------ 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. ------ 151360/16350951. ------ 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.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(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. ------ 151361/16350978. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a 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. ------ 151362/16351032. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(a b))) REDUCED to normal form. ------ 151363/16351365. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b a)(^b.(^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. ------ 151364/16351446. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.(a a)))) REDUCED to normal form. ------ 151365/16351527. ------ 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))(^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. ------ 151366/16351554. ------ 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. ------ 151367/16351590. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 151368/16351617. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(b (^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. ------ 151369/16351698. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 151370/16351725. ------ 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)))(^x1.(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. ------ 151371/16351950. ------ 1. ==[ start ]==> (((^a.a)(a b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a b))(c ((^y.y) b))) 3. ==[ beta ]==> ((a b)(c ((^y.y) b))) 4. ==[ alpha ]==> ((a b)(c ((^x.x) b))) 5. ==[ beta ]==> ((a b)(c b)) REDUCED to normal form. ------ 151372/16351977. ------ 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. ------ 151373/16352031. ------ 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. ------ 151374/16352067. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z) c)) 5. ==[ beta ]==> ((^y.a)((^z.z) c)) 6. ==[ alpha ]==> ((^x.a)((^y.y) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 151375/16352112. ------ 1. ==[ start ]==> (((^a.b)(a a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 151376/16352139. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 151377/16352319. ------ 1. ==[ start ]==> (((a b)(a a))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(a a))(c (^x.x))) REDUCED to normal form. ------ 151378/16352346. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (^y.(a a)))) 3. ==[ beta ]==> ((a (a a))(b (^y.(a a)))) 4. ==[ alpha ]==> ((a (a a))(b (^x.(a a)))) REDUCED to normal form. ------ 151379/16352355. ------ 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 a) REDUCED to normal form. ------ 151380/16352526. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a b) b)((a a)(^y.a))) 4. ==[ alpha ]==> (((a b) b)((a a)(^x.a))) REDUCED to normal form. ------ 151381/16352553. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a b)(^y.b))) 3. ==[ beta ]==> (((a a) a)((a b)(^y.b))) 4. ==[ alpha ]==> (((a a) a)((a b)(^x.b))) REDUCED to normal form. ------ 151382/16352580. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 151383/16352607. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 151384/16352661. ------ 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. ------ 151385/16352688. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(^z.z))) 7. ==[ beta ]==> (((a (^y.y))(^z.z))((a (^y.y))(^z.z))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 151386/16352715. ------ 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. ------ 151387/16352742. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 151388/16352769. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) b) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b) b)) 5. ==[ beta ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 151389/16352805. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 151390/16352886. ------ 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. ------ 151391/16352913. ------ 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. ------ 151392/16352967. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 151393/16353021. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 151394/16353057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(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)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 151395/16353192. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 151396/16353273. ------ 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. ------ 151397/16353300. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1)(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. ------ 151398/16353354. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(b a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(b a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a (b a))) REDUCED to normal form. ------ 151399/16353444. ------ 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. ------ 151400/16353471. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 151401/16353498. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b a)(^z.a))) REDUCED to normal form. ------ 151402/16353561. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 151403/16353588. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.b)((a a) a))) 3. ==[ beta ]==> ((a (a b))((^y.b)((a a) a))) 4. ==[ alpha ]==> ((a (a b))((^x.b)((a a) a))) 5. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 151404/16353642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151405/16353669. ------ 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. ------ 151406/16353696. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.a)(b a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(b a))) 3. ==[ beta ]==> (((a b) a)((^y.a)(b a))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(b a))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 151407/16353723. ------ 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. ------ 151408/16353750. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)((^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. ------ 151409/16353777. ------ 1. ==[ start ]==> ((a (b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(^y.y))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 151410/16354056. ------ 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. ------ 151411/16354083. ------ 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 ((^x1.x1) 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. ------ 151412/16354119. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 151413/16354137. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((b a)(a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a b))((b a)(a (^x.x)))) REDUCED to normal form. ------ 151414/16354218. ------ 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. ------ 151415/16354326. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 151416/16354344. ------ 1. ==[ start ]==> (((a a)(b a))(c (^d.a))) 2. ==[ alpha ]==> (((a a)(b a))(c (^x.a))) REDUCED to normal form. ------ 151417/16354371. ------ 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.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 151418/16354398. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(a (^b.b))) 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))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 151419/16354425. ------ 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. ------ 151420/16354506. ------ 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. ------ 151421/16354533. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.b)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 151422/16354605. ------ 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. ------ 151423/16354614. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 151424/16354947. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(c ((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(^z.z)))) 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. ------ 151425/16355001. ------ 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)(a a))((^y.y)(a a)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (a (^y.(^z.z))))) 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. ------ 151426/16355010. ------ 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. ------ 151427/16355082. ------ 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)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))((^y1.y1) 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. ------ 151428/16355190. ------ 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. ------ 151429/16355217. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(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. ------ 151430/16355289. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 151431/16355343. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 151432/16355370. ------ 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. ------ 151433/16355397. ------ 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. ------ 151434/16355451. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 151435/16355496. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(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. ------ 151436/16355505. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) a) REDUCED to normal form. ------ 151437/16355532. ------ 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 b)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 151438/16355811. ------ 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. ------ 151439/16355865. ------ 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))) REDUCED to normal form. ------ 151440/16355874. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 151441/16355892. ------ 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. ------ 151442/16355901. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 151443/16355946. ------ 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. ------ 151444/16356027. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y) a)(a b))) 3. ==[ beta ]==> (b (((^y.y) a)(a b))) 4. ==[ alpha ]==> (b (((^x.x) a)(a b))) 5. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 151445/16356144. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 151446/16356171. ------ 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. ------ 151447/16356207. ------ 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. ------ 151448/16356234. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 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. ------ 151449/16356261. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((a (b a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((a (b a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((a (b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 151450/16356288. ------ 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) REDUCED to normal form. ------ 151451/16356315. ------ 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.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(a a)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 151452/16356342. ------ 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. ------ 151453/16356369. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))(^a.a))) 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. ------ 151454/16356396. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 151455/16356423. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 151456/16356477. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 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. ------ 151457/16356504. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((b (a a))((^y.a)(^y.a))) 6. ==[ alpha ]==> ((b (a a))((^x.a)(^y.a))) 7. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 151458/16356531. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.b))) 3. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 151459/16356567. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(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))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 151460/16356702. ------ 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. ------ 151461/16356810. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 151462/16356846. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 151463/16356873. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 151464/16356927. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^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. ------ 151465/16356954. ------ 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. ------ 151466/16357035. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 151467/16357062. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.b))((a a) a)) REDUCED to normal form. ------ 151468/16357116. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a) c)) REDUCED to normal form. ------ 151469/16357260. ------ 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)))) 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. ------ 151470/16357422. ------ 1. ==[ start ]==> (((a b)(a b))(c (^c.a))) 2. ==[ alpha ]==> (((a b)(a b))(c (^x.a))) REDUCED to normal form. ------ 151471/16357449. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(b (^y.b))) 3. ==[ beta ]==> (((a a)((a a) a))(b (^y.b))) 4. ==[ alpha ]==> (((a a)((a a) a))(b (^x.b))) REDUCED to normal form. ------ 151472/16357476. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.(a a)))) REDUCED to normal form. ------ 151473/16357557. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 151474/16357584. ------ 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. ------ 151475/16357611. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 151476/16357890. ------ 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)(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. ------ 151477/16357926. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z)) c)) 3. ==[ beta ]==> ((b c)((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((b c)((^x.(^y.y)) c)) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 151478/16357998. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 151479/16358025. ------ 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))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a) a))) 5. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 151480/16358061. ------ 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. ------ 151481/16358088. ------ 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.(^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. ------ 151482/16358169. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 151483/16358196. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 151484/16358502. ------ 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. ------ 151485/16358556. ------ 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))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 151486/16358583. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 151487/16358610. ------ 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.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 151488/16358664. ------ 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)(^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. ------ 151489/16358691. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^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))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 151490/16358718. ------ 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))(^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. ------ 151491/16358772. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^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. ------ 151492/16358862. ------ 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. ------ 151493/16359168. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z)) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z)) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y)) a)) 5. ==[ beta ]==> (a ((^y.(y y)) a)) 6. ==[ alpha ]==> (a ((^x.(x x)) a)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 151494/16359186. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 151495/16359213. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(a (^y1.y1)))) 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. ------ 151496/16359276. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(^a.a))) 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. ------ 151497/16359303. ------ 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))(^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. ------ 151498/16359357. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) 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. ------ 151499/16359384. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z)) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 151500/16359411. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a) c)) REDUCED to normal form. ------ 151501/16359456. ------ 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 (^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. ------ 151502/16359465. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^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)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 151503/16359492. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y) c)) 5. ==[ beta ]==> ((b (^x.(x x))) c) REDUCED to normal form. ------ 151504/16359519. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 151505/16359573. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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) REDUCED to normal form. ------ 151506/16359591. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (a a))) REDUCED to normal form. ------ 151507/16359609. ------ 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)(^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. ------ 151508/16359636. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 151509/16359663. ------ 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. ------ 151510/16359690. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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))) 5. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 151511/16359717. ------ 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 (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 151512/16359744. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.x))) REDUCED to normal form. ------ 151513/16369650. ------ 1. ==[ start ]==> ((((a a) a)(b a)) c) REDUCED to normal form. ------ 151514/16369830. ------ 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. ------ 151515/16369848. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 151516/16369926. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (^y.((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (^x.((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 151517/16369998. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)(^z.a))) 3. ==[ eta ]==> ((^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. ------ 151518/16370169. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 151519/16370268. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((((^y.(^z.z)) a) a)((((^y.(^z.z)) a) a)(((^y.(^z.z)) a) a))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((((^z.(^x1.x1)) a) a)(((^y1.(^z1.z1)) a) a))) 5. ==[ beta ]==> (((^y.y) a)((((^z.(^x1.x1)) a) a)(((^y1.(^z1.z1)) a) a))) 6. ==[ alpha ]==> (((^x.x) a)((((^y.(^z.z)) a) a)(((^x1.(^y1.y1)) a) a))) 7. ==[ beta ]==> (a ((((^y.(^z.z)) a) a)(((^x1.(^y1.y1)) a) a))) 8. ==[ alpha ]==> (a ((((^x.(^y.y)) a) a)(((^z.(^x1.x1)) a) a))) 9. ==[ beta ]==> (a (((^y.y) a)(((^z.(^x1.x1)) a) a))) 10. ==[ alpha ]==> (a (((^x.x) a)(((^y.(^z.z)) a) a))) 11. ==[ beta ]==> (a (a (((^y.(^z.z)) a) a))) 12. ==[ alpha ]==> (a (a (((^x.(^y.y)) a) a))) 13. ==[ beta ]==> (a (a ((^y.y) a))) 14. ==[ alpha ]==> (a (a ((^x.x) a))) 15. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 151520/16370493. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151521/16371384. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 151522/16371828. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 151523/16372548. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 151524/16373250. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^z.(^x1.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 151525/16373589. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b) a)) 3. ==[ eta ]==> (b (((^y.y) b) a)) 4. ==[ alpha ]==> (b (((^x.x) b) a)) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 151526/16373898. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151527/16374426. ------ 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. ------ 151528/16374519. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 151529/16374816. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 151530/16374825. ------ 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. ------ 151531/16375344. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 151532/16375383. ------ 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)) REDUCED to normal form. ------ 151533/16375662. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(b y))) 3. ==[ eta ]==> ((((^x.x) b) a) b) 4. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 151534/16376157. ------ 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. ------ 151535/16376868. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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 (^x.(a a))) REDUCED to normal form. ------ 151536/16377423. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151537/16378758. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 151538/16378866. ------ 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. ------ 151539/16378983. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(z (z z)))) 3. ==[ beta ]==> (((^y.y) a)(^z.(z (z z)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(y (y y)))) 5. ==[ beta ]==> (a (^y.(y (y y)))) 6. ==[ alpha ]==> (a (^x.(x (x x)))) REDUCED to normal form. ------ 151540/16379082. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(z z)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(z z)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 151541/16379163. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (b (^z.((^x1.x1) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 151542/16379172. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.d)) REDUCED to normal form. ------ 151543/16379307. ------ 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)))) REDUCED to normal form. ------ 151544/16379403. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^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))) REDUCED to normal form. ------ 151545/16379478. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.b)) 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. ------ 151546/16379505. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^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. ------ 151547/16379559. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.a)) REDUCED to normal form. ------ 151548/16379607. ------ 1. ==[ start ]==> (((^a.a) a)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x) a)(((a a) a)(b a))) 3. ==[ beta ]==> (a (((a a) a)(b a))) REDUCED to normal form. ------ 151549/16379634. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(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. ------ 151550/16379661. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.x))((a (a a)) b)) REDUCED to normal form. ------ 151551/16379688. ------ 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 ]==> (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. ------ 151552/16379715. ------ 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. ------ 151553/16379742. ------ 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. ------ 151554/16379760. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 151555/16379841. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 151556/16379859. ------ 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. ------ 151557/16379886. ------ 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)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 151558/16379913. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.a))) 3. ==[ beta ]==> ((a a)((b a)(^y.a))) 4. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 151559/16380003. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (a ((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> (a ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 151560/16380084. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a (^x.(x x)))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(x x)))(b ((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y) b))) 7. ==[ beta ]==> ((a (^x.(x x)))(b b)) REDUCED to normal form. ------ 151561/16380183. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((a (a (a a)))((^y.y) a)) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x) a)) 5. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 151562/16380273. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.(x1 x1)))) 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. ------ 151563/16380300. ------ 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. ------ 151564/16380381. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 151565/16380408. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 151566/16380633. ------ 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. ------ 151567/16380660. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (a (((^y.y) b)((^z.z) a))) 6. ==[ alpha ]==> (a (((^x.x) b)((^y.y) a))) 7. ==[ beta ]==> (a (b ((^y.y) a))) 8. ==[ alpha ]==> (a (b ((^x.x) a))) 9. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 151568/16380687. ------ 1. ==[ start ]==> (((a a)(^b.(^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. ------ 151569/16380714. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)(^z.z))) REDUCED to normal form. ------ 151570/16380741. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 151571/16380768. ------ 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. ------ 151572/16380795. ------ 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))) 9. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 151573/16381056. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.b)((^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 ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 151574/16381164. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(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. ------ 151575/16381299. ------ 1. ==[ start ]==> ((a (^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 151576/16381371. ------ 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. ------ 151577/16381398. ------ 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. ------ 151578/16381425. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b) c)) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b) c)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b) c)) 7. ==[ beta ]==> ((a (^x.x))(b c)) REDUCED to normal form. ------ 151579/16381569. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(a a)))) IRREDUCIBLE: cycle. ------ 151580/16381650. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 151581/16381677. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.y))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 151582/16381686. ------ 1. ==[ start ]==> (((a a)(^a.b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))(c ((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.b))(c b)) REDUCED to normal form. ------ 151583/16381740. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 151584/16381767. ------ 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. ------ 151585/16381794. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 151586/16381821. ------ 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.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 151587/16381848. ------ 1. ==[ start ]==> (((a b)(^a.a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((b a)(a (a a)))) REDUCED to normal form. ------ 151588/16382037. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 151589/16382082. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> ((^y.(a a))(b (^z.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(b (^y.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 151590/16382163. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(a (^z1.z1)))) 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. ------ 151591/16382244. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151592/16382298. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(a b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(a b))) 5. ==[ beta ]==> ((a a)((^y.b)(a b))) 6. ==[ alpha ]==> ((a a)((^x.b)(a b))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 151593/16382325. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(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. ------ 151594/16382379. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(b a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(b a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(b a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(b a))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(b a))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(b a))) 11. ==[ beta ]==> ((^y.(y y))(b a)) 12. ==[ alpha ]==> ((^x.(x x))(b a)) 13. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 151595/16382460. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 151596/16382784. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 151597/16382928. ------ 1. ==[ start ]==> (((a b) c)(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 151598/16382955. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b)((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a) b)((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a) b)((a a)(^y.y))) 8. ==[ alpha ]==> (((a a) b)((a a)(^x.x))) REDUCED to normal form. ------ 151599/16382982. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)((a a) a))) REDUCED to normal form. ------ 151600/16383036. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 151601/16383063. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.b))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 151602/16383117. ------ 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.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151603/16383144. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a) b)) REDUCED to normal form. ------ 151604/16383162. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(a (^z.(a a)))) 3. ==[ beta ]==> (b (a (^z.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 151605/16383261. ------ 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)))) REDUCED to normal form. ------ 151606/16383288. ------ 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)))(((^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. ------ 151607/16383315. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a b)(^y.a))) 3. ==[ beta ]==> ((a (a b))((a b)(^y.a))) 4. ==[ alpha ]==> ((a (a b))((a b)(^x.a))) REDUCED to normal form. ------ 151608/16383342. ------ 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. ------ 151609/16383369. ------ 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)))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(a a)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(a a)))) 9. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a a))) 10. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a))) 11. ==[ beta ]==> ((^y.y)(^z.(a a))) 12. ==[ alpha ]==> ((^x.x)(^y.(a a))) 13. ==[ beta ]==> (^y.(a a)) 14. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 151610/16383450. ------ 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. ------ 151611/16383477. ------ 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. ------ 151612/16383504. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b) a)) 3. ==[ beta ]==> ((a (b a))(b a)) REDUCED to normal form. ------ 151613/16383594. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151614/16383675. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 151615/16383783. ------ 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. ------ 151616/16383810. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^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)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151617/16383846. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 151618/16383873. ------ 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. ------ 151619/16383927. ------ 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. ------ 151620/16383954. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a b)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)(^y.y))) REDUCED to normal form. ------ 151621/16383981. ------ 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. ------ 151622/16384008. ------ 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.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a b)) REDUCED to normal form. ------ 151623/16384152. ------ 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. ------ 151624/16384179. ------ 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.(^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. ------ 151625/16384206. ------ 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 a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 151626/16384233. ------ 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. ------ 151627/16384260. ------ 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. ------ 151628/16384341. ------ 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. ------ 151629/16384350. ------ 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 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151630/16384431. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 151631/16384512. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^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. ------ 151632/16384620. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 151633/16384647. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 151634/16384674. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 151635/16384728. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 151636/16384737. ------ 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. ------ 151637/16384764. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(a a))) 5. ==[ beta ]==> ((^y.b)((b a)(a a))) 6. ==[ alpha ]==> ((^x.b)((b a)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 151638/16384818. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 151639/16384845. ------ 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. ------ 151640/16384872. ------ 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)((^z.z)(^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. ------ 151641/16384926. ------ 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. ------ 151642/16385043. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a a))((b a)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))((b a)(^x.x))) REDUCED to normal form. ------ 151643/16385070. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 151644/16385097. ------ 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. ------ 151645/16385124. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^y.y))((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.(y y)))) REDUCED to normal form. ------ 151646/16385151. ------ 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. ------ 151647/16385232. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z) a)(^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. ------ 151648/16385259. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 151649/16385268. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151650/16385295. ------ 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. ------ 151651/16385430. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)(^b.(^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. ------ 151652/16385547. ------ 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. ------ 151653/16385574. ------ 1. ==[ start ]==> ((((^a.a) b) a)(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(a (b a))) 3. ==[ beta ]==> ((b a)(a (b a))) REDUCED to normal form. ------ 151654/16385601. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 151655/16385628. ------ 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. ------ 151656/16385709. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 151657/16385736. ------ 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. ------ 151658/16385763. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((a b)(^x.a))(a (a b))) REDUCED to normal form. ------ 151659/16385790. ------ 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 (^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. ------ 151660/16385817. ------ 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)(^z.z)))) REDUCED to normal form. ------ 151661/16385934. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 151662/16385961. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 151663/16385988. ------ 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. ------ 151664/16386015. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (^z.b))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.b))) REDUCED to normal form. ------ 151665/16386042. ------ 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 (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a a)((a (^y.y))(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 151666/16386069. ------ 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. ------ 151667/16386096. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 151668/16386123. ------ 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)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 151669/16386150. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a b) c)) REDUCED to normal form. ------ 151670/16386294. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.a))(^b.(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. ------ 151671/16386537. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(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. ------ 151672/16386618. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 151673/16386645. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1) 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. ------ 151674/16386699. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((b a)(b a))((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((b a)(b a))((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.z))) 10. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.y))) 11. ==[ beta ]==> (((b a)(b a))(^y.y)) 12. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 151675/16386780. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 151676/16386888. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151677/16387014. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a)) a)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a)) a)) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 151678/16387041. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b) b)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b) b)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b) b)) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 151679/16387068. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a) c)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a) c)) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 151680/16387257. ------ 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.(^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. ------ 151681/16387284. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.a))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.a)) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.a)) REDUCED to normal form. ------ 151682/16387311. ------ 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. ------ 151683/16387338. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 151684/16387428. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(^y2.y2))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(^y2.y2))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151685/16387509. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 151686/16387653. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b c)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((b c)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((b c)(a (^y.y))) 8. ==[ alpha ]==> ((b c)(a (^x.x))) REDUCED to normal form. ------ 151687/16387680. ------ 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. ------ 151688/16387725. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 151689/16387752. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b (^z.a))) 3. ==[ beta ]==> ((^y.y)(b (^z.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 151690/16387887. ------ 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. ------ 151691/16387995. ------ 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.(^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. ------ 151692/16388121. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a) a)) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 151693/16388148. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z)) 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. ------ 151694/16388175. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z)) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z)) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y)) c)) 5. ==[ beta ]==> ((a b)((^y.(y y)) c)) 6. ==[ alpha ]==> ((a b)((^x.(x x)) c)) 7. ==[ beta ]==> ((a b)(c c)) REDUCED to normal form. ------ 151695/16388283. ------ 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))(^x1.x1))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a b)(a a))(^y.y)) 8. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 151696/16388310. ------ 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. ------ 151697/16388337. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y) 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. ------ 151698/16388391. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 151699/16388418. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((b ((^x.x) 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)((^y.y) a)) 8. ==[ alpha ]==> ((b a)((^x.x) a)) 9. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 151700/16388445. ------ 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. ------ 151701/16388670. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 151702/16388778. ------ 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. ------ 151703/16388895. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 151704/16388940. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (^a.(^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. ------ 151705/16388994. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a (^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (^z.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (^z.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (^y.(y y)))) 7. ==[ beta ]==> ((b b)(a (^y.(y y)))) 8. ==[ alpha ]==> ((b b)(a (^x.(x x)))) REDUCED to normal form. ------ 151706/16389075. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 151707/16389084. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a d)) REDUCED to normal form. ------ 151708/16389111. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (a a))) REDUCED to normal form. ------ 151709/16389138. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (a (^z.z)))) REDUCED to normal form. ------ 151710/16389192. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(a a))) REDUCED to normal form. ------ 151711/16389219. ------ 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. ------ 151712/16389246. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c a)) REDUCED to normal form. ------ 151713/16389318. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 151714/16389336. ------ 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. ------ 151715/16389363. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1)) 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. ------ 151716/16389390. ------ 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)) 5. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 151717/16389417. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((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. ------ 151718/16389444. ------ 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. ------ 151719/16389471. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) a)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 151720/16389497. ------ 1. ==[ start ]==> (^a.((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (^x.((x b)((x x)(^y.y)))) REDUCED to normal form. ------ 151721/16389498. ------ 1. ==[ start ]==> (a ((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (a ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 151722/16399413. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a))) a) 2. ==[ alpha ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 151723/16399419. ------ 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. ------ 151724/16399446. ------ 1. ==[ start ]==> ((^a.(a a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(x x))(((a a) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(b a))(((a a) a)(b a))) REDUCED to normal form. ------ 151725/16399473. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 151726/16399554. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^z.z))(b (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 151727/16399602. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 151728/16399671. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (^y.(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (^x.(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 151729/16399914. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))(^z.z))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 151730/16400007. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(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)(^x.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 151731/16400796. ------ 1. ==[ start ]==> ((^a.((a a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a a)(b (^y.y)))) 3. ==[ beta ]==> ((((a a)(b (^y.y)))((a a)(b (^y.y))))((a a)(b (^y.y)))) 4. ==[ alpha ]==> ((((a a)(b (^x.x)))((a a)(b (^y.y))))((a a)(b (^z.z)))) REDUCED to normal form. ------ 151732/16401129. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 151733/16401903. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))((^x1.x1) b))((a (^z.z))((^x1.x1) b)))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))((^z.z) b))((a (^x1.x1))((^y1.y1) b)))) 5. ==[ beta ]==> (((a (^y.y))((^z.z) b))((a (^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))((^x1.x1) b))) 7. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))((^x1.x1) b))) 8. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))((^z.z) b))) 9. ==[ beta ]==> (((a (^x.x)) b)((a (^y.y)) b)) REDUCED to normal form. ------ 151734/16402293. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 151735/16402302. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 151736/16403004. ------ 1. ==[ start ]==> (((a b)(^b.a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 151737/16404264. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 151738/16404570. ------ 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. ------ 151739/16406406. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 151740/16406613. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 151741/16406622. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 151742/16406847. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^y.(y y))) REDUCED to normal form. ------ 151743/16407621. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 151744/16407954. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((y y) y))) REDUCED to normal form. ------ 151745/16408611. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151746/16408728. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z z)))) 5. ==[ beta ]==> (a (^y.(^z.(z z)))) 6. ==[ alpha ]==> (a (^x.(^y.(y y)))) REDUCED to normal form. ------ 151747/16408836. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 151748/16408908. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^b.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. ------ 151749/16408917. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 151750/16409079. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 151751/16409133. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 151752/16409148. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1)) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 151753/16409196. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 151754/16409277. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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)) REDUCED to normal form. ------ 151755/16409304. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(x x))) REDUCED to normal form. ------ 151756/16409331. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 151757/16409343. ------ 1. ==[ start ]==> ((a a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 151758/16409370. ------ 1. ==[ start ]==> ((a (a a))(((a a) a)(b a))) REDUCED to normal form. ------ 151759/16409397. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(((^x.x)(^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))))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 151760/16409451. ------ 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. ------ 151761/16409478. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 151762/16409523. ------ 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. ------ 151763/16409541. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^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)(^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. ------ 151764/16409568. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 151765/16409595. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 151766/16409631. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 151767/16409676. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.a)((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.a)((b a)(^y.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 151768/16409703. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 151769/16409712. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 151770/16409739. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 151771/16409757. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 151772/16409766. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 151773/16409820. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^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)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 151774/16409838. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 151775/16409928. ------ 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 a)((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a a)((^x.x)((^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. ------ 151776/16409946. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((^y.(y y))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> ((((^y.(^z.z)) a) a)(((^y.(^z.z)) 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. ------ 151777/16409973. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((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. ------ 151778/16410009. ------ 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. ------ 151779/16410036. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(y y))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(x x))) REDUCED to normal form. ------ 151780/16410063. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 151781/16410144. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 151782/16410252. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> ((b b)((^y.y)(^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. ------ 151783/16410585. ------ 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)(^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. ------ 151784/16410612. ------ 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. ------ 151785/16410639. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 151786/16410666. ------ 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. ------ 151787/16410693. ------ 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. ------ 151788/16410720. ------ 1. ==[ start ]==> ((a ((a a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 151789/16410756. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^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. ------ 151790/16410810. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> (a (((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> (a (((^x.x) b)(^y.a))) 7. ==[ beta ]==> (a (b (^y.a))) 8. ==[ alpha ]==> (a (b (^x.a))) REDUCED to normal form. ------ 151791/16410846. ------ 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)))(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 151792/16410918. ------ 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)(a a))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.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. ------ 151793/16410927. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 151794/16410954. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 151795/16410981. ------ 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. ------ 151796/16411008. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 151797/16411035. ------ 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. ------ 151798/16411053. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a (^x.b))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.y))) REDUCED to normal form. ------ 151799/16411224. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 151800/16411413. ------ 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. ------ 151801/16411440. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 151802/16411638. ------ 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. ------ 151803/16411665. ------ 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. ------ 151804/16411692. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)(a b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)(a b))) 5. ==[ beta ]==> ((a (^y.y))((a b)(a b))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(a b))) REDUCED to normal form. ------ 151805/16411719. ------ 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. ------ 151806/16411746. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> (a (((^y.y)(^z.z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> (a (((^x.x)(^y.y))((a a)(^z.z)))) 9. ==[ beta ]==> (a ((^y.y)((a a)(^z.z)))) 10. ==[ alpha ]==> (a ((^x.x)((a a)(^y.y)))) 11. ==[ beta ]==> (a ((a a)(^y.y))) 12. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 151807/16411773. ------ 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. ------ 151808/16411800. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) 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. ------ 151809/16411827. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 151810/16411917. ------ 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.(^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. ------ 151811/16411998. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 151812/16412007. ------ 1. ==[ start ]==> (((a b) b)((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 151813/16412034. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a 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 a)) REDUCED to normal form. ------ 151814/16412052. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.b))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.b))) 5. ==[ beta ]==> ((a a)((a b)(^y.b))) 6. ==[ alpha ]==> ((a a)((a b)(^x.b))) REDUCED to normal form. ------ 151815/16412061. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(a b))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 151816/16412079. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 151817/16412088. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 151818/16412142. ------ 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. ------ 151819/16412169. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((^y.a)(a (^z.(^x1.x1))))((^y.a)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((^x.a)(a (^y.(^z.z))))((^x1.a)(a (^y1.(^z1.z1))))) 9. ==[ beta ]==> (a ((^x1.a)(a (^y1.(^z1.z1))))) 10. ==[ alpha ]==> (a ((^x.a)(a (^y.(^z.z))))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 151820/16412196. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 151821/16412214. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 151822/16412223. ------ 1. ==[ start ]==> (((a b)(^a.(^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. ------ 151823/16412439. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 151824/16412871. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(c (^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151825/16412898. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 151826/16412925. ------ 1. ==[ start ]==> (((a b)(^b.a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 151827/16412952. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^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. ------ 151828/16412979. ------ 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)))(a (^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. ------ 151829/16413492. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 151830/16413618. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 151831/16413825. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) 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. ------ 151832/16413852. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 151833/16413879. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 151834/16414086. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 151835/16414104. ------ 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. ------ 151836/16414185. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 151837/16414266. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> (b (((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 151838/16414383. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 151839/16414410. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 151840/16414491. ------ 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. ------ 151841/16414563. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (b ((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151842/16414716. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 151843/16414743. ------ 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 a)(^z.z)))) REDUCED to normal form. ------ 151844/16414770. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a a)(b a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a a)(b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(b a))) REDUCED to normal form. ------ 151845/16414977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151846/16415022. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.a))(^c.(^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))) REDUCED to normal form. ------ 151847/16415301. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 151848/16415517. ------ 1. ==[ start ]==> (((a b)(^c.a))(d (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(d (^y.b))) REDUCED to normal form. ------ 151849/16415544. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c (^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 151850/16415571. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 151851/16415616. ------ 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))(((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. ------ 151852/16415652. ------ 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. ------ 151853/16416183. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a) d)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a) d)) 3. ==[ beta ]==> (b ((^z.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 151854/16416327. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 151855/16416354. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 151856/16416372. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b)(^a.(^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. ------ 151857/16416399. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((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. ------ 151858/16416408. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 151859/16416435. ------ 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. ------ 151860/16416453. ------ 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. ------ 151861/16416516. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(a 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. ------ 151862/16416534. ------ 1. ==[ start ]==> (((^a.b)(a b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((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. ------ 151863/16416543. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)(a a))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(a a))) 5. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 151864/16416597. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 151865/16416651. ------ 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))(^z1.(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. ------ 151866/16416678. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))(^b.(^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. ------ 151867/16416705. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 151868/16416741. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(b (a b))) REDUCED to normal form. ------ 151869/16416768. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (a a))) REDUCED to normal form. ------ 151870/16416795. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b)(a a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)(a a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(a a))) REDUCED to normal form. ------ 151871/16416822. ------ 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. ------ 151872/16416849. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1) a))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) a))) 9. ==[ beta ]==> (((a a)(^x.x))((^z.z) a)) 10. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 11. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 151873/16416876. ------ 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. ------ 151874/16416903. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) 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)))) 5. ==[ beta ]==> (((a b)(a b))(a (^y.y))) 6. ==[ alpha ]==> (((a b)(a b))(a (^x.x))) REDUCED to normal form. ------ 151875/16416930. ------ 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. ------ 151876/16416957. ------ 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)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a a)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(a b))) REDUCED to normal form. ------ 151877/16417182. ------ 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. ------ 151878/16417371. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^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. ------ 151879/16417542. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.b))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.b))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.b))) REDUCED to normal form. ------ 151880/16417560. ------ 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. ------ 151881/16417641. ------ 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)(^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. ------ 151882/16417650. ------ 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. ------ 151883/16417677. ------ 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)(^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. ------ 151884/16417749. ------ 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)(^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. ------ 151885/16417758. ------ 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.(^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. ------ 151886/16417785. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))(^b.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. ------ 151887/16417812. ------ 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.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 151888/16417875. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 151889/16417902. ------ 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. ------ 151890/16417929. ------ 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. ------ 151891/16417956. ------ 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.x1) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 151892/16417983. ------ 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. ------ 151893/16418010. ------ 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)(^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. ------ 151894/16418343. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z)) 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. ------ 151895/16418532. ------ 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)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151896/16418649. ------ 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)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 151897/16418667. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 151898/16418694. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.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. ------ 151899/16418757. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 151900/16418784. ------ 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. ------ 151901/16418829. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^b.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. ------ 151902/16418838. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)((^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. ------ 151903/16418865. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.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. ------ 151904/16418892. ------ 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))(^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. ------ 151905/16418937. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151906/16418946. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.y1))) REDUCED to normal form. ------ 151907/16418973. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 151908/16419000. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.a))) REDUCED to normal form. ------ 151909/16419054. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 151910/16419072. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z)) a)) REDUCED to normal form. ------ 151911/16419090. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 151912/16419117. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 151913/16419144. ------ 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. ------ 151914/16419171. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b a)) 3. ==[ beta ]==> (((a (a a)) b)(b a)) REDUCED to normal form. ------ 151915/16419198. ------ 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)) REDUCED to normal form. ------ 151916/16419225. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (a a))) REDUCED to normal form. ------ 151917/16419252. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 151918/16419858. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((^x.((^y.(^z.z)) a))((^x1.((^y1.(^z1.z1)) a))(^x2.((^y2.(^z2.z2)) 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. ------ 151919/16423179. ------ 1. ==[ start ]==> ((^a.(b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((^z.z) y))) 3. ==[ eta ]==> (b (^y.((^z.z) y))) 4. ==[ alpha ]==> (b (^x.((^y.y) x))) 5. ==[ eta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 151920/16429176. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a))) b) 2. ==[ alpha ]==> (((a b)((a a)(^x.x))) b) REDUCED to normal form. ------ 151921/16429200. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151922/16429281. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 151923/16429515. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ eta ]==> ((^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. ------ 151924/16429785. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a))(((^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))((^x2.x2)((^y2.(^z2.z2)) a)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)((^y1.(^z1.z1)) a))((^x2.x2)((^y2.(^z2.z2)) a)))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)((^x1.(^y1.y1)) a))((^z1.z1)((^x2.(^y2.y2)) a)))) 7. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.(^y1.y1)) a))((^z1.z1)((^x2.(^y2.y2)) a)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a)))) 9. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a))) 10. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)((^y1.(^z1.z1)) a))) 11. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)((^y1.(^z1.z1)) a))) 12. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.(^y1.y1)) a))) 13. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) a))) 14. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 15. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 16. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 17. ==[ beta ]==> ((^y.(^z.z)) a) 18. ==[ alpha ]==> ((^x.(^y.y)) a) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151925/16429788. ------ 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)))(^x.(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 151926/16430136. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)(^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. ------ 151927/16430976. ------ 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. ------ 151928/16431081. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) b) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1))) 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. ------ 151929/16431363. ------ 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. ------ 151930/16431468. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b a)(a (a a)))) 3. ==[ beta ]==> (^y.(((b a)(a (a a)))((b a)(a (a a))))) 4. ==[ alpha ]==> (^x.(((b a)(a (a a)))((b a)(a (a a))))) REDUCED to normal form. ------ 151931/16431714. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^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. ------ 151932/16432074. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 151933/16432767. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 151934/16433106. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)((^z.z) b))) 3. ==[ eta ]==> (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)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 151935/16433109. ------ 1. ==[ start ]==> ((a (b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))(^x.((^y.y) x))) 3. ==[ eta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 151936/16433655. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 151937/16433757. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 151938/16433943. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(a b))(^y.(^z.z))) 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. ------ 151939/16434546. ------ 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. ------ 151940/16434648. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 151941/16434861. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 151942/16435197. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(b z))) 3. ==[ eta ]==> (((^x.x)((^y.y) b)) b) 4. ==[ beta ]==> (((^y.y) b) b) 5. ==[ alpha ]==> (((^x.x) b) b) 6. ==[ beta ]==> (b b) REDUCED to normal form. ------ 151943/16435701. ------ 1. ==[ start ]==> (((a b)((a a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 151944/16436394. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 151945/16436619. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(a a)))) REDUCED to normal form. ------ 151946/16436940. ------ 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. ------ 151947/16437222. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 151948/16437726. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 151949/16437888. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.y))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.y))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.x))) REDUCED to normal form. ------ 151950/16438023. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.((^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)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(^x.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 151951/16438101. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)(^b.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. ------ 151952/16438275. ------ 1. ==[ start ]==> (((^a.b)(^c.(^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)))) REDUCED to normal form. ------ 151953/16438518. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^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. ------ 151954/16438599. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((^z.z) a))) 7. ==[ beta ]==> ((b b)(^y.((^z.z) a))) 8. ==[ alpha ]==> ((b b)(^x.((^y.y) a))) 9. ==[ beta ]==> ((b b)(^x.a)) REDUCED to normal form. ------ 151955/16438689. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 151956/16438788. ------ 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.((^x2.x2) z1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^x2.x2)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.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. ------ 151957/16438851. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.c)) REDUCED to normal form. ------ 151958/16438968. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 151959/16439022. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 151960/16439049. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 151961/16439076. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 151962/16439103. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 151963/16439133. ------ 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. ------ 151964/16439160. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((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. ------ 151965/16439187. ------ 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)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 151966/16439214. ------ 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. ------ 151967/16439268. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151968/16439295. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.(^y1.y1)) 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. ------ 151969/16439331. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(^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. ------ 151970/16439358. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 151971/16439412. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 151972/16439421. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a (a a))) REDUCED to normal form. ------ 151973/16439448. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 151974/16439493. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 151975/16439520. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 151976/16439547. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 151977/16439601. ------ 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.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 151978/16439637. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 151979/16439664. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 151980/16439691. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(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. ------ 151981/16439718. ------ 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)))((^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. ------ 151982/16439790. ------ 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. ------ 151983/16439961. ------ 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. ------ 151984/16440015. ------ 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. ------ 151985/16440042. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^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. ------ 151986/16440069. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 151987/16440078. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 151988/16440105. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(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. ------ 151989/16440159. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 151990/16440213. ------ 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)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 151991/16440240. ------ 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.(^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. ------ 151992/16440294. ------ 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)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 151993/16440627. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.(^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)))) REDUCED to normal form. ------ 151994/16440654. ------ 1. ==[ start ]==> ((((a a) a) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 151995/16440708. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.b))) REDUCED to normal form. ------ 151996/16440735. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 151997/16440762. ------ 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. ------ 151998/16440816. ------ 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. ------ 151999/16440852. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 152000/16440879. ------ 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.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 152001/16440906. ------ 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. ------ 152002/16440987. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.a)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.a)) REDUCED to normal form. ------ 152003/16441014. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 152004/16441293. ------ 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. ------ 152005/16441329. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a)) b)) 5. ==[ beta ]==> ((^y.a)((^z.(a a)) b)) 6. ==[ alpha ]==> ((^x.a)((^y.(a a)) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 152006/16441356. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) c) REDUCED to normal form. ------ 152007/16441374. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))((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 (^x.(^y.y))) a)) REDUCED to normal form. ------ 152008/16441401. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 152009/16441617. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 152010/16441644. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 152011/16441788. ------ 1. ==[ start ]==> (((a b) b)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 152012/16441842. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)(^y.b))) REDUCED to normal form. ------ 152013/16441869. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 152014/16441950. ------ 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) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((((^y.y) a)(^z.(^x1.(^y1.y1))))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 9. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 10. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 11. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(^z1.(^x2.x2))))) 12. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 152015/16441977. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 152016/16442004. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 152017/16442031. ------ 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. ------ 152018/16442067. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^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. ------ 152019/16442094. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.(^x1.x1)))(^y1.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. ------ 152020/16442175. ------ 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. ------ 152021/16442202. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.b)(^z.b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.b)(^y.b))) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 152022/16442229. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 152023/16442256. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.(^a.a))(^c.(^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)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 152024/16442319. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(c (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(c (a (^x1.(^y1.y1))))) 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. ------ 152025/16442454. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)((^z.z) a))) 3. ==[ beta ]==> (b ((b a)((^z.z) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 152026/16442463. ------ 1. ==[ start ]==> (((a b) c)((^d.a) d)) 2. ==[ alpha ]==> (((a b) c)((^x.a) d)) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 152027/16442535. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)((a a) a))) REDUCED to normal form. ------ 152028/16442562. ------ 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. ------ 152029/16442616. ------ 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. ------ 152030/16442697. ------ 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)((^z.z) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 152031/16442733. ------ 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. ------ 152032/16442760. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 152033/16442850. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 152034/16442877. ------ 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. ------ 152035/16442931. ------ 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. ------ 152036/16442958. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (((a b) a)(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 152037/16442985. ------ 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. ------ 152038/16443012. ------ 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 (^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. ------ 152039/16443039. ------ 1. ==[ start ]==> ((a (b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))((^x.x)((^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. ------ 152040/16443318. ------ 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. ------ 152041/16443345. ------ 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.(^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. ------ 152042/16443381. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z) a)) 3. ==[ beta ]==> ((a (^y.(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. ------ 152043/16443399. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 152044/16443408. ------ 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. ------ 152045/16443462. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 152046/16443480. ------ 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. ------ 152047/16443588. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a (a a))(a a))) REDUCED to normal form. ------ 152048/16443660. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (^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. ------ 152049/16443687. ------ 1. ==[ start ]==> (((a (a a))(a b))(a (^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(a (^x.x))) REDUCED to normal form. ------ 152050/16443714. ------ 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.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 152051/16443768. ------ 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. ------ 152052/16443795. ------ 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. ------ 152053/16443822. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 152054/16443867. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152055/16443876. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^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)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 152056/16444263. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(b (b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(b (b a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(b (b a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (b a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (b a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (b a))) 7. ==[ beta ]==> (((a a)(a a))(b (b a))) REDUCED to normal form. ------ 152057/16444299. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1))) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152058/16444344. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 152059/16444353. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(^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. ------ 152060/16444452. ------ 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)(^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. ------ 152061/16444479. ------ 1. ==[ start ]==> ((a (^b.b))((a (a a))(a b))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 152062/16444524. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 152063/16444578. ------ 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))))) 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. ------ 152064/16444659. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 152065/16444686. ------ 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. ------ 152066/16444758. ------ 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. ------ 152067/16444767. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a b)(a b))) REDUCED to normal form. ------ 152068/16444794. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 152069/16445127. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(a (b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (b a))) 3. ==[ beta ]==> (((^y.y) b)(a (b a))) 4. ==[ alpha ]==> (((^x.x) b)(a (b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 152070/16445154. ------ 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.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. ------ 152071/16445208. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b) a)) REDUCED to normal form. ------ 152072/16445289. ------ 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. ------ 152073/16445406. ------ 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.y1))(^z1.z1))) REDUCED to normal form. ------ 152074/16445433. ------ 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. ------ 152075/16445469. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((a a) b)((^y.b)((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)((^x.b)((^y.y) a))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 152076/16445523. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 152077/16445550. ------ 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. ------ 152078/16445577. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.a)(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(a b))) 7. ==[ beta ]==> ((a a)((^y.a)(a b))) 8. ==[ alpha ]==> ((a a)((^x.a)(a b))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 152079/16445604. ------ 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. ------ 152080/16445631. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.x)((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. ------ 152081/16445685. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 152082/16445766. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 152083/16445829. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(c (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(c (a b))) 3. ==[ beta ]==> ((^y.y)(c (a b))) 4. ==[ alpha ]==> ((^x.x)(c (a b))) 5. ==[ beta ]==> (c (a b)) REDUCED to normal form. ------ 152084/16445964. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((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. ------ 152085/16446072. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((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. ------ 152086/16446135. ------ 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. ------ 152087/16446189. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.a))) REDUCED to normal form. ------ 152088/16446216. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(y1 y1))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 152089/16446297. ------ 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. ------ 152090/16446324. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 152091/16446378. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b) b)) REDUCED to normal form. ------ 152092/16446522. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 152093/16446549. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.(a a))) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a a))) REDUCED to normal form. ------ 152094/16446738. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(b (^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b (^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.b))) REDUCED to normal form. ------ 152095/16446792. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 152096/16446819. ------ 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)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 152097/16446846. ------ 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))((^z.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. ------ 152098/16446873. ------ 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. ------ 152099/16447152. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(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. ------ 152100/16447188. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a) b)) 3. ==[ beta ]==> ((b c)((^y.a) b)) 4. ==[ alpha ]==> ((b c)((^x.a) b)) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 152101/16447215. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^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. ------ 152102/16447260. ------ 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. ------ 152103/16447287. ------ 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)(^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. ------ 152104/16447350. ------ 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. ------ 152105/16447431. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) 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. ------ 152106/16447458. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 152107/16447539. ------ 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)(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 152108/16447566. ------ 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. ------ 152109/16447656. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.a)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.a)) REDUCED to normal form. ------ 152110/16447764. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(b a))(c (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (^y.(y y)))) 5. ==[ beta ]==> ((b a)(c (^y.(y y)))) 6. ==[ alpha ]==> ((b a)(c (^x.(x x)))) REDUCED to normal form. ------ 152111/16447791. ------ 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)))) REDUCED to normal form. ------ 152112/16447818. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a 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. ------ 152113/16447845. ------ 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))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 152114/16447872. ------ 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 y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 152115/16447926. ------ 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 (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. ------ 152116/16447953. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.x)((^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. ------ 152117/16447980. ------ 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))(^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. ------ 152118/16448034. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)(^b.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. ------ 152119/16448124. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 152120/16448205. ------ 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. ------ 152121/16448448. ------ 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 ]==> (((^y.(^z.z)) a)(a (a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(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. ------ 152122/16448475. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 152123/16448529. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)((^z.z) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)((^z.z) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)((^y.y) a))) 7. ==[ beta ]==> ((b b)((a a)((^y.y) a))) 8. ==[ alpha ]==> ((b b)((a a)((^x.x) a))) 9. ==[ beta ]==> ((b b)((a a) a)) REDUCED to normal form. ------ 152124/16448565. ------ 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)(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152125/16448610. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 152126/16448619. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 152127/16448646. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a) a)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 152128/16448673. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z)) b)) REDUCED to normal form. ------ 152129/16448718. ------ 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 ((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152130/16448727. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.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. ------ 152131/16448754. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^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. ------ 152132/16448781. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) c) REDUCED to normal form. ------ 152133/16448835. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 152134/16448871. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 152135/16448898. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 152136/16448925. ------ 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. ------ 152137/16448952. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 152138/16448979. ------ 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)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 152139/16449006. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.y))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 152140/16449033. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 152141/16452969. ------ 1. ==[ start ]==> ((^a.(b a))(^c.(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.z))) 3. ==[ eta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 152142/16458783. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152143/16458966. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a))) c) 2. ==[ alpha ]==> (((a b)((a a)(^x.x))) c) REDUCED to normal form. ------ 152144/16459191. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^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))))) REDUCED to normal form. ------ 152145/16459314. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 152146/16459485. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^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. ------ 152147/16459596. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(y y))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(x x))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.((^z.(^x1.x1)) a))(^y.((^z.(^x1.x1)) 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. ------ 152148/16459809. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152149/16460700. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 152150/16461171. ------ 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. ------ 152151/16462575. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.((^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. ------ 152152/16462905. ------ 1. ==[ start ]==> ((^a.(b a))((a a)(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))((a a)(^y.y))) 3. ==[ eta ]==> (b ((a a)(^y.y))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 152153/16462908. ------ 1. ==[ start ]==> ((a (b a))(^c.(^b.b))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 152154/16463250. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(^y.b)) REDUCED to normal form. ------ 152155/16463742. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((((^x1.x1)(^y1.y1))(^z1.b))(^y.(^z.z))) 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. ------ 152156/16464168. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(z (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)(^y.(y (^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152157/16464660. ------ 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) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 152158/16465005. ------ 1. ==[ start ]==> (((a a)(^b.b))(^a.(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(b y))) 3. ==[ eta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 152159/16465500. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 152160/16465977. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((b b)(^x.(a a))) REDUCED to normal form. ------ 152161/16466739. ------ 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. ------ 152162/16466832. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(a y1))) 3. ==[ eta ]==> (((^x.(x x))(^y.(^z.(^x1.x1)))) a) 4. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) a) 5. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) a) 6. ==[ beta ]==> ((^y.(^z.z)) a) 7. ==[ alpha ]==> ((^x.(^y.y)) a) 8. ==[ beta ]==> (^y.y) 9. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152163/16467021. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(^z1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152164/16467192. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^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. ------ 152165/16467210. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.b))) REDUCED to normal form. ------ 152166/16467822. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.(^b.(^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. ------ 152167/16468074. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 152168/16468317. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^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. ------ 152169/16468407. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^y.a)) REDUCED to normal form. ------ 152170/16468488. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 152171/16468587. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(^b.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. ------ 152172/16468596. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 152173/16468650. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 152174/16468719. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152175/16468722. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 152176/16468767. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.b)) REDUCED to normal form. ------ 152177/16468821. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.y)) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 152178/16468875. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.a)) REDUCED to normal form. ------ 152179/16468902. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 152180/16468950. ------ 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. ------ 152181/16468977. ------ 1. ==[ start ]==> (((a a) a)(((a a) a)(b a))) REDUCED to normal form. ------ 152182/16469004. ------ 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))((^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. ------ 152183/16469031. ------ 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))) 5. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 152184/16469058. ------ 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. ------ 152185/16469085. ------ 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. ------ 152186/16469112. ------ 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 (^x.x)) a)((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 152187/16469130. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(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))))) REDUCED to normal form. ------ 152188/16469202. ------ 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. ------ 152189/16469229. ------ 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 z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(y y)))) REDUCED to normal form. ------ 152190/16469256. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 152191/16469265. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 152192/16469346. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (a ((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 152193/16469373. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((a a)(^y1.y1)))) 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. ------ 152194/16469427. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^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)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 152195/16469445. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))(^b.b))) 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. ------ 152196/16469535. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a))((^y.y)((^z.(^x1.x1)) 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. ------ 152197/16469643. ------ 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. ------ 152198/16469670. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 152199/16469751. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 152200/16469886. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152201/16469976. ------ 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. ------ 152202/16470003. ------ 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 (^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. ------ 152203/16470030. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 152204/16470057. ------ 1. ==[ start ]==> (((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)))(a (a a)))) REDUCED to normal form. ------ 152205/16470084. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.a))((b a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.a))((b a)(^y.y))) REDUCED to normal form. ------ 152206/16470111. ------ 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. ------ 152207/16470138. ------ 1. ==[ start ]==> ((((^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 b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(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. ------ 152208/16470399. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (a ((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(a a))(a (^y.y)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 152209/16470561. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)((^y.b)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(a a)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 152210/16470642. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.b))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 152211/16470660. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) 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. ------ 152212/16470741. ------ 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. ------ 152213/16470768. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a)) b)) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 152214/16470795. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) b) c)) 3. ==[ beta ]==> ((((a a) a)(a a))(b c)) REDUCED to normal form. ------ 152215/16470831. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 152216/16470912. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.b))) IRREDUCIBLE: cycle. ------ 152217/16471020. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 152218/16471047. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^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. ------ 152219/16471083. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((a a)(a a)))) REDUCED to normal form. ------ 152220/16471110. ------ 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. ------ 152221/16471137. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(a a))) 5. ==[ beta ]==> ((^y.a)(((a a)(a a))(a a))) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a))(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 152222/16471164. ------ 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 (^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. ------ 152223/16471191. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 152224/16471380. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b) b)((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 152225/16471425. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.z))) 3. ==[ beta ]==> ((^y.(a a))(c (^z.z))) 4. ==[ alpha ]==> ((^x.(a a))(c (^y.y))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 152226/16471452. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(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. ------ 152227/16471506. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a a))) 5. ==[ beta ]==> ((^y.y)((^y1.(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. ------ 152228/16471641. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((a a)((^y.(a a))((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((a a) a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 152229/16471668. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.b)(a b))) 3. ==[ beta ]==> ((^y.y)((^z.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. ------ 152230/16471722. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152231/16471803. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 152232/16471875. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(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)) 5. ==[ beta ]==> (((a a)(a a))(b b)) REDUCED to normal form. ------ 152233/16471902. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 152234/16472127. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 152235/16472271. ------ 1. ==[ start ]==> (((a b) c)((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)((b a)((^x.x) a))) 3. ==[ beta ]==> (((a b) c)((b a) a)) REDUCED to normal form. ------ 152236/16472298. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 152237/16472325. ------ 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))((^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)))) 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. ------ 152238/16472379. ------ 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. ------ 152239/16472406. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.b))((^z.z)(a a))) 8. ==[ alpha ]==> ((a (^x.b))((^y.y)(a a))) 9. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 152240/16472460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152241/16472487. ------ 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.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 152242/16472505. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b (^z.z))) 3. ==[ beta ]==> (b (b (^z.z))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 152243/16472514. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.a))((a a) b)) REDUCED to normal form. ------ 152244/16472604. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b a)(^y.a))) REDUCED to normal form. ------ 152245/16472631. ------ 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)(^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)))) REDUCED to normal form. ------ 152246/16472658. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(a a))(^b.(^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. ------ 152247/16472685. ------ 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. ------ 152248/16472712. ------ 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)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.b))) 7. ==[ beta ]==> ((^y.y)(((a a) a)(^z.b))) 8. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 9. ==[ beta ]==> (((a a) a)(^y.b)) 10. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 152249/16472739. ------ 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. ------ 152250/16472766. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 152251/16472820. ------ 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))))) REDUCED to normal form. ------ 152252/16472847. ------ 1. ==[ start ]==> ((a (b a))((a a)(^b.b))) 2. ==[ alpha ]==> ((a (b a))((a a)(^x.x))) REDUCED to normal form. ------ 152253/16473018. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 152254/16473153. ------ 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.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. ------ 152255/16473189. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(a ((^z.z) b))) 3. ==[ beta ]==> ((a (^y.(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(a b)) REDUCED to normal form. ------ 152256/16473216. ------ 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. ------ 152257/16473270. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 152258/16473297. ------ 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. ------ 152259/16473324. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.a))((a b)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.y))) REDUCED to normal form. ------ 152260/16473351. ------ 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. ------ 152261/16473522. ------ 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.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a) 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))) REDUCED to normal form. ------ 152262/16473549. ------ 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.(^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. ------ 152263/16473576. ------ 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. ------ 152264/16473603. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.(z z)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a 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. ------ 152265/16473630. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 152266/16473684. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.b)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 152267/16473693. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152268/16473774. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(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. ------ 152269/16473990. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(^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. ------ 152270/16474017. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(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. ------ 152271/16474080. ------ 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. ------ 152272/16474107. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.b)(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.b)(a (a (^y.(^z.z))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152273/16474161. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 152274/16474188. ------ 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)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.(x x)))((a a) a)) REDUCED to normal form. ------ 152275/16474215. ------ 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. ------ 152276/16474269. ------ 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)))(^z.z))((^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. ------ 152277/16474413. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a)(^z.z))) 3. ==[ beta ]==> (((^y.y)(a b))((b a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a b))((b a)(^y.y))) 5. ==[ beta ]==> ((a b)((b a)(^y.y))) 6. ==[ alpha ]==> ((a b)((b a)(^x.x))) REDUCED to normal form. ------ 152278/16474440. ------ 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. ------ 152279/16474467. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.a))) 6. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 152280/16474494. ------ 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. ------ 152281/16474521. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a) a)(^b.(^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. ------ 152282/16474575. ------ 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. ------ 152283/16474602. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 152284/16474611. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(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. ------ 152285/16474638. ------ 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 a)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))((a a)(^y2.y2)))) 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. ------ 152286/16474773. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 152287/16474881. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152288/16474890. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(c (a a))) REDUCED to normal form. ------ 152289/16474917. ------ 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. ------ 152290/16474944. ------ 1. ==[ start ]==> (((a a)(^b.b))(a (b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(a (b a))) REDUCED to normal form. ------ 152291/16474971. ------ 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.y1))(a a))) REDUCED to normal form. ------ 152292/16475052. ------ 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. ------ 152293/16475079. ------ 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))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(^z.z))) 7. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 8. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 152294/16475106. ------ 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. ------ 152295/16475133. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 152296/16475160. ------ 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 (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 152297/16475277. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(^y.a))) 3. ==[ beta ]==> (((a a) b)((a b)(^y.a))) 4. ==[ alpha ]==> (((a a) b)((a b)(^x.a))) REDUCED to normal form. ------ 152298/16475304. ------ 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.(x1 x1)))) REDUCED to normal form. ------ 152299/16475331. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 152300/16475385. ------ 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)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.b))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.b))) 7. ==[ beta ]==> ((a a)(((^y.y) a)(^z.b))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.b))) 9. ==[ beta ]==> ((a a)(a (^y.b))) 10. ==[ alpha ]==> ((a a)(a (^x.b))) REDUCED to normal form. ------ 152301/16475412. ------ 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. ------ 152302/16475439. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 152303/16475466. ------ 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.x1)) a)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z)) a)) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 152304/16475493. ------ 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)(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a) b)) REDUCED to normal form. ------ 152305/16475637. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.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. ------ 152306/16475880. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c (^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152307/16475916. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((b b)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((b b)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((b b)((a a)(a a))) REDUCED to normal form. ------ 152308/16475961. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 152309/16475988. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a (^y1.y1)))) 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. ------ 152310/16476042. ------ 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. ------ 152311/16476123. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 152312/16476384. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a)) a)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a)) a)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a)) a)) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 152313/16476411. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b) b)) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 152314/16476600. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a 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. ------ 152315/16476627. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 152316/16476654. ------ 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))(^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. ------ 152317/16476681. ------ 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. ------ 152318/16476771. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.y1)(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.y1)(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.x2)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.x2)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152319/16476852. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))(^b.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. ------ 152320/16476960. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.y1)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152321/16476996. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a)(a a))) 3. ==[ beta ]==> ((b c)(((a a) a)(a a))) REDUCED to normal form. ------ 152322/16477023. ------ 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 (^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)))) 5. ==[ beta ]==> ((((a a)(a a)) b)(a (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a)) b)(a (^x.x))) REDUCED to normal form. ------ 152323/16477131. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 152324/16477149. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a (^x1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a (^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.b))) REDUCED to normal form. ------ 152325/16477230. ------ 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))((^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. ------ 152326/16477518. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a ((^x.x) 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)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 152327/16477653. ------ 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))(^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. ------ 152328/16477680. ------ 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. ------ 152329/16477734. ------ 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. ------ 152330/16477761. ------ 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)))) 5. ==[ beta ]==> ((b a)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 152331/16477788. ------ 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.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 152332/16478013. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (b (b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 152333/16478121. ------ 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))((^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. ------ 152334/16478238. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 152335/16478256. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 152336/16478337. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (^b.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. ------ 152337/16478346. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a a) a)) REDUCED to normal form. ------ 152338/16478418. ------ 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 (^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. ------ 152339/16478427. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 152340/16478481. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (a a))) REDUCED to normal form. ------ 152341/16478526. ------ 1. ==[ start ]==> (((^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.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152342/16478535. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 152343/16478562. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 152344/16478589. ------ 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. ------ 152345/16478643. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 152346/16478661. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 152347/16478679. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 152348/16478706. ------ 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. ------ 152349/16478733. ------ 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. ------ 152350/16478760. ------ 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)) 5. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 152351/16478787. ------ 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))) REDUCED to normal form. ------ 152352/16478814. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a) a)) REDUCED to normal form. ------ 152353/16478841. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 152354/16478867. ------ 1. ==[ start ]==> (^a.(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (^x.(((^y.y)(x x))((^z.z)(x x)))) 3. ==[ beta ]==> (^x.((x x)((^z.z)(x x)))) 4. ==[ alpha ]==> (^x.((x x)((^y.y)(x x)))) 5. ==[ beta ]==> (^x.((x x)(x x))) REDUCED to normal form. ------ 152355/16478868. ------ 1. ==[ start ]==> (a (((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (a (((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (a ((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 152356/16488810. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a))) a) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a))) a) 3. ==[ beta ]==> (((a a)((^y.y)(a a))) a) 4. ==[ alpha ]==> (((a a)((^x.x)(a a))) a) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 152357/16488816. ------ 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))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 152358/16488843. ------ 1. ==[ start ]==> ((^a.(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> (((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)))) REDUCED to normal form. ------ 152359/16488870. ------ 1. ==[ start ]==> ((^a.b)(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.b)(((a a) a)(b a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 152360/16488951. ------ 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) a)((a a)(a a)))(^y.y)) 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. ------ 152361/16489026. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 152362/16489068. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 152363/16489311. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 152364/16490193. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((((a (^y.y))((a a)(a a)))((a (^y.y))((a a)(a a))))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((((a (^x.x))((a a)(a a)))((a (^y.y))((a a)(a a))))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 152365/16490526. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 152366/16491300. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)(a (^x1.(^y1.y1))))(((^z.z) a)(a (^x1.(^y1.y1)))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)(a (^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.(^x2.x2)))))) 5. ==[ beta ]==> ((((^y.y) a)(a (^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (a (^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 152367/16491726. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^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)))) REDUCED to normal form. ------ 152368/16493076. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 152369/16493382. ------ 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. ------ 152370/16493994. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152371/16496271. ------ 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.y1)(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 152372/16497045. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.b))) REDUCED to normal form. ------ 152373/16497378. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((y y) y))) REDUCED to normal form. ------ 152374/16497513. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(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)))) 5. ==[ beta ]==> (((a b)(a a))(^x.(^z.z))) 6. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 152375/16498260. ------ 1. ==[ start ]==> ((((^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 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152376/16498341. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 152377/16498422. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.a))) REDUCED to normal form. ------ 152378/16498545. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152379/16498620. ------ 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. ------ 152380/16498647. ------ 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))) REDUCED to normal form. ------ 152381/16498701. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.b)) REDUCED to normal form. ------ 152382/16498728. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 152383/16498755. ------ 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. ------ 152384/16498767. ------ 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)((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. ------ 152385/16498794. ------ 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. ------ 152386/16498821. ------ 1. ==[ start ]==> ((a b)(((a a) a)(b a))) REDUCED to normal form. ------ 152387/16498875. ------ 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. ------ 152388/16498902. ------ 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. ------ 152389/16498920. ------ 1. ==[ start ]==> (((a a) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 152390/16498974. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 152391/16498992. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 152392/16499019. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 152393/16499055. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 152394/16499100. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 152395/16499127. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 152396/16499181. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (a (((^y.y)(a a))(^z.(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. ------ 152397/16499190. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 152398/16499208. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 152399/16499217. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 152400/16499262. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 152401/16499352. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 152402/16499397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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. ------ 152403/16499487. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 152404/16499514. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 152405/16499676. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 152406/16500009. ------ 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.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. ------ 152407/16500036. ------ 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. ------ 152408/16500063. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 152409/16500090. ------ 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. ------ 152410/16500117. ------ 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. ------ 152411/16500144. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 152412/16500234. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a (((a a)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 152413/16500270. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.b)((^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 ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 152414/16500297. ------ 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. ------ 152415/16500315. ------ 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. ------ 152416/16500351. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(^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)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 152417/16500378. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(a a))(a b))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 152418/16500396. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)(^z.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a b)(^z.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a b)(^y.(a a)))) 7. ==[ beta ]==> ((a a)((a b)(^y.(a a)))) 8. ==[ alpha ]==> ((a a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 152419/16500405. ------ 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. ------ 152420/16500459. ------ 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. ------ 152421/16500477. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 152422/16500648. ------ 1. ==[ start ]==> (((^a.b) a)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.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. ------ 152423/16500810. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 152424/16500864. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 152425/16500918. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 152426/16501017. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.y) c)) 3. ==[ beta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 152427/16501062. ------ 1. ==[ start ]==> (((a a)(a b))((b a)(a (a a)))) REDUCED to normal form. ------ 152428/16501089. ------ 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)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 152429/16501116. ------ 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)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(^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 (^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. ------ 152430/16501143. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a b)(a b))) REDUCED to normal form. ------ 152431/16501170. ------ 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.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)(((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)(((a 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. ------ 152432/16501197. ------ 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. ------ 152433/16501224. ------ 1. ==[ start ]==> (((a b)(a a))((a (a a))(b a))) REDUCED to normal form. ------ 152434/16501251. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) 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. ------ 152435/16501341. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.y1))) 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. ------ 152436/16501422. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 152437/16501485. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 152438/16501503. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 152439/16501512. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 152440/16501566. ------ 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. ------ 152441/16501593. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(b a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(b a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(b a))) 7. ==[ beta ]==> (((^y.(y y))(b a))((^y.(y y))(b a))) 8. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))(b a))) 9. ==[ beta ]==> (((b a)(b a))((^y.(y y))(b a))) 10. ==[ alpha ]==> (((b a)(b a))((^x.(x x))(b a))) 11. ==[ beta ]==> (((b a)(b a))((b a)(b a))) REDUCED to normal form. ------ 152442/16501620. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 152443/16501638. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 152444/16501647. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 152445/16501674. ------ 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)(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. ------ 152446/16501863. ------ 1. ==[ start ]==> (((^a.b) c)((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 152447/16502097. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) 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. ------ 152448/16502349. ------ 1. ==[ start ]==> (((a b)(^b.a))(b (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 152449/16502403. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b)(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. ------ 152450/16502772. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a) c)) 5. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 152451/16502916. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(^a.a))(^b.(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. ------ 152452/16503024. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(^x1.x1))) 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. ------ 152453/16503042. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(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)) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 152454/16503123. ------ 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. ------ 152455/16503249. ------ 1. ==[ start ]==> (((a a)(b a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> (((a a)(b a))((a (a a))(a a))) REDUCED to normal form. ------ 152456/16503276. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 152457/16503303. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.z))(b a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))(b a))) 5. ==[ beta ]==> ((a (a a))((a (^y.y))(b a))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(b a))) REDUCED to normal form. ------ 152458/16503330. ------ 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. ------ 152459/16503528. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152460/16503690. ------ 1. ==[ start ]==> (((^a.b)(^b.(^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. ------ 152461/16503834. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 152462/16503942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152463/16504140. ------ 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. ------ 152464/16504167. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y) 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)))) 5. ==[ beta ]==> (((a (^x.x))(b a))(a (a a))) REDUCED to normal form. ------ 152465/16504194. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 152466/16504221. ------ 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. ------ 152467/16504401. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(^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. ------ 152468/16504446. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(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. ------ 152469/16504608. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b) d)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b) d)) 3. ==[ beta ]==> (b ((a b) d)) REDUCED to normal form. ------ 152470/16504725. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 152471/16504752. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^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. ------ 152472/16504851. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a)) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 152473/16505076. ------ 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. ------ 152474/16505607. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b) c)) 3. ==[ beta ]==> (b ((^z.b) c)) 4. ==[ alpha ]==> (b ((^x.b) c)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 152475/16505751. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b (^y.(a a)))) 3. ==[ beta ]==> ((b b)(b (^y.(a a)))) 4. ==[ alpha ]==> ((b b)(b (^x.(a a)))) REDUCED to normal form. ------ 152476/16505796. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 152477/16505823. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 152478/16505832. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 152479/16505877. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (((b a)(b a))(^y.(y y))) 8. ==[ alpha ]==> (((b a)(b a))(^x.(x x))) REDUCED to normal form. ------ 152480/16505940. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 152481/16505958. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (^y.y))(^z.b))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.b))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 152482/16505967. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 152483/16506021. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 152484/16506075. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 152485/16506102. ------ 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))(^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. ------ 152486/16506129. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 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. ------ 152487/16506192. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b (a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b (a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (a b))) REDUCED to normal form. ------ 152488/16506219. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 152489/16506246. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(a a))) REDUCED to normal form. ------ 152490/16506273. ------ 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. ------ 152491/16506300. ------ 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)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^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))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^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. ------ 152492/16506327. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 152493/16506354. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) 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))(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. ------ 152494/16506381. ------ 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 (^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 152495/16506606. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a a)(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a a)(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a a)(^x2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152496/16506687. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^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. ------ 152497/16506966. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.a))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 152498/16506993. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.b))) REDUCED to normal form. ------ 152499/16507065. ------ 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. ------ 152500/16507074. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a b)(^x.(a a)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 152501/16507101. ------ 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. ------ 152502/16507173. ------ 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. ------ 152503/16507209. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(^a.(^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. ------ 152504/16507236. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 152505/16507299. ------ 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 (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 152506/16507326. ------ 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. ------ 152507/16507353. ------ 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. ------ 152508/16507380. ------ 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. ------ 152509/16507407. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> ((b a)(((^x.x) 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. ------ 152510/16507434. ------ 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. ------ 152511/16507461. ------ 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)(^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. ------ 152512/16507767. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1)) 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. ------ 152513/16507848. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^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. ------ 152514/16507956. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^b.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. ------ 152515/16508073. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^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. ------ 152516/16508118. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1)) 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. ------ 152517/16508172. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^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. ------ 152518/16508181. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.a))) REDUCED to normal form. ------ 152519/16508208. ------ 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 (^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a (^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152520/16508253. ------ 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))(^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. ------ 152521/16508262. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 152522/16508289. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 152523/16508316. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 152524/16508370. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(^b.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. ------ 152525/16508397. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (^z.z))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (^z.z))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (^y.y))) REDUCED to normal form. ------ 152526/16508424. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 152527/16508478. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 152528/16508496. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 152529/16508541. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (a a))) REDUCED to normal form. ------ 152530/16508568. ------ 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. ------ 152531/16508595. ------ 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. ------ 152532/16508622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 152533/16508649. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a b)) REDUCED to normal form. ------ 152534/16508676. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 152535/16508703. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 152536/16518654. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a))) b) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a))) b) 3. ==[ beta ]==> (((a a)((^y.y)(a a))) b) 4. ==[ alpha ]==> (((a a)((^x.x)(a a))) b) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 152537/16518678. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152538/16518759. ------ 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 (^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152539/16518993. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(a (a a)))) 3. ==[ eta ]==> ((^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. ------ 152540/16519263. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1)))(((^y.(^z.z))(b (^x1.x1)))((^y.(^z.z))(b (^x1.x1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.(^y1.y1))(b (^z1.z1)))((^x2.(^y2.y2))(b (^z2.z2))))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(b (^z1.z1)))((^x2.(^y2.y2))(b (^z2.z2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2))))) 7. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 8. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b (^z1.z1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 12. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152541/16519614. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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. ------ 152542/16519707. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 152543/16520085. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 152544/16520481. ------ 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. ------ 152545/16520559. ------ 1. ==[ start ]==> ((^a.(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)(^z.a))) 3. ==[ beta ]==> (((^y.y)(^z.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. ------ 152546/16520946. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(((a (^z.(^x1.x1)))((^y1.y1) a))((a (^z.(^x1.x1)))((^y1.y1) a)))) 4. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))((^x1.x1) a))((a (^y1.(^z1.z1)))((^x2.x2) a)))) 5. ==[ beta ]==> (^x.(((a (^y.(^z.z))) a)((a (^y1.(^z1.z1)))((^x2.x2) a)))) 6. ==[ alpha ]==> (^x.(((a (^y.(^z.z))) a)((a (^x1.(^y1.y1)))((^z1.z1) a)))) 7. ==[ beta ]==> (^x.(((a (^y.(^z.z))) a)((a (^x1.(^y1.y1))) a))) REDUCED to normal form. ------ 152547/16521828. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(^a.a))(^c.(^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. ------ 152548/16522584. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ eta ]==> (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. ------ 152549/16522947. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(a b))(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y) b))) 5. ==[ beta ]==> (((a b)(a b))(^x.b)) REDUCED to normal form. ------ 152550/16523133. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 152551/16523262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^a.(^b.b))) 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. ------ 152552/16524024. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152553/16524153. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 152554/16524339. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(z z))(a b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 152555/16524702. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(^y.y))(a (^z.(^x1.x1)))) b) 4. ==[ beta ]==> ((^y.y) b) 5. ==[ alpha ]==> ((^x.x) b) 6. ==[ beta ]==> b REDUCED to normal form. ------ 152556/16525206. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 152557/16525338. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.(^y1.y1)))((^y.(^z.z))(^x1.(^y1.y1))))(((^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))))(((^z2.(^x3.x3))(^y3.(^z3.z3)))((^x4.(^y4.y4))(^z4.(^x5.x5))))) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))(((^z2.(^x3.x3))(^y3.(^z3.z3)))((^x4.(^y4.y4))(^z4.(^x5.x5))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))(((^z1.(^x2.x2))(^y2.(^z2.z2)))((^x3.(^y3.y3))(^z3.(^x4.x4))))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))(((^z1.(^x2.x2))(^y2.(^z2.z2)))((^x3.(^y3.y3))(^z3.(^x4.x4))))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1))(^x2.(^y2.y2)))((^z2.(^x3.x3))(^y3.(^z3.z3))))) 9. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))(^x2.(^y2.y2)))((^z2.(^x3.x3))(^y3.(^z3.z3))))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2))))) 11. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 13. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 15. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152558/16526124. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 152559/16526340. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.(z z)))) REDUCED to normal form. ------ 152560/16526418. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 152561/16527231. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 152562/16527393. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 152563/16527528. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 152564/16527579. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(^a.(^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. ------ 152565/16527672. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.((^a.a)(^a.a)))) 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 ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152566/16528023. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y y)))) 5. ==[ beta ]==> (^y.(y (y y))) 6. ==[ alpha ]==> (^x.(x (x x))) REDUCED to normal form. ------ 152567/16528194. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(^b.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. ------ 152568/16528275. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 152569/16528398. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152570/16528419. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 152571/16528473. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^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. ------ 152572/16528527. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 152573/16528554. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(a a))) REDUCED to normal form. ------ 152574/16528581. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 152575/16528608. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.(^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))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 152576/16528638. ------ 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)))) 3. ==[ beta ]==> ((a (^x.x))((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. ------ 152577/16528665. ------ 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. ------ 152578/16528692. ------ 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. ------ 152579/16528719. ------ 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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 152580/16528773. ------ 1. ==[ start ]==> (((^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 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. ------ 152581/16528800. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(b (^y1.y1)))) 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. ------ 152582/16528827. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^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. ------ 152583/16528863. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.(^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)(^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. ------ 152584/16528917. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((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. ------ 152585/16528953. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 152586/16528998. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)(^y.a))) REDUCED to normal form. ------ 152587/16529025. ------ 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. ------ 152588/16529052. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 152589/16529079. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 152590/16529142. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(^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)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 152591/16529169. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b ((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.z) b))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b b)) REDUCED to normal form. ------ 152592/16529196. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(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. ------ 152593/16529223. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 152594/16529295. ------ 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. ------ 152595/16529466. ------ 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. ------ 152596/16529493. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 152597/16529547. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 152598/16529574. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^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. ------ 152599/16529664. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 152600/16529718. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 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. ------ 152601/16529727. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 152602/16529745. ------ 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. ------ 152603/16529799. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((b a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 152604/16530042. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^y1.y1)))) 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. ------ 152605/16530132. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (b (((^y.y) b)(^z.a))) 6. ==[ alpha ]==> (b (((^x.x) b)(^y.a))) 7. ==[ beta ]==> (b (b (^y.a))) 8. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 152606/16530159. ------ 1. ==[ start ]==> ((((a a) a) a)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 152607/16530213. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) REDUCED to normal form. ------ 152608/16530240. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(^z.b))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.b))) REDUCED to normal form. ------ 152609/16530267. ------ 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. ------ 152610/16530357. ------ 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 (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 152611/16530384. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 152612/16530411. ------ 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. ------ 152613/16530438. ------ 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. ------ 152614/16530510. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 152615/16530519. ------ 1. ==[ start ]==> ((a (a b))((^b.b)(^b.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. ------ 152616/16530798. ------ 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. ------ 152617/16530879. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (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. ------ 152618/16530888. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.b) c)) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y) c)) 3. ==[ beta ]==> (((a b)(^x.x)) c) REDUCED to normal form. ------ 152619/16530906. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(a a)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 152620/16531122. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 152621/16531149. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 152622/16531293. ------ 1. ==[ start ]==> (((a b) b)((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) b)((b a)(^x.(x x)))) REDUCED to normal form. ------ 152623/16531320. ------ 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.(^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)))) REDUCED to normal form. ------ 152624/16531347. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 152625/16531374. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b)(^z.b))) REDUCED to normal form. ------ 152626/16531428. ------ 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. ------ 152627/16531482. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) a)(^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. ------ 152628/16531509. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 152629/16531599. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^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. ------ 152630/16531626. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 152631/16531707. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 152632/16531734. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a b)(a (^x.x))) b) REDUCED to normal form. ------ 152633/16531788. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(^a.a))(^c.(^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. ------ 152634/16531959. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 152635/16531968. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 152636/16532040. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z)(^x1.x1)))) 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. ------ 152637/16532067. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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. ------ 152638/16532121. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(a a))) 8. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(a a))) 9. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 152639/16532202. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 152640/16532265. ------ 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. ------ 152641/16532301. ------ 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)))(a (^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. ------ 152642/16532355. ------ 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. ------ 152643/16532382. ------ 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. ------ 152644/16532409. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((a a) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((a a) a))) 7. ==[ beta ]==> ((^y.y)((^z.b)((a a) a))) 8. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 9. ==[ beta ]==> ((^y.b)((a a) a)) 10. ==[ alpha ]==> ((^x.b)((a a) a)) 11. ==[ beta ]==> b REDUCED to normal form. ------ 152645/16532463. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 152646/16532490. ------ 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. ------ 152647/16532517. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 152648/16532544. ------ 1. ==[ start ]==> ((a (b a))((^a.(^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. ------ 152649/16532904. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(a ((^y.y) b))) 3. ==[ beta ]==> (((a b)(a b))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a b))(a ((^x.x) b))) 5. ==[ beta ]==> (((a b)(a b))(a b)) REDUCED to normal form. ------ 152650/16532913. ------ 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. ------ 152651/16532985. ------ 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. ------ 152652/16532994. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 152653/16533093. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 152654/16533192. ------ 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. ------ 152655/16533219. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(a (^b.b))) 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. ------ 152656/16533246. ------ 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.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.(^x1.x1)))(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. ------ 152657/16533327. ------ 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. ------ 152658/16533849. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 152659/16533957. ------ 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)(^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. ------ 152660/16533984. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^x.x))((^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. ------ 152661/16534110. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(a (^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. ------ 152662/16534164. ------ 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 (^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. ------ 152663/16534191. ------ 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. ------ 152664/16534218. ------ 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. ------ 152665/16534263. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^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. ------ 152666/16534272. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))((a 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. ------ 152667/16534299. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(a b))) 3. ==[ beta ]==> ((a b)((^y.(y y))(a b))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(a b))) 5. ==[ beta ]==> ((a b)((a b)(a b))) REDUCED to normal form. ------ 152668/16534632. ------ 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. ------ 152669/16534659. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(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. ------ 152670/16534713. ------ 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. ------ 152671/16534794. ------ 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))((^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. ------ 152672/16534902. ------ 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)(^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. ------ 152673/16534938. ------ 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. ------ 152674/16534974. ------ 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 a)) REDUCED to normal form. ------ 152675/16535001. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 152676/16535028. ------ 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. ------ 152677/16535055. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.z))((^x1.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. ------ 152678/16535082. ------ 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 x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((a a) a))) 7. ==[ beta ]==> ((a a)((^y.(y y))((a a) a))) 8. ==[ alpha ]==> ((a a)((^x.(x x))((a a) a))) 9. ==[ beta ]==> ((a a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 152679/16535109. ------ 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. ------ 152680/16535136. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 152681/16535163. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^y.y))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^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. ------ 152682/16535244. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 152683/16535271. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 152684/16535298. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^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. ------ 152685/16535469. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 152686/16535577. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^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. ------ 152687/16535694. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 152688/16535721. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.a))) REDUCED to normal form. ------ 152689/16535802. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a (^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (^y.a))) REDUCED to normal form. ------ 152690/16535829. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 152691/16535883. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) a)) REDUCED to normal form. ------ 152692/16535937. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a) a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a) c)) REDUCED to normal form. ------ 152693/16536027. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a a)((a a)(a a))) a) REDUCED to normal form. ------ 152694/16536054. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 152695/16536081. ------ 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)(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(a a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 152696/16536297. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(a (^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a (^z.(a a)))) REDUCED to normal form. ------ 152697/16536324. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(a a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(a a))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 152698/16536378. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 152699/16536657. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 152700/16536693. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b) a)) 3. ==[ beta ]==> ((b c)((^y.b) a)) 4. ==[ alpha ]==> ((b c)((^x.b) a)) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 152701/16536720. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a) b)) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 152702/16536765. ------ 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. ------ 152703/16536792. ------ 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. ------ 152704/16536846. ------ 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 a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)((a a) a))) REDUCED to normal form. ------ 152705/16536936. ------ 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. ------ 152706/16536963. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.b))(a (^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(y y)))) REDUCED to normal form. ------ 152707/16537044. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a) a)) REDUCED to normal form. ------ 152708/16537071. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.a))((^z.z) b)) 6. ==[ alpha ]==> ((b (^x.a))((^y.y) b)) 7. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 152709/16537161. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^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. ------ 152710/16537323. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 152711/16537350. ------ 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. ------ 152712/16537377. ------ 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))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 152713/16537431. ------ 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.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 152714/16537458. ------ 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. ------ 152715/16537485. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.z))) 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. ------ 152716/16537539. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(^a.(^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. ------ 152717/16537629. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a ((^z.z)(^x1.x1)))) 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. ------ 152718/16537710. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b ((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 152719/16537818. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c c)) 3. ==[ beta ]==> ((^y.(^z.z))(c c)) 4. ==[ alpha ]==> ((^x.(^y.y))(c c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152720/16537953. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(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. ------ 152721/16537980. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(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. ------ 152722/16538034. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b b)((a (^y.y))(a (^z.z)))) 8. ==[ alpha ]==> ((b b)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 152723/16538043. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^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. ------ 152724/16538115. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c b)) 3. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 152725/16538124. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 152726/16538151. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a)(^b.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. ------ 152727/16538178. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 152728/16538223. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152729/16538232. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) c)) REDUCED to normal form. ------ 152730/16538259. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.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. ------ 152731/16538286. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^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. ------ 152732/16538340. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 152733/16538358. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b b)) REDUCED to normal form. ------ 152734/16538376. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 152735/16538403. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^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)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 152736/16538430. ------ 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)(^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. ------ 152737/16538457. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 152738/16538484. ------ 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)))) REDUCED to normal form. ------ 152739/16538511. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(a a))) 3. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 152740/16538538. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 152741/16538565. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 152742/16548777. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 152743/16548873. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ eta ]==> ((^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. ------ 152744/16549182. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 152745/16549368. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152746/16549596. ------ 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. ------ 152747/16550259. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 152748/16550439. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) b) c)) 3. ==[ beta ]==> ((((^y.y) b) c) b) 4. ==[ alpha ]==> ((((^x.x) b) c) b) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 152749/16550757. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(b (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 152750/16552464. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b ((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 152751/16552827. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 152752/16552836. ------ 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. ------ 152753/16554219. ------ 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. ------ 152754/16554591. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 152755/16556298. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 152756/16556616. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(y b))) 3. ==[ beta ]==> ((b c)(^y.(y b))) 4. ==[ alpha ]==> ((b c)(^x.(x b))) REDUCED to normal form. ------ 152757/16556958. ------ 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. ------ 152758/16557459. ------ 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. ------ 152759/16557552. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.(^b.(^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. ------ 152760/16557903. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 152761/16558182. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) b)(^y.(y y)))(^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. ------ 152762/16558278. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152763/16558407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^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)) REDUCED to normal form. ------ 152764/16558434. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 152765/16558461. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 152766/16558488. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 152767/16558536. ------ 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)))) 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. ------ 152768/16558563. ------ 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. ------ 152769/16558590. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 152770/16558617. ------ 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))))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 152771/16558644. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 152772/16558671. ------ 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. ------ 152773/16558698. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 152774/16558725. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.(^x1.x1)) 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. ------ 152775/16558743. ------ 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 (^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. ------ 152776/16558788. ------ 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. ------ 152777/16558815. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 152778/16558842. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 5. ==[ beta ]==> ((a a)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 152779/16558851. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((^y.a)((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.y)(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 152780/16558878. ------ 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.(^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. ------ 152781/16558959. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(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. ------ 152782/16559031. ------ 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))(^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. ------ 152783/16559058. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 152784/16559121. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1)))((^y.(^z.z))(b (^x1.x1)))) 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. ------ 152785/16559148. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 152786/16559256. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 152787/16559337. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 152788/16559472. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))(^b.b))) 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. ------ 152789/16559499. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 152790/16559562. ------ 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. ------ 152791/16559589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b (^a.a))(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))) REDUCED to normal form. ------ 152792/16559616. ------ 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))(a (^z.z)))) REDUCED to normal form. ------ 152793/16559643. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b a)) REDUCED to normal form. ------ 152794/16559670. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 152795/16559697. ------ 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. ------ 152796/16559724. ------ 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))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((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. ------ 152797/16560066. ------ 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. ------ 152798/16560147. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(a a))(a b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(a a))(a b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))(a b))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))(a b))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(a b))) 7. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 152799/16560228. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 152800/16560246. ------ 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. ------ 152801/16560273. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^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. ------ 152802/16560354. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z)) a)) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z)) a)) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 152803/16560381. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 152804/16560408. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) b) c)) 2. ==[ alpha ]==> ((a (a b))(((^x.x) b) c)) 3. ==[ beta ]==> ((a (a b))(b c)) REDUCED to normal form. ------ 152805/16560417. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.b)((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.y)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 152806/16560579. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 152807/16560633. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 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. ------ 152808/16560669. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c ((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c ((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c ((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(c b)) REDUCED to normal form. ------ 152809/16560696. ------ 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. ------ 152810/16560723. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(a (b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(a (b (^z.z)))) 6. ==[ alpha ]==> ((^x.a)(a (b (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 152811/16560750. ------ 1. ==[ start ]==> ((((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 a))) REDUCED to normal form. ------ 152812/16560777. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)(a (^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. ------ 152813/16560966. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 152814/16561038. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c (^x1.x1))) 3. ==[ beta ]==> ((^y.y)(c (^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(c (^y.y))) 5. ==[ beta ]==> (c (^y.y)) 6. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 152815/16561173. ------ 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)))((^x2.x2) a))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))((^x2.x2) 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. ------ 152816/16561254. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 152817/16561389. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.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) REDUCED to normal form. ------ 152818/16561461. ------ 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)) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 152819/16561488. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b) b)) 3. ==[ beta ]==> (((a (^x.x))(a b))(b b)) REDUCED to normal form. ------ 152820/16561857. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 152821/16561884. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b a)((^y.y) a))) 3. ==[ beta ]==> (((a a) b)((b a)((^y.y) a))) 4. ==[ alpha ]==> (((a a) b)((b a)((^x.x) a))) 5. ==[ beta ]==> (((a a) b)((b a) a)) REDUCED to normal form. ------ 152822/16561911. ------ 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)))) REDUCED to normal form. ------ 152823/16561965. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)((a a) a))) REDUCED to normal form. ------ 152824/16561992. ------ 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. ------ 152825/16562046. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152826/16562073. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (b a))) REDUCED to normal form. ------ 152827/16562091. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 152828/16562100. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 152829/16562127. ------ 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))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 152830/16562190. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 152831/16562217. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.a))) REDUCED to normal form. ------ 152832/16562244. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 152833/16562271. ------ 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. ------ 152834/16562298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.a))) 7. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 8. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 9. ==[ beta ]==> ((a b)(^y.a)) 10. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 152835/16562325. ------ 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. ------ 152836/16562352. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a b) a)((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (((a b) a)(^y.(a a))) 8. ==[ alpha ]==> (((a b) a)(^x.(a a))) REDUCED to normal form. ------ 152837/16562433. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 152838/16562523. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 152839/16562604. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 152840/16562712. ------ 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. ------ 152841/16562775. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 152842/16562793. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 152843/16562802. ------ 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. ------ 152844/16562856. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 152845/16562883. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 152846/16562910. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.a))((a a)(a (a a)))) REDUCED to normal form. ------ 152847/16562937. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.x1))) REDUCED to normal form. ------ 152848/16563135. ------ 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 (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 152849/16563162. ------ 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. ------ 152850/16563189. ------ 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)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.a))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 152851/16563216. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 152852/16563360. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.a)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 152853/16563441. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.x2))) 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. ------ 152854/16563549. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 152855/16563603. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 152856/16563657. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 152857/16563666. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 152858/16563693. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(b (b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(b (b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(b (b a))) 5. ==[ beta ]==> ((^y.b)(b (b a))) 6. ==[ alpha ]==> ((^x.b)(b (b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 152859/16563747. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(a a))) REDUCED to normal form. ------ 152860/16563774. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 152861/16563801. ------ 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)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a) a)) REDUCED to normal form. ------ 152862/16563855. ------ 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)))(^z.z))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 152863/16564026. ------ 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. ------ 152864/16564053. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 152865/16564080. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (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. ------ 152866/16564107. ------ 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 z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(^y.(y y)))) REDUCED to normal form. ------ 152867/16564188. ------ 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. ------ 152868/16564197. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a b))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(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. ------ 152869/16564224. ------ 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)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.a)((^x2.x2)(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. ------ 152870/16564359. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 152871/16564467. ------ 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 z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 152872/16564503. ------ 1. ==[ start ]==> ((((^a.a) b) a)(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((b a)(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b a)(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((b a)(c (a a))) REDUCED to normal form. ------ 152873/16564521. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 152874/16564530. ------ 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. ------ 152875/16564557. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (b a))) REDUCED to normal form. ------ 152876/16564638. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((a b)((^z.z) a))) 6. ==[ alpha ]==> ((^x.(a a))((a b)((^y.y) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 152877/16564665. ------ 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. ------ 152878/16564692. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 8. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 152879/16564719. ------ 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. ------ 152880/16564746. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a (a b))) REDUCED to normal form. ------ 152881/16564791. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 152882/16564800. ------ 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)(^y1.y1)))) REDUCED to normal form. ------ 152883/16564863. ------ 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) 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. ------ 152884/16564890. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(^x1.a))) REDUCED to normal form. ------ 152885/16564917. ------ 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. ------ 152886/16564944. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^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)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 152887/16564998. ------ 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. ------ 152888/16565025. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 152889/16565079. ------ 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)) a)) REDUCED to normal form. ------ 152890/16565133. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b) c)) REDUCED to normal form. ------ 152891/16565223. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((^y.(y y))(^z.a)) 6. ==[ alpha ]==> ((^x.(x x))(^y.a)) 7. ==[ beta ]==> ((^y.a)(^y.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 152892/16565502. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))(a b))) 3. ==[ beta ]==> ((b b)((a (^y.y))(a b))) 4. ==[ alpha ]==> ((b b)((a (^x.x))(a b))) REDUCED to normal form. ------ 152893/16565529. ------ 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. ------ 152894/16565574. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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 a) REDUCED to normal form. ------ 152895/16565628. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 152896/16565709. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 152897/16565817. ------ 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.(^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. ------ 152898/16565997. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 152899/16566024. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b) b)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b) b)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b) b)) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b) b)) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 152900/16566213. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)(^z.z))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)(^z.z))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 152901/16566240. ------ 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. ------ 152902/16566267. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (b (^x.x)))((^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. ------ 152903/16566357. ------ 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.(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))((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. ------ 152904/16566438. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 152905/16566582. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (a b))) 3. ==[ beta ]==> ((b c)(a (a b))) REDUCED to normal form. ------ 152906/16566609. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)(a a))) REDUCED to normal form. ------ 152907/16566717. ------ 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)(^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. ------ 152908/16566735. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (^x1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (^y1.a))) REDUCED to normal form. ------ 152909/16566744. ------ 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. ------ 152910/16566816. ------ 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 (^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. ------ 152911/16566924. ------ 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. ------ 152912/16567104. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.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)) 5. ==[ beta ]==> ((a b)((^y.a) a)) 6. ==[ alpha ]==> ((a b)((^x.a) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 152913/16567131. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^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. ------ 152914/16567158. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z)) c)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z)) c)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y)) c)) 5. ==[ beta ]==> ((b a)((^y.(y y)) c)) 6. ==[ alpha ]==> ((b a)((^x.(x x)) c)) 7. ==[ beta ]==> ((b a)(c c)) REDUCED to normal form. ------ 152915/16567266. ------ 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))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^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. ------ 152916/16567320. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a (^z.a))) REDUCED to normal form. ------ 152917/16567347. ------ 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 x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.(z z)))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 152918/16567374. ------ 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.(^z.z)))) REDUCED to normal form. ------ 152919/16567428. ------ 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. ------ 152920/16567518. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)(^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. ------ 152921/16567599. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c (^b.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. ------ 152922/16567707. ------ 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. ------ 152923/16567842. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(^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. ------ 152924/16567869. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^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. ------ 152925/16567923. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (^a.(^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. ------ 152926/16567932. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 152927/16567959. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.x1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 152928/16568004. ------ 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) REDUCED to normal form. ------ 152929/16568013. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c b)) REDUCED to normal form. ------ 152930/16568040. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b c)) REDUCED to normal form. ------ 152931/16568112. ------ 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))(^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. ------ 152932/16568121. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (a (^y1.y1)))) REDUCED to normal form. ------ 152933/16568148. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(a ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 152934/16568175. ------ 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))) REDUCED to normal form. ------ 152935/16568247. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 152936/16568265. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 152937/16568292. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 152938/16568319. ------ 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. ------ 152939/16568346. ------ 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)) 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. ------ 152940/16568373. ------ 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)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 152941/16568400. ------ 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. ------ 152942/16568427. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 152943/16568454. ------ 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)(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. ------ 152944/16568480. ------ 1. ==[ start ]==> (^a.(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (^x.(((x x)(^y.y))(x b))) REDUCED to normal form. ------ 152945/16568481. ------ 1. ==[ start ]==> (a (((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (a (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 152946/16578450. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b)) a) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 152947/16578456. ------ 1. ==[ start ]==> ((^a.a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (((a a)(^y.y))(a b)) 4. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 152948/16578483. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((^y.y)(a a)))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(a a)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(a a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 152949/16578510. ------ 1. ==[ start ]==> ((^a.b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((a b)((a a)(^y.y)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 152950/16578591. ------ 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 a))((^z.z) b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.y)) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 152951/16578693. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 152952/16578708. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^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 ]==> (^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. ------ 152953/16579833. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((((^y.y) a)((^z.z) b))(((^y.y) a)((^z.z) b)))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1) b)))(((^y1.y1) a)((^z1.z1) b))) 5. ==[ beta ]==> (((a ((^y.y) b))(((^z.z) a)((^x1.x1) b)))(((^y1.y1) a)((^z1.z1) b))) 6. ==[ alpha ]==> (((a ((^x.x) b))(((^y.y) a)((^z.z) b)))(((^x1.x1) a)((^y1.y1) b))) 7. ==[ beta ]==> (((a b)(((^y.y) a)((^z.z) b)))(((^x1.x1) a)((^y1.y1) b))) 8. ==[ alpha ]==> (((a b)(((^x.x) a)((^y.y) b)))(((^z.z) a)((^x1.x1) b))) 9. ==[ beta ]==> (((a b)(a ((^y.y) b)))(((^z.z) a)((^x1.x1) b))) 10. ==[ alpha ]==> (((a b)(a ((^x.x) b)))(((^y.y) a)((^z.z) b))) 11. ==[ beta ]==> (((a b)(a b))(((^y.y) a)((^z.z) b))) 12. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)((^y.y) b))) 13. ==[ beta ]==> (((a b)(a b))(a ((^y.y) b))) 14. ==[ alpha ]==> (((a b)(a b))(a ((^x.x) b))) 15. ==[ beta ]==> (((a b)(a b))(a b)) REDUCED to normal form. ------ 152954/16580733. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z) c)) 3. ==[ beta ]==> (^y.(((^z.z) c)((^z.z) c))) 4. ==[ alpha ]==> (^x.(((^y.y) c)((^z.z) c))) 5. ==[ beta ]==> (^x.(c ((^z.z) c))) 6. ==[ alpha ]==> (^x.(c ((^y.y) c))) 7. ==[ beta ]==> (^x.(c c)) REDUCED to normal form. ------ 152955/16580940. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (a a))(b a))) 3. ==[ beta ]==> ((^y.y)(((a (a a))(b a))((a (a a))(b a)))) 4. ==[ alpha ]==> ((^x.x)(((a (a a))(b a))((a (a a))(b a)))) 5. ==[ beta ]==> (((a (a a))(b a))((a (a a))(b a))) REDUCED to normal form. ------ 152956/16582743. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 152957/16583940. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(b a))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(b a))) 5. ==[ beta ]==> ((a b)(^y.(b a))) 6. ==[ alpha ]==> ((a b)(^x.(b a))) REDUCED to normal form. ------ 152958/16585713. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(a a))) REDUCED to normal form. ------ 152959/16585938. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> (((a (a a))(b a))(^x.(x x))) REDUCED to normal form. ------ 152960/16586523. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(^a.b))) 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. ------ 152961/16586874. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((a a) a))) REDUCED to normal form. ------ 152962/16587045. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((z z) z))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((z z) z))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((y y) y))) 5. ==[ beta ]==> ((a b)(^y.((y y) y))) 6. ==[ alpha ]==> ((a b)(^x.((x x) x))) REDUCED to normal form. ------ 152963/16587180. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 152964/16587810. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.d)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.d)) 3. ==[ beta ]==> ((^y.y)(^x1.d)) 4. ==[ alpha ]==> ((^x.x)(^y.d)) 5. ==[ beta ]==> (^y.d) 6. ==[ alpha ]==> (^x.d) REDUCED to normal form. ------ 152965/16588008. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 152966/16588089. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^b.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. ------ 152967/16588170. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.(^b.a))) 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. ------ 152968/16588185. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 152969/16588233. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.c)) REDUCED to normal form. ------ 152970/16588287. ------ 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)))) REDUCED to normal form. ------ 152971/16588368. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 152972/16588395. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 152973/16588422. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 152974/16588434. ------ 1. ==[ start ]==> ((a a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 152975/16588461. ------ 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)))) 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. ------ 152976/16588488. ------ 1. ==[ start ]==> ((a b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 152977/16588542. ------ 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. ------ 152978/16588569. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (a (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 152979/16588668. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 152980/16588686. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(^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. ------ 152981/16588767. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 152982/16588794. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 152983/16588803. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 152984/16588848. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (a (((a a)(^y.y))(^z.b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 152985/16588857. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 152986/16588875. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(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. ------ 152987/16588884. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 152988/16588911. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 152989/16589019. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.a)((a a)(a a)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 152990/16589118. ------ 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)(^y.y))((b (^z.z)) 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) REDUCED to normal form. ------ 152991/16589181. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(z z))) REDUCED to normal form. ------ 152992/16589208. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 152993/16589343. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 152994/16589676. ------ 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))(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. ------ 152995/16589703. ------ 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. ------ 152996/16589730. ------ 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. ------ 152997/16589757. ------ 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. ------ 152998/16589784. ------ 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. ------ 152999/16589811. ------ 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))) 5. ==[ beta ]==> ((a ((a a) a))(a b)) REDUCED to normal form. ------ 153000/16589901. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b (^z.z))(^x1.x1))) 5. ==[ beta ]==> (a ((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> (a ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 153001/16589937. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(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 a)) REDUCED to normal form. ------ 153002/16589964. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.x)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x) a)) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 153003/16589982. ------ 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. ------ 153004/16590009. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 153005/16590063. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.b))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.b))) 9. ==[ beta ]==> ((a a)((a a)(^y.b))) 10. ==[ alpha ]==> ((a a)((a a)(^x.b))) REDUCED to normal form. ------ 153006/16590072. ------ 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. ------ 153007/16590099. ------ 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)((^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. ------ 153008/16590315. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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 a)) REDUCED to normal form. ------ 153009/16590333. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b) c)) 3. ==[ beta ]==> ((^y.b)(((^z.z) b) c)) 4. ==[ alpha ]==> ((^x.b)(((^y.y) b) c)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 153010/16590477. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.b)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 153011/16590504. ------ 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. ------ 153012/16590585. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 153013/16590684. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a)) b)) 3. ==[ beta ]==> (b ((^y.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 153014/16590711. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) c)) 3. ==[ beta ]==> ((a (^x.(a a))) c) REDUCED to normal form. ------ 153015/16590729. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a b))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 153016/16590756. ------ 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. ------ 153017/16590783. ------ 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)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(((a a)(^y.y))(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 153018/16590810. ------ 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. ------ 153019/16590837. ------ 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. ------ 153020/16590864. ------ 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. ------ 153021/16590891. ------ 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)(^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. ------ 153022/16590918. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))(b a))) 3. ==[ beta ]==> ((a (a a))((a (a a))(b a))) REDUCED to normal form. ------ 153023/16591089. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 153024/16591098. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 153025/16591143. ------ 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)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))(^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)))) REDUCED to normal form. ------ 153026/16591152. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 153027/16591170. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 153028/16591179. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 153029/16591224. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a) a)(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(a a)))) 9. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(a a)))) 10. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(a a)))) 11. ==[ beta ]==> (((a a) a)(^y.(a a))) 12. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 153030/16591233. ------ 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. ------ 153031/16591260. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))((^y.(^z.z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153032/16591287. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((b a)(b a))) REDUCED to normal form. ------ 153033/16591305. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 153034/16591314. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.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) REDUCED to normal form. ------ 153035/16591341. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^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. ------ 153036/16591530. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 153037/16591764. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z) b)) 3. ==[ beta ]==> (b ((^z.z) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 153038/16592016. ------ 1. ==[ start ]==> (((a b)(^b.a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153039/16592043. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 153040/16592439. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1))) b)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 153041/16592583. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 153042/16592691. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 153043/16592718. ------ 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. ------ 153044/16592916. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(^y.y))(a b))) 3. ==[ beta ]==> (((a a)(b a))((^y.y)(a b))) 4. ==[ alpha ]==> (((a a)(b a))((^x.x)(a b))) 5. ==[ beta ]==> (((a a)(b a))(a b)) REDUCED to normal form. ------ 153045/16592943. ------ 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 a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 153046/16592970. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 153047/16592997. ------ 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. ------ 153048/16593024. ------ 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. ------ 153049/16593177. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153050/16593276. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 153051/16593357. ------ 1. ==[ start ]==> (((^a.b)(^b.(^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)) REDUCED to normal form. ------ 153052/16593474. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 153053/16593582. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.a)(^c.(^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. ------ 153054/16593654. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)((^y.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 (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 153055/16593807. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)((a a) a))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 153056/16593834. ------ 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. ------ 153057/16593861. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 153058/16593888. ------ 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 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)))) REDUCED to normal form. ------ 153059/16593915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a a)(b a))) 3. ==[ beta ]==> (((^y.y)(a b))((a a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))((a a)(b a))) 5. ==[ beta ]==> ((a b)((a a)(b a))) REDUCED to normal form. ------ 153060/16594068. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^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. ------ 153061/16594113. ------ 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. ------ 153062/16594140. ------ 1. ==[ start ]==> (((^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)(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1) a)(^x2.(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. ------ 153063/16594275. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 153064/16594392. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.b)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 153065/16594419. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.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. ------ 153066/16594446. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 153067/16594716. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) REDUCED to normal form. ------ 153068/16595274. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 153069/16595418. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c (^y.b))) 3. ==[ beta ]==> ((b b)(c (^y.b))) 4. ==[ alpha ]==> ((b b)(c (^x.b))) REDUCED to normal form. ------ 153070/16595445. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(b (^x.(a a)))) REDUCED to normal form. ------ 153071/16595490. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^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. ------ 153072/16595499. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^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 a)) REDUCED to normal form. ------ 153073/16595526. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b)(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 153074/16595544. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a) a)(^y.a))) 3. ==[ beta ]==> (((b a)(b a))(((a a) a)(^y.a))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 153075/16595607. ------ 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))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 10. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 153076/16595625. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^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. ------ 153077/16595634. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 153078/16595688. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 153079/16595733. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) 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. ------ 153080/16595742. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 153081/16595769. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.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. ------ 153082/16595796. ------ 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))(^x1.(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. ------ 153083/16595859. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c ((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(c ((a a) a))) REDUCED to normal form. ------ 153084/16595886. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^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. ------ 153085/16595913. ------ 1. ==[ start ]==> (((a (a a))(b a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(a ((^x.x)(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))(a (a a))) REDUCED to normal form. ------ 153086/16595940. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b)(a a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)(a a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 153087/16595967. ------ 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. ------ 153088/16595994. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)((^y.y) a))) 5. ==[ beta ]==> (((a b)(a b))((^y.y) a)) 6. ==[ alpha ]==> (((a b)(a b))((^x.x) a)) 7. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 153089/16596021. ------ 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. ------ 153090/16596048. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a ((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.x1))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 153091/16596102. ------ 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))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a b))) REDUCED to normal form. ------ 153092/16596354. ------ 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) b)) REDUCED to normal form. ------ 153093/16596498. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(^z.b))) 3. ==[ beta ]==> ((b c)((^y.y)(^z.b))) 4. ==[ alpha ]==> ((b c)((^x.x)(^y.b))) 5. ==[ beta ]==> ((b c)(^y.b)) 6. ==[ alpha ]==> ((b c)(^x.b)) REDUCED to normal form. ------ 153094/16596570. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^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. ------ 153095/16596633. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 153096/16596660. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (^x1.a))) REDUCED to normal form. ------ 153097/16596732. ------ 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.(^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. ------ 153098/16596741. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 153099/16596768. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.b))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.b))(a ((^z.z) a))) 8. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y) a))) 9. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 153100/16596849. ------ 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. ------ 153101/16596876. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 153102/16596903. ------ 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.(^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. ------ 153103/16596966. ------ 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. ------ 153104/16596993. ------ 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)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (^y.y))) REDUCED to normal form. ------ 153105/16597020. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a ((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(a ((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a ((a a) a))) 5. ==[ beta ]==> ((a b)(a ((a a) a))) REDUCED to normal form. ------ 153106/16597047. ------ 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. ------ 153107/16597074. ------ 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. ------ 153108/16597101. ------ 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.z) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 153109/16597128. ------ 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. ------ 153110/16597155. ------ 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)(^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. ------ 153111/16597263. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c d)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c d)) 3. ==[ beta ]==> ((b ((^y.y) a))(c d)) 4. ==[ alpha ]==> ((b ((^x.x) a))(c d)) 5. ==[ beta ]==> ((b a)(c d)) REDUCED to normal form. ------ 153112/16597515. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.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. ------ 153113/16597623. ------ 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)(^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. ------ 153114/16597740. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(^a.(^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. ------ 153115/16597839. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.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. ------ 153116/16597848. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 153117/16597875. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b (^b.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. ------ 153118/16597920. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 153119/16597929. ------ 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) REDUCED to normal form. ------ 153120/16597956. ------ 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)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 153121/16597983. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 153122/16598028. ------ 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 (^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. ------ 153123/16598037. ------ 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))(^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. ------ 153124/16598064. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^b.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. ------ 153125/16598091. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.y))) REDUCED to normal form. ------ 153126/16598145. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 153127/16598163. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 153128/16598181. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b b)) 3. ==[ beta ]==> (((a a)(^y.y))(b b)) 4. ==[ alpha ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 153129/16598208. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a c)) REDUCED to normal form. ------ 153130/16598235. ------ 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. ------ 153131/16598262. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(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. ------ 153132/16598289. ------ 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. ------ 153133/16598316. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b a)) REDUCED to normal form. ------ 153134/16598343. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 153135/16598370. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 153136/16598397. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 153137/16608375. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b)) b) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b)) b) REDUCED to normal form. ------ 153138/16608399. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153139/16608480. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153140/16608984. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> (((^x.a)((a a)(a a)))(((^y.a)((a a)(a a)))((^z.a)((a a)(a a))))) 5. ==[ beta ]==> (a (((^y.a)((a a)(a a)))((^z.a)((a a)(a a))))) 6. ==[ alpha ]==> (a (((^x.a)((a a)(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)) REDUCED to normal form. ------ 153141/16609335. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153142/16610229. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(^b.(b (^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)))) REDUCED to normal form. ------ 153143/16610280. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z))) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 153144/16610667. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (^y.((((^z.z) b)(a (^x1.x1)))(((^z.z) b)(a (^x1.x1))))) 4. ==[ alpha ]==> (^x.((((^y.y) b)(a (^z.z)))(((^x1.x1) b)(a (^y1.y1))))) 5. ==[ beta ]==> (^x.((b (a (^z.z)))(((^x1.x1) b)(a (^y1.y1))))) 6. ==[ alpha ]==> (^x.((b (a (^y.y)))(((^z.z) b)(a (^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. ------ 153145/16610967. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)(^y1.((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))) REDUCED to normal form. ------ 153146/16611336. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))(^y.((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 153147/16612305. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(b a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(b a))) 3. ==[ eta ]==> (b ((^y.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 153148/16612854. ------ 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. ------ 153149/16613010. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.(^b.b))) 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))) REDUCED to normal form. ------ 153150/16613142. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^x1.b)((^y1.y1)(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (b (^x1.(^y1.y1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 153151/16613613. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 153152/16613745. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153153/16613901. ------ 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. ------ 153154/16614060. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(^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. ------ 153155/16614954. ------ 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)))) REDUCED to normal form. ------ 153156/16615647. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 153157/16615872. ------ 1. ==[ start ]==> (((a (a a))(b a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 153158/16616088. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 153159/16616139. ------ 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. ------ 153160/16616979. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.a))) 5. ==[ beta ]==> ((a b)(^y.(^z.a))) 6. ==[ alpha ]==> ((a b)(^x.(^y.a))) REDUCED to normal form. ------ 153161/16617300. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ eta ]==> ((^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. ------ 153162/16617942. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.a))) REDUCED to normal form. ------ 153163/16618023. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.z)) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.z)) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 153164/16618104. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 153165/16618167. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 153166/16618221. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 153167/16618275. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 153168/16618302. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 153169/16618329. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 153170/16618356. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 153171/16618386. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 153172/16618413. ------ 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)(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. ------ 153173/16618440. ------ 1. ==[ start ]==> (((^a.a)(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a b)((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. ------ 153174/16618467. ------ 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. ------ 153175/16618521. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153176/16618548. ------ 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)(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. ------ 153177/16618575. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 153178/16618602. ------ 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 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. ------ 153179/16618665. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 153180/16618746. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153181/16618773. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b a)(^y.a))) 3. ==[ beta ]==> ((a a)((b a)(^y.a))) 4. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 153182/16618800. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 153183/16618827. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 153184/16618854. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a b)(^c.(^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. ------ 153185/16618917. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(^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)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 153186/16618944. ------ 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. ------ 153187/16618971. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 153188/16619043. ------ 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. ------ 153189/16619070. ------ 1. ==[ start ]==> (((a (a a)) a)((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a)) a)((b (^x.x)) b)) REDUCED to normal form. ------ 153190/16619241. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 153191/16619268. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 153192/16619322. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 153193/16619412. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 153194/16619466. ------ 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)) REDUCED to normal form. ------ 153195/16619493. ------ 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. ------ 153196/16619547. ------ 1. ==[ start ]==> (((^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)))(a (a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 153197/16619790. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))((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. ------ 153198/16619880. ------ 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.(^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. ------ 153199/16619907. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)(^y.a))) 3. ==[ beta ]==> ((((a a) a) a)(b (^y.a))) 4. ==[ alpha ]==> ((((a a) a) a)(b (^x.a))) REDUCED to normal form. ------ 153200/16619961. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153201/16620015. ------ 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. ------ 153202/16620042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 153203/16620105. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(^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. ------ 153204/16620132. ------ 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 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 153205/16620159. ------ 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. ------ 153206/16620186. ------ 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. ------ 153207/16620213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(b (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(b (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 153208/16620258. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 153209/16620267. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 153210/16620627. ------ 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 a))) REDUCED to normal form. ------ 153211/16620636. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 153212/16620654. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(a (^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. ------ 153213/16620870. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(b a))) 3. ==[ beta ]==> ((^y.(a a))((a (a a))(b a))) 4. ==[ alpha ]==> ((^x.(a a))((a (a a))(b a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 153214/16620897. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 153215/16620951. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((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. ------ 153216/16621041. ------ 1. ==[ start ]==> (((a b) b)((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b) b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 153217/16621068. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b a)(^y.(y y)))) 3. ==[ beta ]==> (((a a) a)((b a)(^y.(y y)))) 4. ==[ alpha ]==> (((a a) a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 153218/16621095. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 153219/16621122. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(^z.a))) REDUCED to normal form. ------ 153220/16621176. ------ 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. ------ 153221/16621257. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 153222/16621284. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.a))(^b.b))) 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))) REDUCED to normal form. ------ 153223/16621320. ------ 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)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 153224/16621347. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 153225/16621374. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b)(^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)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 153226/16621401. ------ 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. ------ 153227/16621482. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 153228/16621509. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 153229/16621707. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (b (((^z.z) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 153230/16621716. ------ 1. ==[ start ]==> (((a b) c)((^b.b) b)) 2. ==[ alpha ]==> (((a b) c)((^x.x) b)) 3. ==[ beta ]==> (((a b) c) b) REDUCED to normal form. ------ 153231/16621743. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 153232/16621788. ------ 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. ------ 153233/16621815. ------ 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)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 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. ------ 153234/16621869. ------ 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. ------ 153235/16621950. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(b a))) 3. ==[ beta ]==> (b (((^z.z) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 153236/16622049. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b)(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. ------ 153237/16622076. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(a (^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. ------ 153238/16622157. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 153239/16622184. ------ 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. ------ 153240/16622211. ------ 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) REDUCED to normal form. ------ 153241/16622238. ------ 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. ------ 153242/16622265. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 153243/16622292. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(b a))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(b a))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 153244/16622652. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)(a b))(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b)(a b))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 153245/16622715. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 153246/16622733. ------ 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. ------ 153247/16622769. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z)) d)) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 153248/16622841. ------ 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. ------ 153249/16622940. ------ 1. ==[ start ]==> (((a (a a))(a b))(c (^d.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(c (^x.a))) REDUCED to normal form. ------ 153250/16622967. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(b (^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. ------ 153251/16622994. ------ 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)(^y.y))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 153252/16623021. ------ 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. ------ 153253/16623120. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 153254/16623129. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 153255/16623597. ------ 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 (a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 153256/16623606. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) 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. ------ 153257/16623660. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 153258/16623705. ------ 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. ------ 153259/16623732. ------ 1. ==[ start ]==> ((a (^b.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 153260/16623885. ------ 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. ------ 153261/16623966. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 153262/16624011. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a) a)(^b.(^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. ------ 153263/16624047. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(^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. ------ 153264/16624380. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(c ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(c ((^y.y)(a a)))) 5. ==[ beta ]==> (b (c ((^y.y)(a a)))) 6. ==[ alpha ]==> (b (c ((^x.x)(a a)))) 7. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 153265/16624407. ------ 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. ------ 153266/16624461. ------ 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.z))(a a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 153267/16624497. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a)) c)) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a)) c)) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a)) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 153268/16624542. ------ 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. ------ 153269/16624650. ------ 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 (^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. ------ 153270/16624722. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 153271/16624749. ------ 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 a)) REDUCED to normal form. ------ 153272/16624776. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((a (b a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> ((a (b a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 153273/16624830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 153274/16624857. ------ 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. ------ 153275/16624884. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)(a b))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 153276/16624911. ------ 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.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 153277/16624938. ------ 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. ------ 153278/16624992. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 153279/16625019. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(^z.a))) 3. ==[ beta ]==> ((b (a a))((^y.b)(^z.a))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(^y.a))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 153280/16625217. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 153281/16625325. ------ 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. ------ 153282/16625406. ------ 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.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. ------ 153283/16625442. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^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. ------ 153284/16625469. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153285/16625550. ------ 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. ------ 153286/16625577. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b))(a (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.b))(a (^y.a))) REDUCED to normal form. ------ 153287/16625631. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 153288/16625685. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b) b)) REDUCED to normal form. ------ 153289/16625712. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a) a) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a) c)) REDUCED to normal form. ------ 153290/16625775. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))(^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. ------ 153291/16625802. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 153292/16625829. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(^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. ------ 153293/16625856. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^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. ------ 153294/16626045. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b (^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.b))) REDUCED to normal form. ------ 153295/16626072. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(a (^z.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 153296/16626099. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 153297/16626126. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 153298/16626468. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b) a)) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 153299/16626513. ------ 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 (^x.x))((^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. ------ 153300/16626540. ------ 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. ------ 153301/16626594. ------ 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)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^x2.x2))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) REDUCED to normal form. ------ 153302/16626684. ------ 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.(^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. ------ 153303/16626711. ------ 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. ------ 153304/16626819. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.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)) REDUCED to normal form. ------ 153305/16626846. ------ 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)(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 153306/16626909. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.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. ------ 153307/16626936. ------ 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)))) 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. ------ 153308/16626963. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(^c.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))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 7. ==[ beta ]==> ((a b)(^y.a)) 8. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 153309/16627071. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (^y.(y y)))) 3. ==[ beta ]==> (((a b)(a a))(c (^y.(y y)))) 4. ==[ alpha ]==> (((a b)(a a))(c (^x.(x x)))) REDUCED to normal form. ------ 153310/16627098. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 153311/16627179. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 153312/16627206. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.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. ------ 153313/16627233. ------ 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. ------ 153314/16627287. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 153315/16627377. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (a (a a)))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 153316/16627458. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)(a (^y1.y1)))) 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. ------ 153317/16627683. ------ 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. ------ 153318/16627728. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(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)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 153319/16627782. ------ 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. ------ 153320/16627791. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a) b)) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 153321/16627872. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(^a.a))) 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. ------ 153322/16627899. ------ 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))(^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. ------ 153323/16627926. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.a))) REDUCED to normal form. ------ 153324/16627980. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1)) b)) REDUCED to normal form. ------ 153325/16628007. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((a a) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a) c)) REDUCED to normal form. ------ 153326/16628034. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 153327/16628124. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^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. ------ 153328/16628151. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 153329/16628178. ------ 1. ==[ start ]==> ((((^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))) 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. ------ 153330/16628205. ------ 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)))) 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. ------ 153331/16628232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 153332/16628259. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 153333/16628286. ------ 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. ------ 153334/16628313. ------ 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)(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. ------ 153335/16628340. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 153336/16628613. ------ 1. ==[ start ]==> ((^a.(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 153337/16638090. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.(^b.a))) 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. ------ 153338/16638327. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b)) c) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b)) c) REDUCED to normal form. ------ 153339/16638603. ------ 1. ==[ start ]==> ((^a.(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (^x.(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 153340/16638606. ------ 1. ==[ start ]==> ((a (^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 153341/16638675. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(a a))(^z.a))) 3. ==[ eta ]==> ((^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. ------ 153342/16638846. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 153343/16639425. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x)(^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. ------ 153344/16640061. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 153345/16640241. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 153346/16640586. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 153347/16643103. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x1.(^y1.y1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 153348/16643277. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^b.(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))))) REDUCED to normal form. ------ 153349/16643574. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153350/16643583. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 153351/16644021. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 153352/16644663. ------ 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. ------ 153353/16645410. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 153354/16646100. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 153355/16646418. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((a a) a))) 3. ==[ beta ]==> ((b c)(^y.((a a) a))) 4. ==[ alpha ]==> ((b c)(^x.((a a) a))) REDUCED to normal form. ------ 153356/16646445. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(x b))) REDUCED to normal form. ------ 153357/16647261. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1)) a)) 3. ==[ eta ]==> ((^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. ------ 153358/16647840. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 153359/16648011. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z) y))) 3. ==[ eta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 153360/16648080. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (^x1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 153361/16648083. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.z))) REDUCED to normal form. ------ 153362/16648128. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153363/16648182. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.b)) 3. ==[ beta ]==> (((a (a a)) b)(^y.b)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.b)) REDUCED to normal form. ------ 153364/16648236. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.b)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 153365/16648263. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 153366/16648317. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 153367/16648365. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (a (((a a)(^y.y))(a b))) 4. ==[ alpha ]==> (a (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 153368/16648392. ------ 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)))) 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. ------ 153369/16648419. ------ 1. ==[ start ]==> (((a a)(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 153370/16648446. ------ 1. ==[ start ]==> (((^a.a) b)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x) b)(((a a) a)(b a))) 3. ==[ beta ]==> (b (((a a) a)(b a))) REDUCED to normal form. ------ 153371/16648473. ------ 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.(^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. ------ 153372/16648500. ------ 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. ------ 153373/16648527. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 153374/16648554. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 153375/16648581. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.(^x1.x1)) 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. ------ 153376/16648599. ------ 1. ==[ start ]==> ((a (^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 153377/16648617. ------ 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. ------ 153378/16648644. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 153379/16648671. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^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. ------ 153380/16648680. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 153381/16648707. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 153382/16648842. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 153383/16648887. ------ 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)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153384/16648914. ------ 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. ------ 153385/16648950. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.a)((a a)(a a)))((^y.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. ------ 153386/16648977. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 153387/16649139. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 153388/16649301. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 153389/16649328. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a a))(^b.b))) 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)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153390/16649391. ------ 1. ==[ start ]==> (((a (a a)) b)(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(b (b (^x.x)))) REDUCED to normal form. ------ 153391/16649418. ------ 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 ]==> (((^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. ------ 153392/16649445. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 153393/16649472. ------ 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))(a (^z.z)))) REDUCED to normal form. ------ 153394/16649499. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.a))(b ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.a))(b ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.a))(b a)) REDUCED to normal form. ------ 153395/16649526. ------ 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. ------ 153396/16649553. ------ 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))) 9. ==[ beta ]==> ((b a)(^y.y)) 10. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 153397/16649760. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(c (^y1.(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. ------ 153398/16649895. ------ 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. ------ 153399/16649922. ------ 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.(^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. ------ 153400/16650057. ------ 1. ==[ start ]==> ((a (^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 153401/16650102. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 153402/16650129. ------ 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. ------ 153403/16650210. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 153404/16650237. ------ 1. ==[ start ]==> ((a (a b))(((a a)(a a)) b)) REDUCED to normal form. ------ 153405/16650246. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 153406/16650408. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^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. ------ 153407/16650435. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 153408/16650516. ------ 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. ------ 153409/16650552. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(b ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(b ((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)(b ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.a)(b ((a a)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 153410/16650579. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 153411/16650606. ------ 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. ------ 153412/16650642. ------ 1. ==[ start ]==> (((a a)(a b))((^b.b) c)) 2. ==[ alpha ]==> (((a a)(a b))((^x.x) c)) 3. ==[ beta ]==> (((a a)(a b)) c) REDUCED to normal form. ------ 153413/16650795. ------ 1. ==[ start ]==> (((^a.b) b)(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(((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. ------ 153414/16650921. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.(a a)))) 5. ==[ beta ]==> ((^y.y)(b (^y1.(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. ------ 153415/16651002. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 153416/16651083. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 153417/16651137. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.b)(a b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(a b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(a b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(a b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(a b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a b))) 9. ==[ beta ]==> ((^y.y)((^z.b)(a b))) 10. ==[ alpha ]==> ((^x.x)((^y.b)(a b))) 11. ==[ beta ]==> ((^y.b)(a b)) 12. ==[ alpha ]==> ((^x.b)(a b)) 13. ==[ beta ]==> b REDUCED to normal form. ------ 153418/16651218. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 153419/16651317. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a)) a)) REDUCED to normal form. ------ 153420/16651344. ------ 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)) 5. ==[ beta ]==> ((a ((a a) a))(b b)) REDUCED to normal form. ------ 153421/16651542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 153422/16651686. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a b) c)(b (a a))) REDUCED to normal form. ------ 153423/16651713. ------ 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)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 153424/16651740. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a) a)) REDUCED to normal form. ------ 153425/16651794. ------ 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)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)((^z.z)(^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. ------ 153426/16651821. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)((a a) a))) 3. ==[ beta ]==> ((a (^y.b))((a b)((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))((a b)((a a) a))) REDUCED to normal form. ------ 153427/16651875. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153428/16651902. ------ 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. ------ 153429/16651929. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a b)(^x.a))(a (b a))) REDUCED to normal form. ------ 153430/16651956. ------ 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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 153431/16651983. ------ 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))(^y.y))((a a) b)) REDUCED to normal form. ------ 153432/16652019. ------ 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. ------ 153433/16652046. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153434/16652073. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a)(^y.a))) 3. ==[ beta ]==> ((a (a b))((b a)(^y.a))) 4. ==[ alpha ]==> ((a (a b))((b a)(^x.a))) REDUCED to normal form. ------ 153435/16652100. ------ 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. ------ 153436/16652127. ------ 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)))(((^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. ------ 153437/16652154. ------ 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. ------ 153438/16652181. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a) a)(^y.b))) 3. ==[ beta ]==> (((a b) a)(((a a) a)(^y.b))) 4. ==[ alpha ]==> (((a b) a)(((a a) a)(^x.b))) REDUCED to normal form. ------ 153439/16652208. ------ 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. ------ 153440/16652352. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (b ((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 153441/16652433. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 153442/16652541. ------ 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. ------ 153443/16652604. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (b a))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (b a))) REDUCED to normal form. ------ 153444/16652622. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 153445/16652631. ------ 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. ------ 153446/16652685. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 153447/16652712. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 153448/16652739. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 153449/16652766. ------ 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))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a (a a)))) REDUCED to normal form. ------ 153450/16652991. ------ 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. ------ 153451/16653018. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 153452/16653045. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 153453/16653099. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 153454/16653108. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153455/16653189. ------ 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 z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a a)((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))((^y.y)(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. ------ 153456/16653270. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.a)(a (^a.(^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. ------ 153457/16653378. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 153458/16653405. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.b)(^b.(^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. ------ 153459/16653432. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 153460/16653486. ------ 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.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(a a)))) 9. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^y.(a a)))) 10. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(a a)))) 11. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 153461/16653522. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(c ((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.b)(c ((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.b)(c ((a a)(^y.y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 153462/16653567. ------ 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 ((^x1.x1)(^y1.(^z1.(^x2.x2))))) 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. ------ 153463/16653576. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 153464/16653603. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((b a)(a a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)(a a))) REDUCED to normal form. ------ 153465/16653630. ------ 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. ------ 153466/16653684. ------ 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. ------ 153467/16653882. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 153468/16653909. ------ 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.(^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. ------ 153469/16653936. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(^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. ------ 153470/16653990. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 153471/16654017. ------ 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 b)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 7. ==[ beta ]==> ((a b)(^y.a)) 8. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 153472/16654026. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(^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. ------ 153473/16654053. ------ 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 z1))(a b))) 3. ==[ beta ]==> ((^y.y)((^z1.(z1 z1))(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. ------ 153474/16654188. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 153475/16654296. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(^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. ------ 153476/16654350. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 153477/16654359. ------ 1. ==[ start ]==> (((a a)(^b.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(c (a a))) REDUCED to normal form. ------ 153478/16654386. ------ 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. ------ 153479/16654467. ------ 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. ------ 153480/16654494. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a b) a)) REDUCED to normal form. ------ 153481/16654521. ------ 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. ------ 153482/16654548. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 153483/16654575. ------ 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. ------ 153484/16654629. ------ 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 (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(a a))) REDUCED to normal form. ------ 153485/16654656. ------ 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. ------ 153486/16654692. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 153487/16654719. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153488/16654746. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(^y.a))) 3. ==[ beta ]==> ((a (b a))((a b)(^y.a))) 4. ==[ alpha ]==> ((a (b a))((a b)(^x.a))) REDUCED to normal form. ------ 153489/16654773. ------ 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. ------ 153490/16654800. ------ 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)(a a)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 11. ==[ beta ]==> ((a a)(^y.(^z.z))) 12. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 153491/16654827. ------ 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. ------ 153492/16654854. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> (((a b)((a a) a))(a (^y.b))) 4. ==[ alpha ]==> (((a b)((a a) a))(a (^x.b))) REDUCED to normal form. ------ 153493/16654881. ------ 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 (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 153494/16654962. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a) b)) REDUCED to normal form. ------ 153495/16654989. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b) c)) 3. ==[ beta ]==> ((b (a a))((a b) c)) REDUCED to normal form. ------ 153496/16655052. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))(^b.(^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 ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153497/16655331. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((b b)(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)((a a) a))) 5. ==[ beta ]==> ((b b)(a ((a a) a))) REDUCED to normal form. ------ 153498/16655358. ------ 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. ------ 153499/16655376. ------ 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. ------ 153500/16655403. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 153501/16655457. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((b a)(b a))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 153502/16655538. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z)(^x1.x1)))) 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. ------ 153503/16655646. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 153504/16655853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a)) a)) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a)) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a)) a)) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 153505/16655880. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.b) b)) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b) b)) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b) b)) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 153506/16655907. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a) c)) 2. ==[ alpha ]==> (((a b)(a b))((^x.a) c)) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 153507/16656069. ------ 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. ------ 153508/16656096. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 153509/16656186. ------ 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)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)((^y2.y2)(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)((^y2.y2)(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153510/16656267. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 153511/16656375. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 153512/16656411. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b ((a a) a))) 3. ==[ beta ]==> ((b c)(b ((a a) a))) REDUCED to normal form. ------ 153513/16656438. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a (a b))) REDUCED to normal form. ------ 153514/16656546. ------ 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. ------ 153515/16656573. ------ 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)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^z1.z1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 153516/16656645. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 153517/16656753. ------ 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)(^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. ------ 153518/16656987. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^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)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 153519/16657149. ------ 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. ------ 153520/16657176. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)(^b.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. ------ 153521/16657203. ------ 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))(^z.(z z)))) REDUCED to normal form. ------ 153522/16657257. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((a ((^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. ------ 153523/16657347. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^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. ------ 153524/16657428. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (^a.(^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. ------ 153525/16657536. ------ 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 z1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153526/16657671. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(^a.(^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. ------ 153527/16657698. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^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. ------ 153528/16657761. ------ 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. ------ 153529/16657788. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153530/16657833. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (^z.(z z)))) 3. ==[ beta ]==> (b (a (^z.(z z)))) 4. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 153531/16657842. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d a)) REDUCED to normal form. ------ 153532/16657869. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c b)) REDUCED to normal form. ------ 153533/16657896. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b c)) REDUCED to normal form. ------ 153534/16657941. ------ 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)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153535/16657950. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (a a))) REDUCED to normal form. ------ 153536/16657977. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (a (^y.y)))) REDUCED to normal form. ------ 153537/16658004. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 153538/16658058. ------ 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. ------ 153539/16658076. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.a))) REDUCED to normal form. ------ 153540/16658094. ------ 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))) 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. ------ 153541/16658121. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 153542/16658148. ------ 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)) 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. ------ 153543/16658175. ------ 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. ------ 153544/16658202. ------ 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 (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 153545/16658229. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) b)) 3. ==[ beta ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 153546/16658256. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 153547/16658283. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 153548/16658310. ------ 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. ------ 153549/16658336. ------ 1. ==[ start ]==> (^a.((b a)((a a) a))) 2. ==[ alpha ]==> (^x.((b x)((x x) x))) REDUCED to normal form. ------ 153550/16658337. ------ 1. ==[ start ]==> (a ((b a)((a a) a))) REDUCED to normal form. ------ 153551/16668069. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.c)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.c)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 153552/16668339. ------ 1. ==[ start ]==> ((^a.a)((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 3. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 153553/16668366. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> ((((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))) REDUCED to normal form. ------ 153554/16668393. ------ 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 REDUCED to normal form. ------ 153555/16668474. ------ 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)(^x1.x1))(a (^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.y1)) 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. ------ 153556/16668834. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 153557/16669008. ------ 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. ------ 153558/16669716. ------ 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. ------ 153559/16670049. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 153560/16670616. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a)) b)) 3. ==[ beta ]==> (^y.(((^z.(a a)) b)((^z.(a a)) b))) 4. ==[ alpha ]==> (^x.(((^y.(a a)) b)((^z.(a a)) b))) 5. ==[ beta ]==> (^x.((a a)((^z.(a a)) b))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a)) b))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 153561/16670823. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))((a a)(^y1.y1)))(((^z.z)(^x1.x1))((a a)(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))((a a)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2))))) 5. ==[ beta ]==> ((((^y.y)(^z.z))((a a)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 9. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 10. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 11. ==[ beta ]==> (((a a)(^x.x))((^z.z)((a a)(^x1.x1)))) 12. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^z.z)))) 13. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 14. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 153562/16673265. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153563/16673571. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 153564/16675407. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153565/16675848. ------ 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.y1)(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z)(y y)))) 7. ==[ beta ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 153566/16676037. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(a b))) REDUCED to normal form. ------ 153567/16676433. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.x))) REDUCED to normal form. ------ 153568/16676784. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(^z.((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((a a) a))) REDUCED to normal form. ------ 153569/16676955. ------ 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. ------ 153570/16677837. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 153571/16677999. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 153572/16678071. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.c)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.c)) REDUCED to normal form. ------ 153573/16678197. ------ 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)))) REDUCED to normal form. ------ 153574/16678224. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(a a))) REDUCED to normal form. ------ 153575/16678278. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.b)) 5. ==[ beta ]==> (((a a)(a a))(^y.b)) 6. ==[ alpha ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 153576/16678305. ------ 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. ------ 153577/16678344. ------ 1. ==[ start ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 153578/16678371. ------ 1. ==[ start ]==> ((a (a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 153579/16678398. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a b)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 153580/16678452. ------ 1. ==[ start ]==> (((a a)(a a))(((a a) a)(b a))) REDUCED to normal form. ------ 153581/16678479. ------ 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)))((^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. ------ 153582/16678677. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((^y.a)(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((^x.a)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 153583/16678704. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 153584/16678713. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (a a))) REDUCED to normal form. ------ 153585/16678740. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 153586/16678758. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y) a)((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(^y.a))) 5. ==[ beta ]==> (a ((b a)(^y.a))) 6. ==[ alpha ]==> (a ((b a)(^x.a))) REDUCED to normal form. ------ 153587/16678785. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.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. ------ 153588/16678821. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 153589/16678839. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 153590/16678929. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) 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)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> ((a a)(b ((^y.y) b))) 8. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 9. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 153591/16679010. ------ 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. ------ 153592/16679028. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.(^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 ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 153593/16679055. ------ 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. ------ 153594/16679091. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 153595/16679118. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 153596/16679145. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1)))(^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. ------ 153597/16679253. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 153598/16679586. ------ 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)(^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. ------ 153599/16679613. ------ 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. ------ 153600/16679640. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 153601/16679667. ------ 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. ------ 153602/16679694. ------ 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. ------ 153603/16679721. ------ 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. ------ 153604/16679892. ------ 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. ------ 153605/16679919. ------ 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 (^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 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. ------ 153606/16679928. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^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. ------ 153607/16679982. ------ 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. ------ 153608/16680009. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 153609/16680036. ------ 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. ------ 153610/16680054. ------ 1. ==[ start ]==> ((a (^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 153611/16680243. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.b)(((a a)(a a)) b)) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a)) b)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 153612/16680387. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(^y.b))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 153613/16680414. ------ 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. ------ 153614/16680441. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 153615/16680495. ------ 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 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 153616/16680522. ------ 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. ------ 153617/16680549. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 153618/16680621. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 153619/16680639. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) b)(a (^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. ------ 153620/16680666. ------ 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)))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 153621/16680693. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b a)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 153622/16680720. ------ 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. ------ 153623/16680747. ------ 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.x1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))((a a) a))) 7. ==[ beta ]==> (a (((^y.y)(a a))((a a) a))) 8. ==[ alpha ]==> (a (((^x.x)(a a))((a a) a))) 9. ==[ beta ]==> (a ((a a)((a a) a))) REDUCED to normal form. ------ 153624/16680774. ------ 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. ------ 153625/16680801. ------ 1. ==[ start ]==> (((a b)(a a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 153626/16680828. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)((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. ------ 153627/16680999. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1) b)(^y1.(^z1.z1)))) 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. ------ 153628/16681008. ------ 1. ==[ start ]==> (((a b) b)((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a b) b)(a (^y.y))) 4. ==[ alpha ]==> (((a b) b)(a (^x.x))) REDUCED to normal form. ------ 153629/16681035. ------ 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)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 153630/16681053. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(a a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b a)(^y.(y y)))) 5. ==[ beta ]==> ((a a)((b a)(^y.(y y)))) 6. ==[ alpha ]==> ((a a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 153631/16681080. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((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))) REDUCED to normal form. ------ 153632/16681089. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 153633/16681134. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a b)(^x1.b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a b)(^x1.b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(^y1.b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.b))) 9. ==[ beta ]==> ((^y.y)((a b)(^z.b))) 10. ==[ alpha ]==> ((^x.x)((a b)(^y.b))) 11. ==[ beta ]==> ((a b)(^y.b)) 12. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 153634/16681143. ------ 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. ------ 153635/16681197. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 153636/16681224. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((b a)(b a))) REDUCED to normal form. ------ 153637/16681251. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.a)(a (^a.(^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) REDUCED to normal form. ------ 153638/16681440. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 153639/16681674. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 153640/16681980. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 153641/16682349. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b) a)) 5. ==[ beta ]==> (b (((^z.z) b) a)) 6. ==[ alpha ]==> (b (((^x.x) b) a)) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 153642/16682493. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.b)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 153643/16682628. ------ 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. ------ 153644/16682700. ------ 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. ------ 153645/16682826. ------ 1. ==[ start ]==> (((a a)(b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 153646/16682853. ------ 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.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(a b))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a b)) REDUCED to normal form. ------ 153647/16682880. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(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 (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. ------ 153648/16682907. ------ 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. ------ 153649/16682934. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z))(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(b a))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(b a))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(b a))) REDUCED to normal form. ------ 153650/16682961. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 153651/16683087. ------ 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. ------ 153652/16683105. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153653/16683186. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> ((a a)((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 153654/16683267. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 153655/16683384. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 153656/16683411. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 153657/16683492. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 153658/16683519. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 153659/16683573. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153660/16683717. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a) a)(^z.z))) REDUCED to normal form. ------ 153661/16683744. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(b a))((a a) a)) REDUCED to normal form. ------ 153662/16683771. ------ 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. ------ 153663/16683798. ------ 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)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y) 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))(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. ------ 153664/16683825. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^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)))) REDUCED to normal form. ------ 153665/16683852. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a a)(b a))) REDUCED to normal form. ------ 153666/16683978. ------ 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. ------ 153667/16684023. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(^a.a))(^c.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. ------ 153668/16684050. ------ 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. ------ 153669/16684185. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 153670/16684302. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 153671/16684329. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((b a)((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((b a)((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((b a)((^y.b)(^y.b))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.b))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 153672/16684356. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 153673/16684653. ------ 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. ------ 153674/16685184. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 153675/16685409. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 153676/16685436. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 153677/16685454. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 153678/16685517. ------ 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. ------ 153679/16685535. ------ 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. ------ 153680/16685544. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.b))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 10. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 153681/16685598. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a 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. ------ 153682/16685643. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(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. ------ 153683/16685652. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 153684/16685679. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 153685/16685823. ------ 1. ==[ start ]==> (((a (a a))(b a))(b (a b))) REDUCED to normal form. ------ 153686/16685850. ------ 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.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 153687/16685877. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b)(a a))) 3. ==[ beta ]==> ((((a a) a)(a a))((a b)(a a))) REDUCED to normal form. ------ 153688/16685904. ------ 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. ------ 153689/16685931. ------ 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.x1) a))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^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))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^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. ------ 153690/16685958. ------ 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. ------ 153691/16686012. ------ 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))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))((a a) a))) REDUCED to normal form. ------ 153692/16686039. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a a)(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))((a a)(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 153693/16686183. ------ 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.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2) a)(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2) a)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153694/16686264. ------ 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. ------ 153695/16686408. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 153696/16686435. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.b)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.b)) REDUCED to normal form. ------ 153697/16686480. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) b)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 153698/16686507. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) 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. ------ 153699/16686642. ------ 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. ------ 153700/16686651. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 153701/16686678. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 153702/16686750. ------ 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.(^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. ------ 153703/16686759. ------ 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)(^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. ------ 153704/16686786. ------ 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. ------ 153705/16686930. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)(b (^y.y))) 8. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 153706/16686957. ------ 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. ------ 153707/16686984. ------ 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. ------ 153708/16687011. ------ 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. ------ 153709/16687038. ------ 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)((^z.z) a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) 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. ------ 153710/16687065. ------ 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. ------ 153711/16687092. ------ 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)(^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. ------ 153712/16687425. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> (b ((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> (b ((^x.(x x)) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 153713/16687533. ------ 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))(^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. ------ 153714/16687650. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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))) 7. ==[ beta ]==> (a ((^y.y)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 153715/16687668. ------ 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. ------ 153716/16687695. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) c)) 5. ==[ beta ]==> ((a (^y.y)) c) 6. ==[ alpha ]==> ((a (^x.x)) c) REDUCED to normal form. ------ 153717/16687749. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z)) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z)) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z)) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z)) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y)) a)) 7. ==[ beta ]==> ((b b)((^y.(y y)) a)) 8. ==[ alpha ]==> ((b b)((^x.(x x)) a)) 9. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 153718/16687839. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 153719/16687866. ------ 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))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 153720/16687893. ------ 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 (^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. ------ 153721/16687938. ------ 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) a) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153722/16687947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.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. ------ 153723/16687974. ------ 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))(^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. ------ 153724/16688001. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^b.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. ------ 153725/16688055. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^a.(^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. ------ 153726/16688118. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b b)) REDUCED to normal form. ------ 153727/16688172. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b (a a))) 3. ==[ beta ]==> (((a (a a)) b)(b (a a))) REDUCED to normal form. ------ 153728/16688199. ------ 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)))) REDUCED to normal form. ------ 153729/16688226. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(a a))) REDUCED to normal form. ------ 153730/16688253. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 153731/16688280. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 153732/16688307. ------ 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. ------ 153733/16688598. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.((^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.(^y.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 153734/16697256. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 153735/16698363. ------ 1. ==[ start ]==> ((^a.(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153736/16698444. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153737/16698606. ------ 1. ==[ start ]==> ((^a.(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (^x.((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> (^x.((a a)(^z.z))) 6. ==[ alpha ]==> (^x.((a a)(^y.y))) REDUCED to normal form. ------ 153738/16698609. ------ 1. ==[ start ]==> ((a (^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 153739/16698627. ------ 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. ------ 153740/16698948. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((^y.(y y))((^z.z) b))(((^y.(y y))((^z.z) b))((^y.(y y))((^z.z) b)))) 4. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.(z z))((^x1.x1) b))((^y1.(y1 y1))((^z1.z1) b)))) 5. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.(z z))((^x1.x1) b))((^y1.(y1 y1))((^z1.z1) b)))) 6. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.(z z))((^x1.x1) b))((^y1.(y1 y1))((^z1.z1) b)))) 7. ==[ beta ]==> ((b ((^y.y) b))(((^z.(z z))((^x1.x1) b))((^y1.(y1 y1))((^z1.z1) b)))) 8. ==[ alpha ]==> ((b ((^x.x) b))(((^y.(y y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 9. ==[ beta ]==> ((b b)(((^y.(y y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 10. ==[ alpha ]==> ((b b)(((^x.(x x))((^y.y) b))((^z.(z z))((^x1.x1) b)))) 11. ==[ beta ]==> ((b b)((((^y.y) b)((^y.y) b))((^z.(z z))((^x1.x1) b)))) 12. ==[ alpha ]==> ((b b)((((^x.x) b)((^y.y) b))((^z.(z z))((^x1.x1) b)))) 13. ==[ beta ]==> ((b b)((b ((^y.y) b))((^z.(z z))((^x1.x1) b)))) 14. ==[ alpha ]==> ((b b)((b ((^x.x) b))((^y.(y y))((^z.z) b)))) 15. ==[ beta ]==> ((b b)((b b)((^y.(y y))((^z.z) b)))) 16. ==[ alpha ]==> ((b b)((b b)((^x.(x x))((^y.y) b)))) 17. ==[ beta ]==> ((b b)((b b)(((^y.y) b)((^y.y) b)))) 18. ==[ alpha ]==> ((b b)((b b)(((^x.x) b)((^y.y) b)))) 19. ==[ beta ]==> ((b b)((b b)(b ((^y.y) b)))) 20. ==[ alpha ]==> ((b b)((b b)(b ((^x.x) b)))) 21. ==[ beta ]==> ((b b)((b b)(b b))) REDUCED to normal form. ------ 153741/16699446. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.x)((^y.y)(^z.z)))(^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. ------ 153742/16699824. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> (a (^z.(b (^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(b (^y.y)))) REDUCED to normal form. ------ 153743/16700220. ------ 1. ==[ start ]==> ((((a a) a)(a a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 153744/16700607. ------ 1. ==[ start ]==> (((^a.b)(a a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 153745/16700631. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (^y.((((a a)(a a))(a a))(((a a)(a a))(a a)))) 4. ==[ alpha ]==> (^x.((((a a)(a a))(a a))(((a a)(a a))(a a)))) REDUCED to normal form. ------ 153746/16701327. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 153747/16701513. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((((^z.b)(^x1.b))((^z.b)(^x1.b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.b)(^y.b))((^z.b)(^x1.b)))(^y1.y1)) 5. ==[ beta ]==> ((b ((^z.b)(^x1.b)))(^y1.y1)) 6. ==[ alpha ]==> ((b ((^x.b)(^y.b)))(^z.z)) 7. ==[ beta ]==> ((b b)(^z.z)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 153748/16701687. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (b (^z.((z z)(z z)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 153749/16702269. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))((a a)(^z.z)))) 3. ==[ eta ]==> (b ((^y.(y y))((a a)(^z.z)))) 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. ------ 153750/16702818. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 153751/16703001. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 153752/16703106. ------ 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. ------ 153753/16703709. ------ 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. ------ 153754/16703892. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 153755/16704024. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 153756/16704441. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(b z))) 3. ==[ eta ]==> (((^x.(x x))((a a)(^y.y))) b) 4. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y))) b) 5. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 153757/16705023. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(^z.a))) 3. ==[ beta ]==> ((((^y.b)(^z.a))((^y.b)(^z.a)))(((^y.b)(^z.a))((^y.b)(^z.a)))) 4. ==[ alpha ]==> ((((^x.b)(^y.a))((^z.b)(^x1.a)))(((^y1.b)(^z1.a))((^x2.b)(^y2.a)))) 5. ==[ beta ]==> ((b ((^z.b)(^x1.a)))(((^y1.b)(^z1.a))((^x2.b)(^y2.a)))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.a)))(((^z.b)(^x1.a))((^y1.b)(^z1.a)))) 7. ==[ beta ]==> ((b b)(((^z.b)(^x1.a))((^y1.b)(^z1.a)))) 8. ==[ alpha ]==> ((b b)(((^x.b)(^y.a))((^z.b)(^x1.a)))) 9. ==[ beta ]==> ((b b)(b ((^z.b)(^x1.a)))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(^y.a)))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 153758/16705197. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^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. ------ 153759/16705413. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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 ]==> (^x.(a a)) REDUCED to normal form. ------ 153760/16705863. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 153761/16706079. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 153762/16706103. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 153763/16706799. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 153764/16706970. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.a))) REDUCED to normal form. ------ 153765/16707264. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 153766/16707267. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 153767/16707762. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(z (z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(z (z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(z (z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(z (z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(y (y y)))) 7. ==[ beta ]==> ((b b)(^y.(y (y y)))) 8. ==[ alpha ]==> ((b b)(^x.(x (x x)))) REDUCED to normal form. ------ 153768/16707843. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (b (^z.((^x1.x1) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 153769/16707852. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.d)) REDUCED to normal form. ------ 153770/16708014. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 153771/16708083. ------ 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. ------ 153772/16708104. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(^b.a))) 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. ------ 153773/16708158. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(a (^y.y)))) REDUCED to normal form. ------ 153774/16708212. ------ 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.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153775/16708266. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 153776/16708293. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(a a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(a a))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(a a))) REDUCED to normal form. ------ 153777/16708320. ------ 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. ------ 153778/16708377. ------ 1. ==[ start ]==> ((a (^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 153779/16708404. ------ 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 ]==> ((^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. ------ 153780/16708431. ------ 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)(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(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. ------ 153781/16708458. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 153782/16708512. ------ 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))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153783/16708539. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) 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. ------ 153784/16708566. ------ 1. ==[ start ]==> (((^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)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 153785/16708593. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 153786/16708620. ------ 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. ------ 153787/16708638. ------ 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. ------ 153788/16708656. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 153789/16708737. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(y y)))) REDUCED to normal form. ------ 153790/16708764. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 153791/16708791. ------ 1. ==[ start ]==> (((a a)(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 153792/16708818. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 153793/16708845. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 153794/16708881. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 153795/16708935. ------ 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. ------ 153796/16708953. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(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. ------ 153797/16708962. ------ 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)))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((a (a (a a)))(b ((^y.y) b))) 6. ==[ alpha ]==> ((a (a (a a)))(b ((^x.x) b))) 7. ==[ beta ]==> ((a (a (a a)))(b b)) REDUCED to normal form. ------ 153798/16709061. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a (a a)) a)((^y.y) a)) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x) a)) 5. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 153799/16709088. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b (^y.y)) b)) REDUCED to normal form. ------ 153800/16709115. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(a a)) c)) REDUCED to normal form. ------ 153801/16709259. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 153802/16709286. ------ 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. ------ 153803/16709457. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)(a ((^z.(^x1.x1)) 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. ------ 153804/16709484. ------ 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. ------ 153805/16709520. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a)) c)) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a)) c)) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 153806/16709538. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.z) a))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b a)) REDUCED to normal form. ------ 153807/16709781. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1) 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. ------ 153808/16709835. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a a)(b (^z.z)))) 5. ==[ beta ]==> (a ((a a)(b (^z.z)))) 6. ==[ alpha ]==> (a ((a a)(b (^x.x)))) REDUCED to normal form. ------ 153809/16709871. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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))) REDUCED to normal form. ------ 153810/16709898. ------ 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. ------ 153811/16709952. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) REDUCED to normal form. ------ 153812/16709979. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 153813/16710006. ------ 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. ------ 153814/16710033. ------ 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)(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. ------ 153815/16710060. ------ 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. ------ 153816/16710123. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 153817/16710150. ------ 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. ------ 153818/16710177. ------ 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. ------ 153819/16710204. ------ 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.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 153820/16710231. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(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. ------ 153821/16710249. ------ 1. ==[ start ]==> (((^a.b) a)((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b) a)((b (^y.y)) a)) 3. ==[ beta ]==> (b ((b (^y.y)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 153822/16710618. ------ 1. ==[ start ]==> (((^a.b)(a a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(a (b (^y.y)))) 3. ==[ beta ]==> (b (a (b (^y.y)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 153823/16710645. ------ 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. ------ 153824/16710861. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 153825/16710888. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 153826/16710942. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) b))) 7. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 9. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 153827/16711032. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 153828/16711059. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.(^a.a)))(^b.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))) REDUCED to normal form. ------ 153829/16711086. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 153830/16711113. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153831/16711167. ------ 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. ------ 153832/16711194. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a) a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))(((a a) a)(^z.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a) a)(^y.(a a)))) 7. ==[ beta ]==> ((((a a) a)(^y.(a a)))(((a a) a)(^y.(a a)))) 8. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 153833/16711221. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 153834/16711275. ------ 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)(^x.x))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153835/16711311. ------ 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)(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. ------ 153836/16711338. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a a)(a a))) REDUCED to normal form. ------ 153837/16711392. ------ 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. ------ 153838/16711419. ------ 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. ------ 153839/16711473. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 153840/16711500. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.(a a))(^c.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. ------ 153841/16711527. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(^z.b))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 153842/16711698. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a ((a a)(a a)))) 3. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 153843/16711707. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b) c)((^x.(a a)) a)) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 153844/16711734. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y) b)) 3. ==[ beta ]==> (((a a) b)((^y.y) b)) 4. ==[ alpha ]==> (((a a) b)((^x.x) b)) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 153845/16711779. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))((b a) a)) REDUCED to normal form. ------ 153846/16711806. ------ 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)(^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. ------ 153847/16711860. ------ 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 b)((a a) a))) REDUCED to normal form. ------ 153848/16711941. ------ 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 a)(^z.z)))) 4. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 153849/16712067. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(a a))) 3. ==[ beta ]==> (((a (^x.x))(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. ------ 153850/16712094. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 153851/16712175. ------ 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. ------ 153852/16712202. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a b) a)((^y.b)((a a) a))) 4. ==[ alpha ]==> (((a b) a)((^x.b)((a a) a))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 153853/16712256. ------ 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.x1)(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. ------ 153854/16712283. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> ((a (b a))(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 153855/16712643. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (b a))) 3. ==[ beta ]==> (((a b)(a b))(c (b a))) REDUCED to normal form. ------ 153856/16712706. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 153857/16712724. ------ 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. ------ 153858/16712733. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 153859/16712832. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a b)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.x1))) REDUCED to normal form. ------ 153860/16712985. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153861/16713012. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 153862/16713039. ------ 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.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 153863/16713111. ------ 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.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153864/16713120. ------ 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. ------ 153865/16713588. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 153866/16713624. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 153867/16713696. ------ 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)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1) 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. ------ 153868/16713723. ------ 1. ==[ start ]==> ((a (^b.b))((a b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 153869/16713849. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(c (^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(c (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 153870/16713903. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 153871/16714002. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153872/16714011. ------ 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. ------ 153873/16714038. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 153874/16714452. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(a (b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(a (b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(a (b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (b a))) REDUCED to normal form. ------ 153875/16714488. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.(^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. ------ 153876/16714515. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 153877/16714533. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((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. ------ 153878/16714542. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.b) d)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b) d)) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 153879/16714641. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 153880/16714767. ------ 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 a)) REDUCED to normal form. ------ 153881/16714794. ------ 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.z) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 153882/16714848. ------ 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. ------ 153883/16714875. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))((a a) a))) 3. ==[ beta ]==> (((a b)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 153884/16714902. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.a)(a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 153885/16714929. ------ 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.(^z.z))((^x1.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. ------ 153886/16715010. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 153887/16715037. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)(^y.a))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 153888/16715208. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(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. ------ 153889/16715316. ------ 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. ------ 153890/16715397. ------ 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. ------ 153891/16715424. ------ 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))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 153892/16715460. ------ 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)(a a))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^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. ------ 153893/16715541. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.(z z))) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 153894/16715568. ------ 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. ------ 153895/16715622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 153896/16715676. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a) a)) REDUCED to normal form. ------ 153897/16715703. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b) b)) REDUCED to normal form. ------ 153898/16715766. ------ 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))(^z.(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. ------ 153899/16715793. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 8. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 153900/16715820. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.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. ------ 153901/16715847. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 153902/16715874. ------ 1. ==[ start ]==> ((((^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.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 153903/16716063. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b (^z.b))) 3. ==[ beta ]==> ((b (a (^y.y)))(b (^z.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b (^y.b))) REDUCED to normal form. ------ 153904/16716090. ------ 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. ------ 153905/16716117. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(a a))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 153906/16716504. ------ 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 ]==> ((b (^y.y))(((a a) a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 153907/16716531. ------ 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 (^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. ------ 153908/16716585. ------ 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. ------ 153909/16716675. ------ 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. ------ 153910/16716702. ------ 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.(^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. ------ 153911/16716783. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 153912/16716810. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(^z.a))) 3. ==[ beta ]==> ((b (^y.a))((a a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 153913/16716837. ------ 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. ------ 153914/16716900. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))(^b.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. ------ 153915/16716927. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 153916/16716954. ------ 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.(^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. ------ 153917/16717089. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 153918/16717116. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 153919/16717170. ------ 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)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 153920/16717197. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(a (^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(a (^y.y)))) 7. ==[ beta ]==> ((b a)((a (^y.y))(a (^y.y)))) 8. ==[ alpha ]==> ((b a)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 153921/16717224. ------ 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.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 153922/16717278. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 153923/16717368. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c ((^z.z) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c ((^z.z) 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. ------ 153924/16717449. ------ 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. ------ 153925/16717674. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 153926/16717719. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c (a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c (a (^y.y)))) 5. ==[ beta ]==> (c (a (^y.y))) 6. ==[ alpha ]==> (c (a (^x.x))) REDUCED to normal form. ------ 153927/16717773. ------ 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. ------ 153928/16717782. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y)) a)) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 153929/16717809. ------ 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) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153930/16717854. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)((^z.z) a))) 3. ==[ beta ]==> (b ((a a)((^z.z) a))) 4. ==[ alpha ]==> (b ((a a)((^x.x) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 153931/16717863. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) d) REDUCED to normal form. ------ 153932/16717890. ------ 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)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 153933/16717917. ------ 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))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 153934/16717971. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^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)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 153935/16717998. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z)) b)) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z)) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 153936/16718025. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a) c)) REDUCED to normal form. ------ 153937/16718079. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^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. ------ 153938/16718097. ------ 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. ------ 153939/16718115. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 153940/16718142. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^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. ------ 153941/16718169. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(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. ------ 153942/16718196. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^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)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 153943/16718223. ------ 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)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^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. ------ 153944/16718250. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.x))) REDUCED to normal form. ------ 153945/16718277. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 153946/16718304. ------ 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)(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(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. ------ 153947/16718331. ------ 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)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 153948/16728720. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 153949/16728891. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 153950/16728990. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (a a))(^b.b))) 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. ------ 153951/16729083. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.(^y1.y1)) 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. ------ 153952/16729215. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 153953/16729497. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 153954/16730106. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 153955/16730286. ------ 1. ==[ start ]==> ((^a.(a b))((b (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x b))((b (^y.y)) a)) 3. ==[ beta ]==> (((b (^y.y)) a) b) 4. ==[ alpha ]==> (((b (^x.x)) a) b) REDUCED to normal form. ------ 153956/16730658. ------ 1. ==[ start ]==> (((a b)(^a.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(b (^z.z)))) REDUCED to normal form. ------ 153957/16731369. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 153958/16731729. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 153959/16731738. ------ 1. ==[ start ]==> (((a b) c)(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.((x x)(x x)))) REDUCED to normal form. ------ 153960/16732311. ------ 1. ==[ start ]==> ((^a.(b a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((a (a a))(^y.(^z.z)))) 3. ==[ eta ]==> (b ((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 153961/16732404. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.z)) 5. ==[ beta ]==> (((^y.b)(^y.b))(^z.z)) 6. ==[ alpha ]==> (((^x.b)(^y.b))(^z.z)) 7. ==[ beta ]==> (b (^z.z)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 153962/16732737. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 153963/16733148. ------ 1. ==[ start ]==> ((^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 y1)))) 3. ==[ beta ]==> ((((^x1.x1)(a a))(^y1.(y1 y1)))(^y.(^z.z))) 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))) REDUCED to normal form. ------ 153964/16733655. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 153965/16734066. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)(^b.(^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. ------ 153966/16735065. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b) c)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b) c)) 3. ==[ beta ]==> ((((a b) c)((a b) c))(((a b) c)((a b) c))) REDUCED to normal form. ------ 153967/16735239. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 153968/16735464. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 153969/16735698. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153970/16736145. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)(^z.z))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 153971/16736319. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(a z))) 3. ==[ eta ]==> (((^x.b)(^y.(a a))) a) 4. ==[ beta ]==> (b a) REDUCED to normal form. ------ 153972/16736697. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^z.(^x1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 153973/16737306. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 153974/16737588. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153975/16737804. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(z z)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(z z)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 153976/16737813. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 153977/16737894. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 153978/16737993. ------ 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.((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 153979/16738125. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^a.(^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. ------ 153980/16738146. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.c)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.c)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.c)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.c)) REDUCED to normal form. ------ 153981/16738308. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 153982/16738362. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 153983/16738437. ------ 1. ==[ start ]==> (((^a.a) a)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x) a)((b a)((a a) a))) 3. ==[ beta ]==> (a ((b a)((a a) a))) REDUCED to normal form. ------ 153984/16738464. ------ 1. ==[ start ]==> (((a a) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 153985/16738491. ------ 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. ------ 153986/16738518. ------ 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. ------ 153987/16738545. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 153988/16738572. ------ 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. ------ 153989/16738599. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (a a)) b)) REDUCED to normal form. ------ 153990/16738626. ------ 1. ==[ start ]==> (((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 a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 153991/16738653. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 153992/16738716. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.(^z.z)) a)(^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. ------ 153993/16738743. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((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. ------ 153994/16738833. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 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. ------ 153995/16738914. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 153996/16738932. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 153997/16738986. ------ 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. ------ 153998/16739013. ------ 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. ------ 153999/16739022. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(y y))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (((^y.(y y))((^z.z) b))((^y.(y y))((^z.z) 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. ------ 154000/16739049. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.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 REDUCED to normal form. ------ 154001/16739103. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) 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. ------ 154002/16739211. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 154003/16739238. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 154004/16739373. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 154005/16739400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 154006/16739454. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 154007/16739463. ------ 1. ==[ start ]==> (((a (a a)) b)(c ((a a)(a a)))) REDUCED to normal form. ------ 154008/16739490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(b (b (^a.a)))) 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. ------ 154009/16739517. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^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. ------ 154010/16739544. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 154011/16739571. ------ 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. ------ 154012/16739598. ------ 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. ------ 154013/16739625. ------ 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.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(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. ------ 154014/16739994. ------ 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)((^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. ------ 154015/16740129. ------ 1. ==[ start ]==> ((a (^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 154016/16740201. ------ 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. ------ 154017/16740228. ------ 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. ------ 154018/16740309. ------ 1. ==[ start ]==> ((a (a b))((b (^a.a)) a)) 2. ==[ alpha ]==> ((a (a b))((b (^x.x)) a)) REDUCED to normal form. ------ 154019/16740399. ------ 1. ==[ start ]==> (((^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 z1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) IRREDUCIBLE: cycle. ------ 154020/16740480. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^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. ------ 154021/16740507. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 154022/16740588. ------ 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. ------ 154023/16740624. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c ((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(c ((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c ((^z.z) b))) 5. ==[ beta ]==> ((^y.a)(c ((^z.z) b))) 6. ==[ alpha ]==> ((^x.a)(c ((^y.y) b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 154024/16740651. ------ 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. ------ 154025/16740678. ------ 1. ==[ start ]==> (((a b)(^a.a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 154026/16740714. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a)) b)) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 154027/16740741. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.b) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y) c)) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) c) REDUCED to normal form. ------ 154028/16740867. ------ 1. ==[ start ]==> (((^a.b) b)((a b)(a b))) 2. ==[ alpha ]==> (((^x.b) b)((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 154029/16740993. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c (^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (^y1.y1))) 5. ==[ beta ]==> ((^y.y)(c (^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(c (^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 154030/16741074. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(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 a)) REDUCED to normal form. ------ 154031/16741128. ------ 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)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 154032/16741209. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(a a))((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))((a a) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((a a) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((a a) a))) 9. ==[ beta ]==> ((^y.y)((^z.(a a))((a a) a))) 10. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a) a))) 11. ==[ beta ]==> ((^y.(a a))((a a) a)) 12. ==[ alpha ]==> ((^x.(a a))((a a) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154033/16741290. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 154034/16741362. ------ 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))) 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. ------ 154035/16741389. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 154036/16741416. ------ 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. ------ 154037/16741443. ------ 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. ------ 154038/16741614. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 154039/16741749. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 154040/16741758. ------ 1. ==[ start ]==> (((a b) c)(a ((a a)(a a)))) REDUCED to normal form. ------ 154041/16741785. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a a) b)(((^y.y) b)(a a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b)(a a))) 5. ==[ beta ]==> (((a a) b)(b (a a))) REDUCED to normal form. ------ 154042/16741812. ------ 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)))) REDUCED to normal form. ------ 154043/16741866. ------ 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)(^z.z))(a (a a)))) REDUCED to normal form. ------ 154044/16741893. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.b))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 154045/16741947. ------ 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. ------ 154046/16741974. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 154047/16742001. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 154048/16742028. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(b a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 154049/16742055. ------ 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.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 154050/16742118. ------ 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. ------ 154051/16742145. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 154052/16742172. ------ 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. ------ 154053/16742199. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 9. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 154054/16742226. ------ 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. ------ 154055/16742253. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a b)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a b)(^y.a))) 3. ==[ beta ]==> (((a b) a)((a b)(^y.a))) 4. ==[ alpha ]==> (((a b) a)((a b)(^x.a))) REDUCED to normal form. ------ 154056/16742280. ------ 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. ------ 154057/16742307. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(a a))) REDUCED to normal form. ------ 154058/16742334. ------ 1. ==[ start ]==> ((a (b a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 154059/16742424. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (b ((^z.z)((^x1.x1) 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. ------ 154060/16742613. ------ 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. ------ 154061/16742640. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 154062/16742703. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (b a))) REDUCED to normal form. ------ 154063/16742757. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 154064/16742784. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 154065/16742811. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.a))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))((b a)(a (^y.y)))) REDUCED to normal form. ------ 154066/16742838. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 154067/16743090. ------ 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.(^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))) REDUCED to normal form. ------ 154068/16743117. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 154069/16743171. ------ 1. ==[ start ]==> ((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 x1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(z z)))) REDUCED to normal form. ------ 154070/16743180. ------ 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))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(a (a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154071/16743261. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a b))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 154072/16743342. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154073/16743477. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 154074/16743504. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 154075/16743558. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.b))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.b))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 154076/16743648. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (b a))) REDUCED to normal form. ------ 154077/16743675. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 154078/16743702. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a)(a a))) REDUCED to normal form. ------ 154079/16743756. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a) a)) REDUCED to normal form. ------ 154080/16743981. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((b a)(^y.y))) 3. ==[ beta ]==> (((a a)(a (a a)))((b a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))((b a)(^x.x))) REDUCED to normal form. ------ 154081/16744008. ------ 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. ------ 154082/16744062. ------ 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 z)))) REDUCED to normal form. ------ 154083/16744089. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)(^b.(^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. ------ 154084/16744098. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(^y1.y1)))) 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. ------ 154085/16744125. ------ 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.(^x2.x2))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))((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. ------ 154086/16744260. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a)(^a.a))) 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. ------ 154087/16744422. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.b))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.b))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.b))) 7. ==[ beta ]==> (b ((^y.b)(^y.b))) 8. ==[ alpha ]==> (b ((^x.b)(^y.b))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 154088/16744449. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(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. ------ 154089/16744539. ------ 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.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(a a))) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154090/16744566. ------ 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. ------ 154091/16744593. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.a))((a b) a)) REDUCED to normal form. ------ 154092/16744620. ------ 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. ------ 154093/16744647. ------ 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 y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 154094/16744701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a b))) REDUCED to normal form. ------ 154095/16744728. ------ 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. ------ 154096/16744791. ------ 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.x1))(^y1.y1))) REDUCED to normal form. ------ 154097/16744818. ------ 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.(^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. ------ 154098/16744845. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)(^y.a))) REDUCED to normal form. ------ 154099/16744872. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a) 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. ------ 154100/16744899. ------ 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. ------ 154101/16744926. ------ 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. ------ 154102/16744953. ------ 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)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 154103/16744980. ------ 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.(a a)))) REDUCED to normal form. ------ 154104/16745034. ------ 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.x1)) a)) REDUCED to normal form. ------ 154105/16745061. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a)) b)) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a)) b)) 5. ==[ beta ]==> ((b (a a))((a a) b)) REDUCED to normal form. ------ 154106/16745088. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b) c)) REDUCED to normal form. ------ 154107/16745124. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.a)(^z.(z z))) 6. ==[ alpha ]==> ((^x.a)(^y.(y y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 154108/16745259. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(^c.(^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)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 154109/16745403. ------ 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. ------ 154110/16745430. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a ((a a) a))) REDUCED to normal form. ------ 154111/16745475. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(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. ------ 154112/16745484. ------ 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)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 154113/16745529. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a))(a a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a))(a a))) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 154114/16745610. ------ 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. ------ 154115/16745718. ------ 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.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)((^z1.z1)(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. ------ 154116/16745952. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(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)) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 154117/16745979. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b) b)) 2. ==[ alpha ]==> (((a b)(a b))((^x.b) b)) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 154118/16746168. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 154119/16746258. ------ 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. ------ 154120/16746339. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 154121/16746447. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154122/16746483. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b c)(c ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b c)(c ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b c)(c (^y.y))) 6. ==[ alpha ]==> ((b c)(c (^x.x))) REDUCED to normal form. ------ 154123/16746510. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b ((a a) a))) REDUCED to normal form. ------ 154124/16746618. ------ 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. ------ 154125/16746645. ------ 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. ------ 154126/16746717. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a (^z.b))) 3. ==[ beta ]==> (b (a (^z.b))) 4. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 154127/16746825. ------ 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. ------ 154128/16746951. ------ 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. ------ 154129/16747059. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a) a)) 5. ==[ beta ]==> ((b a)((^y.a) a)) 6. ==[ alpha ]==> ((b a)((^x.a) a)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 154130/16747086. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z)) 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. ------ 154131/16747113. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y)) c)) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y)) c)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x)) c)) 5. ==[ beta ]==> (((a b)(a a))(c c)) REDUCED to normal form. ------ 154132/16747221. ------ 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))(^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. ------ 154133/16747248. ------ 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. ------ 154134/16747275. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 154135/16747329. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 154136/16747419. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.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. ------ 154137/16747608. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154138/16747743. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 154139/16747770. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.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. ------ 154140/16747824. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.(y y)))) 9. ==[ beta ]==> ((b b)(^y.(y y))) 10. ==[ alpha ]==> ((b b)(^x.(x x))) REDUCED to normal form. ------ 154141/16747833. ------ 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. ------ 154142/16747860. ------ 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. ------ 154143/16747905. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b (^b.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. ------ 154144/16747914. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 154145/16747968. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c b)) REDUCED to normal form. ------ 154146/16748013. ------ 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)((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154147/16748049. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (a a))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (a a))) REDUCED to normal form. ------ 154148/16748076. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (a (^y.y)))) REDUCED to normal form. ------ 154149/16748130. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 154150/16748148. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 154151/16748193. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 154152/16748220. ------ 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. ------ 154153/16748247. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y)) a)) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y)) a)) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x)) a)) REDUCED to normal form. ------ 154154/16748274. ------ 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. ------ 154155/16748301. ------ 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. ------ 154156/16748328. ------ 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. ------ 154157/16748355. ------ 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. ------ 154158/16748382. ------ 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. ------ 154159/16748435. ------ 1. ==[ start ]==> (^a.((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (^x.((x (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^x.((x (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (^x.((x (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 154160/16748436. ------ 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 (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 154161/16758459. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a))) a) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1))) a) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1)) a) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 154162/16758465. ------ 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 (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 154163/16758492. ------ 1. ==[ start ]==> ((^a.(a a))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x x))((b a)((a a) a))) 3. ==[ beta ]==> (((b a)((a a) a))((b a)((a a) a))) REDUCED to normal form. ------ 154164/16758519. ------ 1. ==[ start ]==> ((^a.b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 154165/16758600. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 154166/16758756. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^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. ------ 154167/16758960. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 154168/16759161. ------ 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)(^x.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 154169/16759842. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((((^y.y)(^z.z))(b a))(((^y.y)(^z.z))(b a)))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(b a)))(((^y1.y1)(^z1.z1))(b a))) 5. ==[ beta ]==> ((((^y.y)(b a))(((^z.z)(^x1.x1))(b a)))(((^y1.y1)(^z1.z1))(b a))) 6. ==[ alpha ]==> ((((^x.x)(b a))(((^y.y)(^z.z))(b a)))(((^x1.x1)(^y1.y1))(b a))) 7. ==[ beta ]==> (((b a)(((^y.y)(^z.z))(b a)))(((^x1.x1)(^y1.y1))(b a))) 8. ==[ alpha ]==> (((b a)(((^x.x)(^y.y))(b a)))(((^z.z)(^x1.x1))(b a))) 9. ==[ beta ]==> (((b a)((^y.y)(b a)))(((^z.z)(^x1.x1))(b a))) 10. ==[ alpha ]==> (((b a)((^x.x)(b a)))(((^y.y)(^z.z))(b a))) 11. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))(b a))) 12. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))(b a))) 13. ==[ beta ]==> (((b a)(b a))((^y.y)(b a))) 14. ==[ alpha ]==> (((b a)(b a))((^x.x)(b a))) 15. ==[ beta ]==> (((b a)(b a))(b a)) REDUCED to normal form. ------ 154170/16760175. ------ 1. ==[ start ]==> ((^a.(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a b)(^z.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 154171/16760349. ------ 1. ==[ start ]==> (((^a.b) a)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(y (^z.z)))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 154172/16760949. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((((a a) a)((^z.z)(a a)))(((a a) a)((^z.z)(a a))))) 4. ==[ alpha ]==> ((^x.x)((((a a) a)((^y.y)(a a)))(((a a) a)((^z.z)(a a))))) 5. ==[ beta ]==> ((((a a) a)((^y.y)(a a)))(((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a) a)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((((a a) a)(a a))(((a a) a)((^x.x)(a a)))) 9. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 154173/16761807. ------ 1. ==[ start ]==> (((a b) c)(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(a a)))) REDUCED to normal form. ------ 154174/16762473. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.x1))) 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. ------ 154175/16762806. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 154176/16763112. ------ 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. ------ 154177/16763724. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 154178/16764003. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^c.(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(b a))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(b a))) REDUCED to normal form. ------ 154179/16764813. ------ 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) b)(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 154180/16765776. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^b.((^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))(^x1.(a a))) REDUCED to normal form. ------ 154181/16766001. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^x.(x x))) REDUCED to normal form. ------ 154182/16766388. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^z.(^x1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 154183/16766775. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 154184/16766937. ------ 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. ------ 154185/16767108. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.((z z) z))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.((y y) y))) 5. ==[ beta ]==> ((b a)(^y.((y y) y))) 6. ==[ alpha ]==> ((b a)(^x.((x x) x))) REDUCED to normal form. ------ 154186/16767774. ------ 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)))) REDUCED to normal form. ------ 154187/16767873. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.d)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.d)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.d)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.d)) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.d)) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.d)) 7. ==[ beta ]==> ((b b)(^y.d)) 8. ==[ alpha ]==> ((b b)(^x.d)) REDUCED to normal form. ------ 154188/16767882. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 154189/16767963. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 154190/16767990. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 154191/16768071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.a)) REDUCED to normal form. ------ 154192/16768194. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^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. ------ 154193/16768296. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.c)) 3. ==[ beta ]==> (((a (a a)) b)(^y.c)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.c)) REDUCED to normal form. ------ 154194/16768350. ------ 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. ------ 154195/16768377. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 154196/16768431. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.b)) REDUCED to normal form. ------ 154197/16768485. ------ 1. ==[ start ]==> (((a (^a.(^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. ------ 154198/16768497. ------ 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 (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 154199/16768524. ------ 1. ==[ start ]==> ((a (a a))((b a)((a a) a))) REDUCED to normal form. ------ 154200/16768551. ------ 1. ==[ start ]==> ((a b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a b)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 154201/16768605. ------ 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. ------ 154202/16768632. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)(b a))) REDUCED to normal form. ------ 154203/16768767. ------ 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. ------ 154204/16768785. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(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. ------ 154205/16768830. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 154206/16768857. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 154207/16768866. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 154208/16768893. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 154209/16768911. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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)))) REDUCED to normal form. ------ 154210/16768920. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 154211/16768938. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.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. ------ 154212/16768992. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 154213/16769082. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(^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)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 154214/16769100. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.(y y))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((^x.(x x))((a (a a))(^y.y))) 5. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))(^y.y))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 154215/16769127. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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. ------ 154216/16769163. ------ 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. ------ 154217/16769190. ------ 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)((^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. ------ 154218/16769208. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(a (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. ------ 154219/16769235. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((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. ------ 154220/16769298. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(z z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y y))) REDUCED to normal form. ------ 154221/16769406. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 154222/16769541. ------ 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. ------ 154223/16769739. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 154224/16769766. ------ 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. ------ 154225/16769793. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 154226/16769820. ------ 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. ------ 154227/16769847. ------ 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. ------ 154228/16769874. ------ 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))((^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. ------ 154229/16770045. ------ 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. ------ 154230/16770072. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.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. ------ 154231/16770081. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 154232/16770108. ------ 1. ==[ start ]==> ((((^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)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 154233/16770126. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) 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. ------ 154234/16770189. ------ 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. ------ 154235/16770207. ------ 1. ==[ start ]==> ((a (^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a b)(^y.(a a)))) REDUCED to normal form. ------ 154236/16770378. ------ 1. ==[ start ]==> (((^a.b) a)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 154237/16770396. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b (^z.z)) a)) 3. ==[ beta ]==> ((^y.b)((b (^z.z)) a)) 4. ==[ alpha ]==> ((^x.b)((b (^y.y)) a)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 154238/16770540. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 154239/16770567. ------ 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. ------ 154240/16770594. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 154241/16770675. ------ 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. ------ 154242/16770702. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 154243/16770792. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(a a))(a a))) REDUCED to normal form. ------ 154244/16770819. ------ 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 (^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. ------ 154245/16770846. ------ 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)))((^z1.z1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 154246/16770873. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 154247/16770900. ------ 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))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a (((a a)(^y.y))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (a (((a a)(^x.x))((^y.y)(^z.z)))) 9. ==[ beta ]==> (a (((a a)(^x.x))(^z.z))) 10. ==[ alpha ]==> (a (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 154248/16770927. ------ 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. ------ 154249/16770954. ------ 1. ==[ start ]==> (((a b)(a a))((a b)(a b))) REDUCED to normal form. ------ 154250/16770981. ------ 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 (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. ------ 154251/16771152. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 154252/16771161. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(a a))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 154253/16771188. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)(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. ------ 154254/16771206. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.a))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 154255/16771215. ------ 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)))((^y1.y1) 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. ------ 154256/16771233. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 154257/16771296. ------ 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. ------ 154258/16771323. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(a b))) 5. ==[ beta ]==> ((^y.(y y))((^z.b)(a b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.b)(a b))) 7. ==[ beta ]==> (((^y.b)(a b))((^y.b)(a b))) 8. ==[ alpha ]==> (((^x.b)(a b))((^y.b)(a b))) 9. ==[ beta ]==> (b ((^y.b)(a b))) 10. ==[ alpha ]==> (b ((^x.b)(a b))) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 154259/16771350. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 154260/16771368. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 154261/16771377. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((a 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. ------ 154262/16771404. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a)(^x.x))((b a)(b a))) REDUCED to normal form. ------ 154263/16771593. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 154264/16771836. ------ 1. ==[ start ]==> (((a b) c)((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.x)(^y.(a a)))) 3. ==[ beta ]==> (((a b) c)(^y.(a a))) 4. ==[ alpha ]==> (((a b) c)(^x.(a a))) REDUCED to normal form. ------ 154265/16772169. ------ 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))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a) b)) REDUCED to normal form. ------ 154266/16772502. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)(^z.z))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(^z.z))) 5. ==[ beta ]==> (b ((a a)(^z.z))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 154267/16772583. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((b a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 154268/16772646. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 154269/16772754. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 8. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 154270/16772835. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 154271/16772853. ------ 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. ------ 154272/16772979. ------ 1. ==[ start ]==> (((a a)(b a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a b)((^x.x)(^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. ------ 154273/16773006. ------ 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. ------ 154274/16773033. ------ 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.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> ((a (a a))((^y.y)(a b))) 8. ==[ alpha ]==> ((a (a a))((^x.x)(a b))) 9. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 154275/16773060. ------ 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. ------ 154276/16773087. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) a)((a a)(^x1.x1)))) 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. ------ 154277/16773114. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 154278/16773141. ------ 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. ------ 154279/16773258. ------ 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 a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154280/16773339. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((a a)(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.b))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.b))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.b))) 9. ==[ beta ]==> ((a a)(^y.b)) 10. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 154281/16773564. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 154282/16773645. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.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. ------ 154283/16773672. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 154284/16773753. ------ 1. ==[ start ]==> ((((^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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 154285/16773870. ------ 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. ------ 154286/16773897. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a) a)((^y.y)(^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. ------ 154287/16773924. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)((a a) a))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)((a a) a))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 154288/16773951. ------ 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. ------ 154289/16773978. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)(a ((^y.y)(a a)))) 8. ==[ alpha ]==> ((a b)(a ((^x.x)(a a)))) 9. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 154290/16774005. ------ 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. ------ 154291/16774032. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a a)(b a))) 3. ==[ beta ]==> (((a b)(^y.y))((a a)(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)(b a))) REDUCED to normal form. ------ 154292/16774131. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154293/16774176. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a) a)(^b.(^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. ------ 154294/16774338. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a) a)) 3. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 154295/16774455. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 154296/16774482. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^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))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 154297/16774509. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 154298/16774536. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 154299/16774662. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 154300/16774806. ------ 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. ------ 154301/16774842. ------ 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)))) 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. ------ 154302/16775445. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a) d)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a) d)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a) d)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154303/16775562. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(a a)))) REDUCED to normal form. ------ 154304/16775607. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (((b a)(b a))((a a)(^y.y))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 154305/16775670. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 154306/16775688. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 154307/16775697. ------ 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. ------ 154308/16775751. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 154309/16775796. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154310/16775805. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 154311/16775832. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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 a)) REDUCED to normal form. ------ 154312/16775859. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)(^a.(^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. ------ 154313/16775976. ------ 1. ==[ start ]==> (((a (a a))(b a))(c ((a a) a))) REDUCED to normal form. ------ 154314/16776003. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(b (a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b (a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 154315/16776030. ------ 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.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. ------ 154316/16776057. ------ 1. ==[ start ]==> (((a b)(a b))((a b)(a a))) REDUCED to normal form. ------ 154317/16776084. ------ 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. ------ 154318/16776111. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1) a)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z) a)) 9. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 154319/16776165. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) 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. ------ 154320/16776192. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 154321/16776219. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a a)(a b))) REDUCED to normal form. ------ 154322/16776336. ------ 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. ------ 154323/16776417. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a a)(^z.b))) 3. ==[ beta ]==> (b ((a a)(^z.b))) 4. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 154324/16776561. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 154325/16776588. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^a.a))(^c.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. ------ 154326/16776633. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.b) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.b) a)) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 154327/16776804. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.b))) REDUCED to normal form. ------ 154328/16776831. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(a a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 154329/16776903. ------ 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.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154330/16776912. ------ 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. ------ 154331/16776939. ------ 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)(^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. ------ 154332/16776966. ------ 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. ------ 154333/16777083. ------ 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. ------ 154334/16777110. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 154335/16777137. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 154336/16777164. ------ 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. ------ 154337/16777191. ------ 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. ------ 154338/16777218. ------ 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)((^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. ------ 154339/16777245. ------ 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. ------ 154340/16777497. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) 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. ------ 154341/16777578. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (b ((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154342/16777803. ------ 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)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 154343/16777821. ------ 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 ]==> (((^y.(^z.z)) a)((a (a a)) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((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. ------ 154344/16777848. ------ 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. ------ 154345/16777911. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(z z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y y))) REDUCED to normal form. ------ 154346/16777983. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^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. ------ 154347/16777992. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 154348/16778019. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 154349/16778046. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 154350/16778091. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a a)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154351/16778100. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 154352/16778127. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.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. ------ 154353/16778154. ------ 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))(^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. ------ 154354/16778226. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^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. ------ 154355/16778244. ------ 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. ------ 154356/16778271. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c a)) REDUCED to normal form. ------ 154357/16778298. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b b)) 3. ==[ beta ]==> ((a ((a a)(a a)))(b b)) REDUCED to normal form. ------ 154358/16778325. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a c)) 3. ==[ beta ]==> (((a (a a)) b)(a c)) REDUCED to normal form. ------ 154359/16778352. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 154360/16778379. ------ 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. ------ 154361/16778406. ------ 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. ------ 154362/16778433. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b a)) 5. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 154363/16778460. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a b)) REDUCED to normal form. ------ 154364/16778514. ------ 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)))(^x1.x1))(a a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 154365/16780416. ------ 1. ==[ start ]==> ((^a.(a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.(y (^z.z)))) 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. ------ 154366/16780803. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(b (^x1.x1)))(^z.(b (^x1.x1))))) 4. ==[ alpha ]==> (^x.((^y.(b (^z.z)))(^x1.(b (^y1.y1))))) 5. ==[ beta ]==> (^x.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 154367/16786275. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154368/16788546. ------ 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)))(^x1.x1)) b) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 154369/16788570. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154370/16788651. ------ 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.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154371/16788813. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (^y.((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (^x.((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 154372/16788861. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 154373/16789155. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(^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)(((^y1.(^z1.z1))(a (^x2.(^y2.y2))))((^z2.(^x3.x3))(a (^y3.(^z3.z3)))))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2)))))) 7. ==[ beta ]==> (((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 8. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 11. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 12. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154374/16789506. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^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. ------ 154375/16789680. ------ 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. ------ 154376/16790445. ------ 1. ==[ start ]==> (((^a.b) a)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154377/16790451. ------ 1. ==[ start ]==> ((^a.(a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)(b (^z.z)))) 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. ------ 154378/16790454. ------ 1. ==[ start ]==> ((a (a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.(x (^y.y)))) REDUCED to normal form. ------ 154379/16790838. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(a (b (^z.z)))) 3. ==[ beta ]==> (^y.((a (b (^z.z)))(a (b (^z.z))))) 4. ==[ alpha ]==> (^x.((a (b (^y.y)))(a (b (^z.z))))) REDUCED to normal form. ------ 154380/16790841. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 154381/16791561. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 154382/16791720. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((^z.(a a))(^x1.a))((^z.(a a))(^x1.a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(a a))(^y.a))((^z.(a a))(^x1.a)))(^y1.y1)) 5. ==[ beta ]==> (((a a)((^z.(a a))(^x1.a)))(^y1.y1)) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.a)))(^z.z)) 7. ==[ beta ]==> (((a a)(a a))(^z.z)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 154383/16792476. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ eta ]==> (b ((^y.(^z.z))((^x1.x1)(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. ------ 154384/16792920. ------ 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. ------ 154385/16793025. ------ 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))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 154386/16793235. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.(^b.b))) 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))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 154387/16793916. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154388/16794126. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 154389/16794231. ------ 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. ------ 154390/16795179. ------ 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 a)(^y1.y1)))) REDUCED to normal form. ------ 154391/16795230. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((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)))((^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)))((^x3.(a a))(^y3.(^z3.z3))))) 5. ==[ beta ]==> (((a a)((^x1.(a a))(^y1.(^z1.z1))))(((^x2.(a a))(^y2.(^z2.z2)))((^x3.(a a))(^y3.(^z3.z3))))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(^z.z))))(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 7. ==[ beta ]==> (((a a)(a a))(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1))))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^x1.(a a))(^y1.(^z1.z1))))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(^y.(^z.z))))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 154392/16795872. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 154393/16796097. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 154394/16796310. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(a (^z.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154395/16796313. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 154396/16796700. ------ 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))) REDUCED to normal form. ------ 154397/16796862. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (b (^z.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 154398/16797204. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.a))) 5. ==[ beta ]==> ((b a)(^y.(^z.a))) 6. ==[ alpha ]==> ((b a)(^x.(^y.a))) REDUCED to normal form. ------ 154399/16797471. ------ 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. ------ 154400/16797645. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 154401/16797753. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(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. ------ 154402/16797978. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.d)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.d)) REDUCED to normal form. ------ 154403/16798167. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.a))) REDUCED to normal form. ------ 154404/16798290. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 154405/16798338. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 154406/16798392. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(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)))) REDUCED to normal form. ------ 154407/16798446. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154408/16798500. ------ 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.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 154409/16798527. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(a a))) REDUCED to normal form. ------ 154410/16798581. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^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))) REDUCED to normal form. ------ 154411/16798611. ------ 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 (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 154412/16798638. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 154413/16798665. ------ 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. ------ 154414/16798692. ------ 1. ==[ start ]==> ((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)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 154415/16798746. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154416/16798773. ------ 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))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 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. ------ 154417/16798800. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.y))((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. ------ 154418/16798827. ------ 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)(((^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. ------ 154419/16798854. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 154420/16798899. ------ 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. ------ 154421/16798971. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 154422/16798998. ------ 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)))) 5. ==[ beta ]==> ((a a)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 154423/16799025. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 154424/16799052. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^x1.a))) REDUCED to normal form. ------ 154425/16799079. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 154426/16799115. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 154427/16799142. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 154428/16799187. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154429/16799196. ------ 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. ------ 154430/16799322. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 154431/16799349. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b (^z.z)) b)) REDUCED to normal form. ------ 154432/16799439. ------ 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. ------ 154433/16799520. ------ 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. ------ 154434/16799547. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^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. ------ 154435/16799691. ------ 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. ------ 154436/16799718. ------ 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. ------ 154437/16799772. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 154438/16800015. ------ 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.(^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. ------ 154439/16800069. ------ 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)(^y.a))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.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)))) REDUCED to normal form. ------ 154440/16800132. ------ 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. ------ 154441/16800186. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.a))) REDUCED to normal form. ------ 154442/16800213. ------ 1. ==[ start ]==> ((((^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 y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 154443/16800240. ------ 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. ------ 154444/16800294. ------ 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. ------ 154445/16800330. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 154446/16800384. ------ 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. ------ 154447/16800411. ------ 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. ------ 154448/16800438. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 154449/16800465. ------ 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)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 154450/16800492. ------ 1. ==[ start ]==> ((a (a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.x)(b (^y.y)))) 3. ==[ beta ]==> ((a (a b))(b (^y.y))) 4. ==[ alpha ]==> ((a (a b))(b (^x.x))) REDUCED to normal form. ------ 154451/16800852. ------ 1. ==[ start ]==> (((^a.b)(a a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 154452/16800879. ------ 1. ==[ start ]==> ((a (^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(a (b (^y.y)))) REDUCED to normal form. ------ 154453/16801095. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.(a a))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154454/16801122. ------ 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))((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. ------ 154455/16801176. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(a (^z1.(^x2.x2))))) 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. ------ 154456/16801266. ------ 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. ------ 154457/16801293. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b)(^a.(^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. ------ 154458/16801320. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 154459/16801347. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a)(^z.(z z)))) REDUCED to normal form. ------ 154460/16801401. ------ 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. ------ 154461/16801428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a b)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a b)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(^z.b))) 5. ==[ beta ]==> ((^y.(y y))((a b)(^z.b))) 6. ==[ alpha ]==> ((^x.(x x))((a b)(^y.b))) 7. ==[ beta ]==> (((a b)(^y.b))((a b)(^y.b))) 8. ==[ alpha ]==> (((a b)(^x.b))((a b)(^y.b))) REDUCED to normal form. ------ 154462/16801455. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 154463/16801482. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(^a.a))(^c.(^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. ------ 154464/16801545. ------ 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)(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) REDUCED to normal form. ------ 154465/16801572. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 154466/16801599. ------ 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)))) 5. ==[ beta ]==> ((a ((a a) a))((a a)(a a))) REDUCED to normal form. ------ 154467/16801653. ------ 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. ------ 154468/16801680. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 154469/16801698. ------ 1. ==[ start ]==> (((^a.b) c)((b a) d)) 2. ==[ alpha ]==> (((^x.b) c)((b a) d)) 3. ==[ beta ]==> (b ((b a) d)) REDUCED to normal form. ------ 154470/16801761. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 154471/16801932. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b ((^z.z) b))) 3. ==[ beta ]==> (b (b ((^z.z) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 154472/16801968. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a)) a)) 3. ==[ beta ]==> (((a a) b)((^y.(a a)) a)) 4. ==[ alpha ]==> (((a a) b)((^x.(a a)) a)) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 154473/16801995. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 154474/16802013. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 154475/16802040. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((b a)((^x1.x1) 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. ------ 154476/16802094. ------ 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)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))((^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. ------ 154477/16802175. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((^y1.y1)(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. ------ 154478/16802274. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 154479/16802328. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(a a))) 3. ==[ beta ]==> ((a (a b))((^y.y)(a a))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(a a))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 154480/16802355. ------ 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. ------ 154481/16802436. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 154482/16802463. ------ 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. ------ 154483/16802517. ------ 1. ==[ start ]==> ((a (b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 154484/16802958. ------ 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. ------ 154485/16802967. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) a)) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 154486/16802994. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 154487/16803066. ------ 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))(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a (a a)))) REDUCED to normal form. ------ 154488/16803246. ------ 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. ------ 154489/16803273. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(a (^b.b))) 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. ------ 154490/16803300. ------ 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.(^x1.(^y1.y1)))(a 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. ------ 154491/16803345. ------ 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))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154492/16803822. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 154493/16803885. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1))) a)) 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. ------ 154494/16803930. ------ 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 a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154495/16803957. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.x))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 154496/16804164. ------ 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. ------ 154497/16804236. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154498/16804245. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 154499/16804272. ------ 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. ------ 154500/16804686. ------ 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. ------ 154501/16804749. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 154502/16804767. ------ 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. ------ 154503/16804776. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 154504/16804875. ------ 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. ------ 154505/16804947. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(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. ------ 154506/16805001. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(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))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 154507/16805028. ------ 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 a)) REDUCED to normal form. ------ 154508/16805055. ------ 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)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)((^z.z) a))) 7. ==[ beta ]==> ((a a)((^y.b)((^z.z) a))) 8. ==[ alpha ]==> ((a a)((^x.b)((^y.y) a))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 154509/16805082. ------ 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. ------ 154510/16805109. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^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. ------ 154511/16805136. ------ 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 x1))((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 154512/16805163. ------ 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) REDUCED to normal form. ------ 154513/16805217. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 154514/16805244. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^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))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 154515/16805271. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a))(^a.(^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. ------ 154516/16805442. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(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. ------ 154517/16805550. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((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. ------ 154518/16805631. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(a ((a a) a))) REDUCED to normal form. ------ 154519/16805658. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a (^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(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. ------ 154520/16805775. ------ 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. ------ 154521/16805802. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a b)(^x.b))(^z.(z z))) 6. ==[ alpha ]==> (((a b)(^x.b))(^y.(y y))) REDUCED to normal form. ------ 154522/16805856. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.a))) REDUCED to normal form. ------ 154523/16805910. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 154524/16805937. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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. ------ 154525/16805964. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b) b)) REDUCED to normal form. ------ 154526/16806027. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 154527/16806054. ------ 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 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. ------ 154528/16806081. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 154529/16806108. ------ 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.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 154530/16806135. ------ 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)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^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. ------ 154531/16806297. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c (^z.a))) 3. ==[ beta ]==> ((b (a (^y.y)))(c (^z.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c (^y.a))) REDUCED to normal form. ------ 154532/16806324. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(b (^x.b))) REDUCED to normal form. ------ 154533/16806351. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 154534/16806738. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(a (a b))) 3. ==[ beta ]==> ((b (^y.y))(a (a b))) 4. ==[ alpha ]==> ((b (^x.x))(a (a b))) REDUCED to normal form. ------ 154535/16806765. ------ 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))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 154536/16806801. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 154537/16806819. ------ 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. ------ 154538/16806900. ------ 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))) REDUCED to normal form. ------ 154539/16806936. ------ 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. ------ 154540/16807017. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 154541/16807044. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 154542/16807134. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(^a.(^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. ------ 154543/16807161. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 154544/16807188. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.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. ------ 154545/16807215. ------ 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.(^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. ------ 154546/16807242. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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))) 7. ==[ beta ]==> ((b a)(^y.a)) 8. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 154547/16807431. ------ 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)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 154548/16807458. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 154549/16807512. ------ 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. ------ 154550/16807683. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 154551/16807791. ------ 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. ------ 154552/16807908. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 154553/16808007. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b ((^z.z) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b ((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b ((^z.z) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(b ((^z.z) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b ((^y.y) a))) 7. ==[ beta ]==> ((b b)(b ((^y.y) a))) 8. ==[ alpha ]==> ((b b)(b ((^x.x) a))) 9. ==[ beta ]==> ((b b)(b a)) REDUCED to normal form. ------ 154554/16808043. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1)) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154555/16808088. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (b ((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 154556/16808097. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 154557/16808151. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 154558/16808196. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(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. ------ 154559/16808205. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.a))) REDUCED to normal form. ------ 154560/16808232. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^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 (^x.(x x)))(a a)) REDUCED to normal form. ------ 154561/16808259. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y)) b)) REDUCED to normal form. ------ 154562/16808313. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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) 9. ==[ beta ]==> a REDUCED to normal form. ------ 154563/16808331. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(a a))) REDUCED to normal form. ------ 154564/16808349. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^a.(^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. ------ 154565/16808376. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.a))) REDUCED to normal form. ------ 154566/16808403. ------ 1. ==[ start ]==> ((((^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))) 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. ------ 154567/16808430. ------ 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)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 154568/16808457. ------ 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.(^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)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 154569/16808484. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^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. ------ 154570/16808511. ------ 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. ------ 154571/16808538. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 154572/16808565. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 154573/16808619. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(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))) REDUCED to normal form. ------ 154574/16810530. ------ 1. ==[ start ]==> ((^a.(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.(^z.(^x1.x1)))) 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. ------ 154575/16818936. ------ 1. ==[ start ]==> ((^a.(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (^x.(c (^y.(^z.z)))) REDUCED to normal form. ------ 154576/16818975. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^c.((^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154577/16819008. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ eta ]==> ((^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. ------ 154578/16819278. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3))))(((^y3.y3)(^z3.z3))(^x4.(^y4.(^z4.z4)))))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3))))(((^y3.y3)(^z3.z3))(^x4.(^y4.(^z4.z4)))))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))(((^x3.x3)(^y3.y3))(^z3.(^x4.(^y4.y4)))))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))(((^x3.x3)(^y3.y3))(^z3.(^x4.(^y4.y4)))))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))(((^z2.z2)(^x3.x3))(^y3.(^z3.(^x4.x4)))))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154579/16819398. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a (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. ------ 154580/16819503. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154581/16819812. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a (^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 154582/16820190. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(b (^z.z)))) 5. ==[ beta ]==> (b (^y.(b (^z.z)))) 6. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 154583/16820394. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(a b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 154584/16820577. ------ 1. ==[ start ]==> ((a (a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154585/16820586. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(^y.(y (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 154586/16822026. ------ 1. ==[ start ]==> (((a b) c)(^d.((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)(^x.((^y.y) b))) 3. ==[ beta ]==> (((a b) c)(^x.b)) REDUCED to normal form. ------ 154587/16822053. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.((y y)(y y)))) 3. ==[ beta ]==> (((a a) b)(^y.((y y)(y y)))) 4. ==[ alpha ]==> (((a a) b)(^x.((x x)(x x)))) REDUCED to normal form. ------ 154588/16822599. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ eta ]==> (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 (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 154589/16823043. ------ 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. ------ 154590/16823052. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 154591/16823436. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x1.x1))(^y1.a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 154592/16823970. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 154593/16824354. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)(^z.(z z)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 154594/16824528. ------ 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))) REDUCED to normal form. ------ 154595/16824807. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.(a a))) b) 4. ==[ beta ]==> (((^y.y)(^z.(a a))) b) 5. ==[ alpha ]==> (((^x.x)(^y.(a a))) b) 6. ==[ beta ]==> ((^y.(a a)) b) 7. ==[ alpha ]==> ((^x.(a a)) b) 8. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154596/16825353. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((((^y.y)(a a)) b)(((^y.y)(a a)) b))((((^y.y)(a a)) b)(((^y.y)(a a)) b))) 4. ==[ alpha ]==> (((((^x.x)(a a)) b)(((^y.y)(a a)) b))((((^z.z)(a a)) b)(((^x1.x1)(a a)) b))) 5. ==[ beta ]==> ((((a a) b)(((^y.y)(a a)) b))((((^z.z)(a a)) b)(((^x1.x1)(a a)) b))) 6. ==[ alpha ]==> ((((a a) b)(((^x.x)(a a)) b))((((^y.y)(a a)) b)(((^z.z)(a a)) b))) 7. ==[ beta ]==> ((((a a) b)((a a) b))((((^y.y)(a a)) b)(((^z.z)(a a)) b))) 8. ==[ alpha ]==> ((((a a) b)((a a) b))((((^x.x)(a a)) b)(((^y.y)(a a)) b))) 9. ==[ beta ]==> ((((a a) b)((a a) b))(((a a) b)(((^y.y)(a a)) b))) 10. ==[ alpha ]==> ((((a a) b)((a a) b))(((a a) b)(((^x.x)(a a)) b))) 11. ==[ beta ]==> ((((a a) b)((a a) b))(((a a) b)((a a) b))) REDUCED to normal form. ------ 154597/16825797. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154598/16826823. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 154599/16826994. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 154600/16827594. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154601/16827768. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 154602/16828011. ------ 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))) REDUCED to normal form. ------ 154603/16828128. ------ 1. ==[ start ]==> ((((^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 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(z1 (z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(y1 (y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 (y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 (x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154604/16828209. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 154605/16828398. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.(^y.y)) a)(^z.z))(^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. ------ 154606/16828461. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.c)) REDUCED to normal form. ------ 154607/16828515. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 154608/16828569. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.b)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.b)) REDUCED to normal form. ------ 154609/16828623. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.b)) 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. ------ 154610/16828650. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 154611/16828704. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.a)) REDUCED to normal form. ------ 154612/16828752. ------ 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 (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 154613/16828779. ------ 1. ==[ start ]==> (((a a) a)((b a)((a a) a))) REDUCED to normal form. ------ 154614/16828806. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 154615/16828833. ------ 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. ------ 154616/16828860. ------ 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)((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. ------ 154617/16828887. ------ 1. ==[ start ]==> (((a a) b)(((a a) a)(b a))) REDUCED to normal form. ------ 154618/16828914. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(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. ------ 154619/16828941. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 154620/16828968. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((a a)(a a)))) REDUCED to normal form. ------ 154621/16828986. ------ 1. ==[ start ]==> ((a (^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 154622/16829022. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 154623/16829058. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) 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))) 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. ------ 154624/16829148. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 154625/16829175. ------ 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.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 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. ------ 154626/16829247. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 154627/16829274. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 154628/16829328. ------ 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. ------ 154629/16829337. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(^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)((^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. ------ 154630/16829364. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 154631/16829418. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154632/16829445. ------ 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))((^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. ------ 154633/16829553. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 154634/16829688. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 154635/16829769. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 154636/16829832. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 154637/16829859. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a ((^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. ------ 154638/16829886. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b (^z.z))(a a))) 3. ==[ beta ]==> ((a (^y.a))((b (^z.z))(a a))) 4. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(a a))) REDUCED to normal form. ------ 154639/16829913. ------ 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. ------ 154640/16829940. ------ 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)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 154641/16830201. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c (^z.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c (^z.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c (^z.(a a)))) 5. ==[ beta ]==> (a (c (^z.(a a)))) 6. ==[ alpha ]==> (a (c (^x.(a a)))) REDUCED to normal form. ------ 154642/16830237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)((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. ------ 154643/16830363. ------ 1. ==[ start ]==> (((^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)))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(a (a a)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a (a a)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 154644/16830444. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a b))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 154645/16830462. ------ 1. ==[ start ]==> (((a a)((a a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 154646/16830543. ------ 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. ------ 154647/16830570. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 154648/16830633. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.y)(b (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 154649/16830714. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.a))) IRREDUCIBLE: cycle. ------ 154650/16830795. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 154651/16830822. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 154652/16830849. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(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. ------ 154653/16830984. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 154654/16830993. ------ 1. ==[ start ]==> (((a b)(^a.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(b ((a a)(a a)))) REDUCED to normal form. ------ 154655/16831083. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z) c)) 5. ==[ beta ]==> ((a (^y.y))((^z.z) c)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) c)) 7. ==[ beta ]==> ((a (^x.x)) c) REDUCED to normal form. ------ 154656/16831182. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) b)(((^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. ------ 154657/16831443. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (^x1.x1)))) 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)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 154658/16831470. ------ 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)))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1) 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. ------ 154659/16831605. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 154660/16831677. ------ 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)(a a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^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. ------ 154661/16831704. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 154662/16831758. ------ 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. ------ 154663/16831785. ------ 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. ------ 154664/16831929. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 154665/16832064. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 154666/16832073. ------ 1. ==[ start ]==> (((a b) c)(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)(b ((^x.x) b))) 3. ==[ beta ]==> (((a b) c)(b b)) REDUCED to normal form. ------ 154667/16832100. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(a ((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)(a ((a a)(a a)))) REDUCED to normal form. ------ 154668/16832127. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (a a))) REDUCED to normal form. ------ 154669/16832181. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((b a) a)) REDUCED to normal form. ------ 154670/16832208. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 154671/16832262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154672/16832289. ------ 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. ------ 154673/16832316. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.a))((^z.z)(a a))) 6. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(a a))) 7. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 154674/16832343. ------ 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))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 154675/16832370. ------ 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))(^y.y))(a (b a))) REDUCED to normal form. ------ 154676/16832460. ------ 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. ------ 154677/16832487. ------ 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. ------ 154678/16832514. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.a))) 7. ==[ beta ]==> ((^y.y)((b a)(^z.a))) 8. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 9. ==[ beta ]==> ((b a)(^y.a)) 10. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 154679/16832541. ------ 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. ------ 154680/16832568. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(a a))(^b.(^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. ------ 154681/16832595. ------ 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. ------ 154682/16832622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a) a)(^y.b))) REDUCED to normal form. ------ 154683/16832649. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a (b a))(^y.(a a))) 6. ==[ alpha ]==> ((a (b a))(^x.(a a))) REDUCED to normal form. ------ 154684/16832739. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154685/16832820. ------ 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.(^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. ------ 154686/16832928. ------ 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. ------ 154687/16833009. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a b)(a b))(^y.y)) 8. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 154688/16833072. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 154689/16833090. ------ 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. ------ 154690/16833099. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(a ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a b)) REDUCED to normal form. ------ 154691/16833126. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 154692/16833153. ------ 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)(a (^x1.x1)))) REDUCED to normal form. ------ 154693/16833432. ------ 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 (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 154694/16833486. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 154695/16833576. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.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))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 154696/16833657. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.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) REDUCED to normal form. ------ 154697/16833819. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(x1 x1)))) 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. ------ 154698/16833954. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 154699/16833963. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((a a)(^z.z)))) REDUCED to normal form. ------ 154700/16833990. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b (b a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b (b a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (b a))) REDUCED to normal form. ------ 154701/16834017. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 154702/16834071. ------ 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 (^y1.y1)))) REDUCED to normal form. ------ 154703/16834323. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((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. ------ 154704/16834377. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(^z.a))) REDUCED to normal form. ------ 154705/16834404. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a 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. ------ 154706/16834413. ------ 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. ------ 154707/16834575. ------ 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. ------ 154708/16834683. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154709/16834737. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(^a.a))(^c.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. ------ 154710/16834764. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.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. ------ 154711/16834854. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(a (b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(a (b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (b a))) 5. ==[ beta ]==> ((^y.(a a))(a (b a))) 6. ==[ alpha ]==> ((^x.(a a))(a (b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154712/16834881. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 154713/16834908. ------ 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. ------ 154714/16834935. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 154715/16834962. ------ 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. ------ 154716/16835016. ------ 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. ------ 154717/16835043. ------ 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. ------ 154718/16835133. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (b a))(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 154719/16835160. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 154720/16835187. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.a))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.a))) 6. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.a))) 7. ==[ beta ]==> ((a a)((a b)(^y.a))) 8. ==[ alpha ]==> ((a a)((a b)(^x.a))) REDUCED to normal form. ------ 154721/16835214. ------ 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. ------ 154722/16835241. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(^a.a))(^b.(^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. ------ 154723/16835295. ------ 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) 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. ------ 154724/16835376. ------ 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 ]==> ((b (a a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 154725/16835403. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a)) b)) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a) b)) REDUCED to normal form. ------ 154726/16835439. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.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. ------ 154727/16835574. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 154728/16835718. ------ 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. ------ 154729/16835745. ------ 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. ------ 154730/16835790. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c (^x1.b))) 3. ==[ beta ]==> ((^y.y)(c (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(c (^y.b))) 5. ==[ beta ]==> (c (^y.b)) 6. ==[ alpha ]==> (c (^x.b)) REDUCED to normal form. ------ 154731/16835799. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a b))) REDUCED to normal form. ------ 154732/16835826. ------ 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)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 154733/16835844. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(a (^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 154734/16835925. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 154735/16836033. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 154736/16836294. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a)) a)) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 154737/16836321. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b) b)) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b) b)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b) b)) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 154738/16836573. ------ 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.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))((^z2.z2) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))((^z2.z2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154739/16836654. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 154740/16836762. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^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. ------ 154741/16836798. ------ 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. ------ 154742/16836825. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(c (^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)(c (^x.x))) REDUCED to normal form. ------ 154743/16836870. ------ 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 (^x.x))(^z.b)) 6. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 154744/16836933. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(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. ------ 154745/16836960. ------ 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. ------ 154746/16837032. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b (^z.a))) 3. ==[ beta ]==> (b (b (^z.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 154747/16837041. ------ 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. ------ 154748/16837140. ------ 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.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154749/16837266. ------ 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 (^x.x)))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y) b)) 5. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 154750/16837428. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y)) b)) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 154751/16837455. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 154752/16837563. ------ 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))(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^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. ------ 154753/16837590. ------ 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. ------ 154754/16837644. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 154755/16837734. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(^a.(^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. ------ 154756/16837815. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(^b.(^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. ------ 154757/16837923. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154758/16838058. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 154759/16838085. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154760/16838139. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^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. ------ 154761/16838148. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b ((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(b a)) REDUCED to normal form. ------ 154762/16838175. ------ 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. ------ 154763/16838220. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (^a.(^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. ------ 154764/16838229. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 154765/16838256. ------ 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)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 154766/16838328. ------ 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 (^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. ------ 154767/16838337. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b c)) REDUCED to normal form. ------ 154768/16838391. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (a a))) REDUCED to normal form. ------ 154769/16838445. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 154770/16838481. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^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. ------ 154771/16838508. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) c) REDUCED to normal form. ------ 154772/16838535. ------ 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.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. ------ 154773/16838562. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((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. ------ 154774/16838589. ------ 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.y1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1)) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 154775/16838616. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a) b)) REDUCED to normal form. ------ 154776/16838643. ------ 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)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 154777/16838670. ------ 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)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 154778/16838697. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.y))) REDUCED to normal form. ------ 154779/16838751. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 154780/16838777. ------ 1. ==[ start ]==> (^a.(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (^x.(((^y.y) b)(x (x x)))) 3. ==[ beta ]==> (^x.(b (x (x x)))) REDUCED to normal form. ------ 154781/16838778. ------ 1. ==[ start ]==> (a (((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (a (((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (a (b (a (a a)))) REDUCED to normal form. ------ 154782/16846530. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154783/16848828. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a))) a) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a))) a) 3. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 154784/16848834. ------ 1. ==[ start ]==> ((^a.a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.y) 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. ------ 154785/16848861. ------ 1. ==[ start ]==> ((^a.(a a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^x2.x2))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.z1))) REDUCED to normal form. ------ 154786/16848888. ------ 1. ==[ start ]==> ((^a.b)((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.b)((b a)((a a) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 154787/16848969. ------ 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 ]==> (((a b)((a a)(^z.z)))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 154788/16849329. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 154789/16849557. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 154790/16850211. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^y.y))))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((((a a) a)((a a)(^x.x)))(((a a) a)((a a)(^y.y))))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 154791/16850544. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 154792/16850736. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^c.(^d.(^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. ------ 154793/16851132. ------ 1. ==[ start ]==> (((a a)(a b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(b (^y.y)))) REDUCED to normal form. ------ 154794/16851318. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a b)(a b))) 3. ==[ beta ]==> ((^y.y)(((a b)(a b))((a b)(a b)))) 4. ==[ alpha ]==> ((^x.x)(((a b)(a b))((a b)(a b)))) 5. ==[ beta ]==> (((a b)(a b))((a b)(a b))) REDUCED to normal form. ------ 154795/16852203. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 154796/16853202. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 154797/16854120. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 154798/16854189. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154799/16854678. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 154800/16856172. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^b.((^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)))(^z.(a a))) REDUCED to normal form. ------ 154801/16856397. ------ 1. ==[ start ]==> (((a b)(a b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> (((a b)(a b))(^x.(x x))) REDUCED to normal form. ------ 154802/16856583. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a a)(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154803/16856586. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a b))) REDUCED to normal form. ------ 154804/16857171. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.b))) REDUCED to normal form. ------ 154805/16857504. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.((y y) y))) REDUCED to normal form. ------ 154806/16858278. ------ 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.(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154807/16858386. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 154808/16858467. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^y.a)) REDUCED to normal form. ------ 154809/16858548. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(^b.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. ------ 154810/16858563. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 154811/16858611. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 154812/16858746. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 154813/16858854. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(y1 y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(x1 x1))) REDUCED to normal form. ------ 154814/16858881. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 154815/16858893. ------ 1. ==[ start ]==> ((a a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a a)(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 154816/16858920. ------ 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. ------ 154817/16858947. ------ 1. ==[ start ]==> ((a b)((b a)((a a) a))) REDUCED to normal form. ------ 154818/16859001. ------ 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. ------ 154819/16859028. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 154820/16859163. ------ 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. ------ 154821/16859190. ------ 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. ------ 154822/16859226. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 154823/16859253. ------ 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.(^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. ------ 154824/16859307. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (a (((^y.y) b)(^z.(z z)))) 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. ------ 154825/16859316. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a (a a))) REDUCED to normal form. ------ 154826/16859334. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 154827/16859343. ------ 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.(^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. ------ 154828/16859388. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 154829/16859496. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 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. ------ 154830/16859523. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((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. ------ 154831/16859559. ------ 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. ------ 154832/16859586. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 154833/16859613. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 154834/16859631. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^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. ------ 154835/16859802. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 154836/16859937. ------ 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. ------ 154837/16859964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (a ((^y.a)(^z.(a a)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 154838/16860135. ------ 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)))(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. ------ 154839/16860162. ------ 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. ------ 154840/16860189. ------ 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)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 154841/16860216. ------ 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. ------ 154842/16860243. ------ 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. ------ 154843/16860270. ------ 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. ------ 154844/16860441. ------ 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. ------ 154845/16860468. ------ 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.(^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. ------ 154846/16860477. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 154847/16860504. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.b)((^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)))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 154848/16860522. ------ 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.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 154849/16860531. ------ 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. ------ 154850/16860603. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((a (^x.b))((a a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 154851/16860774. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 154852/16860873. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) b) c)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b) c)) IRREDUCIBLE: cycle. ------ 154853/16860963. ------ 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. ------ 154854/16860990. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 154855/16861044. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 154856/16861098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 154857/16861125. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 154858/16861152. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.a))(^c.(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. ------ 154859/16861188. ------ 1. ==[ start ]==> (((a a)(a b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(a (b (^x.x)))) REDUCED to normal form. ------ 154860/16861215. ------ 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. ------ 154861/16861242. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(b (a (^z.z)))) 8. ==[ alpha ]==> ((a (^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 154862/16861269. ------ 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. ------ 154863/16861296. ------ 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 (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(a (a a)))) 5. ==[ beta ]==> (((^y.y) a)((b a)(a (a a)))) 6. ==[ alpha ]==> (((^x.x) a)((b a)(a (a a)))) 7. ==[ beta ]==> (a ((b a)(a (a a)))) REDUCED to normal form. ------ 154864/16861323. ------ 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. ------ 154865/16861350. ------ 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))) 3. ==[ beta ]==> (((a b)(a a))((a a)((a a) a))) REDUCED to normal form. ------ 154866/16861377. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)(a b))) 3. ==[ beta ]==> ((a (a a))((a b)(a b))) REDUCED to normal form. ------ 154867/16861602. ------ 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.(^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)))) 7. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 154868/16861611. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(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. ------ 154869/16861629. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 154870/16861638. ------ 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)))((^z1.z1) 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. ------ 154871/16861683. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 11. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 12. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 154872/16861692. ------ 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. ------ 154873/16861719. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))((a a) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(a a))((a a) a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(a a))((a a) a))) 7. ==[ beta ]==> (((^y.(a a))((a a) a))((^y.(a a))((a a) a))) 8. ==[ alpha ]==> (((^x.(a a))((a a) a))((^y.(a a))((a a) a))) 9. ==[ beta ]==> ((a a)((^y.(a a))((a a) a))) 10. ==[ alpha ]==> ((a a)((^x.(a a))((a a) a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 154874/16861746. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 154875/16861764. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 154876/16861773. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 154877/16861800. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 154878/16861989. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 154879/16862232. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.a))(^b.b))) 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. ------ 154880/16862259. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a a) b)(^y.(a a))) 6. ==[ alpha ]==> (((a a) b)(^x.(a a))) REDUCED to normal form. ------ 154881/16862304. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b) 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)(^x.x)) b) REDUCED to normal form. ------ 154882/16862565. ------ 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.(^x1.x1))))) REDUCED to normal form. ------ 154883/16862592. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a a) b)) REDUCED to normal form. ------ 154884/16862898. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 154885/16862979. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((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. ------ 154886/16863042. ------ 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 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 154887/16863150. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 154888/16863177. ------ 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. ------ 154889/16863231. ------ 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))(^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. ------ 154890/16863258. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 154891/16863375. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(b a))((a a)(a (a a)))) REDUCED to normal form. ------ 154892/16863402. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 154893/16863429. ------ 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. ------ 154894/16863456. ------ 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. ------ 154895/16863483. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (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. ------ 154896/16863510. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 154897/16863537. ------ 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. ------ 154898/16863564. ------ 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))))) 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. ------ 154899/16863654. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154900/16863735. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((^x.(a 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. ------ 154901/16863816. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) a)(^c.(^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. ------ 154902/16863924. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 154903/16864041. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 154904/16864068. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 154905/16864122. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.a)(^c.(^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. ------ 154906/16864176. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 154907/16864248. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 154908/16864266. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 154909/16864293. ------ 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. ------ 154910/16864320. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 154911/16864347. ------ 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)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(^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))((^y.y)((a a) a))) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.x)((a a) a))) 7. ==[ beta ]==> (((a (a a))(a a))((a a) a)) REDUCED to normal form. ------ 154912/16864374. ------ 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. ------ 154913/16864401. ------ 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. ------ 154914/16864428. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 154915/16864455. ------ 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. ------ 154916/16864527. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 154917/16864572. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(z z)))) 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. ------ 154918/16864599. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a) a)(^b.(^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. ------ 154919/16864734. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(^z.a))) 3. ==[ beta ]==> (b ((a a)(^z.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 154920/16864851. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 154921/16864878. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.a)(^b.(^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)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 154922/16864905. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(^a.a))(^c.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. ------ 154923/16864932. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.b)(^z1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 154924/16865058. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 154925/16865238. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b)((a (^x.x))(a a))) REDUCED to normal form. ------ 154926/16865265. ------ 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)(^x1.x1)))) REDUCED to normal form. ------ 154927/16865598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((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. ------ 154928/16865841. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 154929/16865958. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c (^z.b))) REDUCED to normal form. ------ 154930/16865985. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b (^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b (^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(a a)))) REDUCED to normal form. ------ 154931/16866066. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 154932/16866084. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((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. ------ 154933/16866093. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 154934/16866147. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 10. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 154935/16866192. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154936/16866201. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(a 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. ------ 154937/16866228. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 154938/16866255. ------ 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 a)) REDUCED to normal form. ------ 154939/16866426. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(b (a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(b (a b))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (a b))) REDUCED to normal form. ------ 154940/16866453. ------ 1. ==[ start ]==> (((a b)(a b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(a ((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(a (a a))) REDUCED to normal form. ------ 154941/16866480. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b)(a a))) 3. ==[ beta ]==> (((a a)((a a) a))((a b)(a a))) REDUCED to normal form. ------ 154942/16866507. ------ 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. ------ 154943/16866561. ------ 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. ------ 154944/16866588. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b (a (^x.x)))(a (^z.z))) 8. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 154945/16866615. ------ 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))) REDUCED to normal form. ------ 154946/16866642. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 154947/16866732. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))(^z2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154948/16866813. ------ 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 (^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 154949/16866957. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> ((b c)((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> ((b c)((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> ((b c)((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> ((b c)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 154950/16866984. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.a)(^b.(^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. ------ 154951/16867056. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b) a)) 3. ==[ beta ]==> ((^y.y)((^z.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. ------ 154952/16867110. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1)) c)) 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. ------ 154953/16867200. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b (^y.a))) REDUCED to normal form. ------ 154954/16867227. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a (^z.b))) 3. ==[ beta ]==> (((a a)(^y.b))(a (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.b))) REDUCED to normal form. ------ 154955/16867299. ------ 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. ------ 154956/16867308. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^y1.y1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^y1.y1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^x1.x1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 154957/16867335. ------ 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. ------ 154958/16867362. ------ 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)(^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. ------ 154959/16867533. ------ 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. ------ 154960/16867560. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 154961/16867587. ------ 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. ------ 154962/16867614. ------ 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. ------ 154963/16867641. ------ 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.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. ------ 154964/16867695. ------ 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)(^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. ------ 154965/16867893. ------ 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. ------ 154966/16868199. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^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. ------ 154967/16868217. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((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. ------ 154968/16868244. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((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. ------ 154969/16868298. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z)) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z)) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z)) c)) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z)) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y)) c)) 7. ==[ beta ]==> ((b b)((a (^y.y)) c)) 8. ==[ alpha ]==> ((b b)((a (^x.x)) c)) REDUCED to normal form. ------ 154970/16868307. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^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. ------ 154971/16868334. ------ 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)(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154972/16868379. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.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. ------ 154973/16868388. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 154974/16868415. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (^b.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. ------ 154975/16868442. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.(z z)))) REDUCED to normal form. ------ 154976/16868487. ------ 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))(^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. ------ 154977/16868496. ------ 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 (^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. ------ 154978/16868523. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 154979/16868550. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 154980/16868604. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 154981/16868622. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a) a)) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 154982/16868640. ------ 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))) 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. ------ 154983/16868667. ------ 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. ------ 154984/16868721. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b b)) 3. ==[ beta ]==> (((a (a a)) b)(b b)) REDUCED to normal form. ------ 154985/16868775. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (a a))) REDUCED to normal form. ------ 154986/16868802. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 154987/16868829. ------ 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. ------ 154988/16868856. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b a)) REDUCED to normal form. ------ 154989/16868910. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a (a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (a a))) REDUCED to normal form. ------ 154990/16868937. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a a)) 3. ==[ beta ]==> ((b (a (a a)))(a a)) REDUCED to normal form. ------ 154991/16869273. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ eta ]==> ((^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. ------ 154992/16878678. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((^x.(^y.(y (^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.x1)) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 154993/16878996. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a))) b) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a))) b) 3. ==[ beta ]==> ((b (a (a a))) b) REDUCED to normal form. ------ 154994/16879020. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 154995/16879101. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 154996/16879263. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) 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 ]==> (^x.(a ((a a)(a a)))) REDUCED to normal form. ------ 154997/16879335. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.(z (^x1.x1))))) 3. ==[ eta ]==> ((^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. ------ 154998/16879338. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 154999/16879956. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(a a))(^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. ------ 155000/16880901. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))((a a)(a a))) b) 4. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 155001/16881288. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(b ((a a)(a a)))) 3. ==[ beta ]==> (^y.((b ((a a)(a a)))(b ((a a)(a a))))) 4. ==[ alpha ]==> (^x.((b ((a a)(a a)))(b ((a a)(a a))))) REDUCED to normal form. ------ 155002/16881669. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.((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. ------ 155003/16882038. ------ 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. ------ 155004/16882740. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 155005/16882926. ------ 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) REDUCED to normal form. ------ 155006/16883475. ------ 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))((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 155007/16883712. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 155008/16884366. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155009/16884603. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 155010/16884681. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155011/16885656. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 155012/16886124. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((b a)(b a))(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.((^y.y)(a a)))) 5. ==[ beta ]==> (((b a)(b a))(^x.(a a))) REDUCED to normal form. ------ 155013/16886349. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 155014/16886574. ------ 1. ==[ start ]==> (((a b)(a b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 155015/16886760. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b (^z.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 155016/16887177. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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)) REDUCED to normal form. ------ 155017/16887681. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 155018/16887843. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.z))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.y))) 5. ==[ beta ]==> ((b a)(^y.(^z.y))) 6. ==[ alpha ]==> ((b a)(^x.(^y.x))) REDUCED to normal form. ------ 155019/16887921. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)((^y1.y1) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155020/16888095. ------ 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. ------ 155021/16888644. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^b.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. ------ 155022/16888740. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 155023/16888743. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 155024/16888815. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.(^b.a))) 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. ------ 155025/16888869. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 155026/16888923. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 155027/16888977. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 155028/16889031. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^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))) REDUCED to normal form. ------ 155029/16889058. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 155030/16889088. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.x))(b (a (a a)))) REDUCED to normal form. ------ 155031/16889115. ------ 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 (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 155032/16889142. ------ 1. ==[ start ]==> (((^a.a)(a a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a a))((b a)((a a) a))) 3. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 155033/16889169. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 155034/16889223. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155035/16889250. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 155036/16889277. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(((^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))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^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. ------ 155037/16889304. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 155038/16889331. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 155039/16889403. ------ 1. ==[ start ]==> ((a ((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 155040/16889448. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 155041/16889475. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(a a))(^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. ------ 155042/16889502. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(y y)))) REDUCED to normal form. ------ 155043/16889529. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 155044/16889556. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b a)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 155045/16889619. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 155046/16889646. ------ 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. ------ 155047/16889745. ------ 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. ------ 155048/16889826. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 155049/16889853. ------ 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)) REDUCED to normal form. ------ 155050/16889916. ------ 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. ------ 155051/16889943. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 155052/16890024. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 155053/16890195. ------ 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. ------ 155054/16890249. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b (^z.z))(a a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 155055/16890492. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(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. ------ 155056/16890546. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> (a (((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> (a (((^x.x) a)((^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. ------ 155057/16890663. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 155058/16890690. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (^z.a))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.a))) REDUCED to normal form. ------ 155059/16890717. ------ 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. ------ 155060/16890744. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 155061/16890807. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))(a b))) 3. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 155062/16890834. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 155063/16890888. ------ 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. ------ 155064/16890915. ------ 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 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 155065/16890942. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 155066/16890960. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 155067/16890969. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 155068/16891329. ------ 1. ==[ start ]==> (((^a.b)(a a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a a))(c ((^y.y) b))) 3. ==[ beta ]==> (b (c ((^y.y) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 155069/16891356. ------ 1. ==[ start ]==> ((a (^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 155070/16891572. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(a b))) 3. ==[ beta ]==> ((^y.(a a))((a b)(a b))) 4. ==[ alpha ]==> ((^x.(a a))((a b)(a b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 155071/16891599. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((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. ------ 155072/16891653. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((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. ------ 155073/16891734. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 155074/16891770. ------ 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. ------ 155075/16891797. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 155076/16891824. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 155077/16891878. ------ 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. ------ 155078/16891932. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a b)(^y.b))) REDUCED to normal form. ------ 155079/16891959. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 155080/16892022. ------ 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)(a a))((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(b a))) 5. ==[ beta ]==> (((a a)(a a))((b a)(b a))) REDUCED to normal form. ------ 155081/16892049. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.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) REDUCED to normal form. ------ 155082/16892076. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a 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. ------ 155083/16892103. ------ 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. ------ 155084/16892157. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 155085/16892175. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 155086/16892184. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.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. ------ 155087/16892409. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 155088/16892490. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(b (a a))) REDUCED to normal form. ------ 155089/16892517. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(a (^z1.z1)))) 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. ------ 155090/16892526. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 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. ------ 155091/16892571. ------ 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)(^y.y))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 155092/16892652. ------ 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. ------ 155093/16892778. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a 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. ------ 155094/16892805. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(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. ------ 155095/16892832. ------ 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. ------ 155096/16892859. ------ 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)))(a (^y2.y2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155097/16892913. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 155098/16892940. ------ 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. ------ 155099/16892967. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.b)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 155100/16892994. ------ 1. ==[ start ]==> ((a (b a))((^c.a)(a b))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(a b))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 155101/16893435. ------ 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. ------ 155102/16893471. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z) a)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 155103/16893498. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 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. ------ 155104/16893543. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 155105/16893723. ------ 1. ==[ start ]==> (((a b)(a (a a)))(c (^d.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(c (^x.a))) REDUCED to normal form. ------ 155106/16893750. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b (^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. ------ 155107/16893777. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 155108/16893822. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 155109/16894119. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a) b)) REDUCED to normal form. ------ 155110/16894407. ------ 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))((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. ------ 155111/16894434. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 155112/16894614. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 155113/16894668. ------ 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. ------ 155114/16894713. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155115/16894749. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 155116/16895244. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((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. ------ 155117/16895253. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 155118/16895280. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 155119/16895352. ------ 1. ==[ start ]==> (((^a.(^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)(^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. ------ 155120/16895424. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 155121/16895451. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 155122/16895532. ------ 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 a)) REDUCED to normal form. ------ 155123/16895559. ------ 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. ------ 155124/16895586. ------ 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. ------ 155125/16895613. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 155126/16895640. ------ 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 y))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 155127/16895694. ------ 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.(^y1.y1))((^z1.z1)(a 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. ------ 155128/16895721. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))((^x.x)((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. ------ 155129/16895919. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(c (a b))) 3. ==[ beta ]==> (b (c (a b))) REDUCED to normal form. ------ 155130/16896027. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((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. ------ 155131/16896063. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a) d)) 3. ==[ beta ]==> ((b b)((^y.a) d)) 4. ==[ alpha ]==> ((b b)((^x.a) d)) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 155132/16896108. ------ 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. ------ 155133/16896135. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^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. ------ 155134/16896189. ------ 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)))) 5. ==[ beta ]==> (((b a)(b a))((a a)(a a))) REDUCED to normal form. ------ 155135/16896252. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 155136/16896279. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(^y.a))) REDUCED to normal form. ------ 155137/16896333. ------ 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. ------ 155138/16896387. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 155139/16896414. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 155140/16896441. ------ 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. ------ 155141/16896477. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)(^a.(^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. ------ 155142/16896504. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 155143/16896531. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 155144/16896558. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 155145/16896585. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 155146/16896612. ------ 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.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 155147/16896639. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)(^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. ------ 155148/16896828. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.b))) REDUCED to normal form. ------ 155149/16897143. ------ 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. ------ 155150/16897215. ------ 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. ------ 155151/16897242. ------ 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 b))) 4. ==[ alpha ]==> ((^x.x)(a (a b))) 5. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 155152/16897278. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) b)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 155153/16897296. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(a (^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.y1))) REDUCED to normal form. ------ 155154/16897305. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1)) c)) 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. ------ 155155/16897377. ------ 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 (^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. ------ 155156/16897494. ------ 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. ------ 155157/16897521. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.a))(a (^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.a))(a (^y.(y y)))) REDUCED to normal form. ------ 155158/16897548. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 155159/16897611. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 155160/16897638. ------ 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.(^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. ------ 155161/16897665. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))(^b.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. ------ 155162/16897692. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 155163/16897719. ------ 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)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 155164/16897881. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 155165/16897908. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 155166/16897935. ------ 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)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 155167/16897989. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 155168/16898160. ------ 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. ------ 155169/16898268. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155170/16898385. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 155171/16898484. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c (a (^z.z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c (a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c (a (^z.z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(c (a (^z.z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c (a (^y.y)))) 7. ==[ beta ]==> ((b b)(c (a (^y.y)))) 8. ==[ alpha ]==> ((b b)(c (a (^x.x)))) REDUCED to normal form. ------ 155172/16898493. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y)) c)) REDUCED to normal form. ------ 155173/16898565. ------ 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. ------ 155174/16898574. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 155175/16898601. ------ 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)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 155176/16898682. ------ 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))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 155177/16898709. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^b.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. ------ 155178/16898736. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 155179/16898808. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 155180/16898853. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 155181/16898880. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(a (^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. ------ 155182/16898907. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^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. ------ 155183/16898934. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 155184/16898961. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 155185/16898988. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 155186/16899015. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 155187/16899042. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 155188/16899096. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 155189/16899123. ------ 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. ------ 155190/16908873. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(^b.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. ------ 155191/16909191. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a))) c) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a))) c) 3. ==[ beta ]==> ((b (a (a a))) c) REDUCED to normal form. ------ 155192/16909551. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 155193/16909956. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^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. ------ 155194/16910034. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155195/16910370. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x) a)(^y.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))) REDUCED to normal form. ------ 155196/16910925. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(^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. ------ 155197/16911105. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a (^y.y))(^z.(a a))) b) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 155198/16911492. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.(a a)))((^z.(^x1.x1))(^y1.(a a))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.(a a)))((^y1.(^z1.z1))(^x2.(a a))))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(^x2.(a a))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.(a a))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.(a a)))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(a a)))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155199/16911882. ------ 1. ==[ start ]==> (((a b) b)(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) b)(^x.((a a)(a a)))) REDUCED to normal form. ------ 155200/16912611. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.((y y)(y y)))) REDUCED to normal form. ------ 155201/16913130. ------ 1. ==[ start ]==> ((^a.(b a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.(b x))(((a a) a)(^y.b))) 3. ==[ eta ]==> (b (((a a) a)(^y.b))) 4. ==[ alpha ]==> (b (((a a) a)(^x.b))) REDUCED to normal form. ------ 155202/16913610. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.a))(^y.b)) REDUCED to normal form. ------ 155203/16913967. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(^x1.(^y1.y1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((b a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 155204/16914885. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155205/16915365. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^a.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(b y))) 3. ==[ eta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 155206/16915860. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(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. ------ 155207/16915884. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.((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)(((a a)(^y.y)) a))) 4. ==[ alpha ]==> (((((a a)(^x.x)) a)(((a a)(^y.y)) a))((((a a)(^z.z)) a)(((a a)(^x1.x1)) a))) REDUCED to normal form. ------ 155208/16917381. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 155209/16917552. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((a a) a))) REDUCED to normal form. ------ 155210/16918125. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)(^y1.a))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155211/16918569. ------ 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))) REDUCED to normal form. ------ 155212/16918767. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 155213/16918944. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 155214/16918947. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.a))) REDUCED to normal form. ------ 155215/16919019. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.c)) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.c)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.c)) REDUCED to normal form. ------ 155216/16919127. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 155217/16919181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 155218/16919262. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.x) b)(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. ------ 155219/16919310. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (a (((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> (a (((^x.x) b)(a (a a)))) 5. ==[ beta ]==> (a (b (a (a a)))) REDUCED to normal form. ------ 155220/16919337. ------ 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. ------ 155221/16919364. ------ 1. ==[ start ]==> (((a a)(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 155222/16919391. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x) b)(((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. ------ 155223/16919418. ------ 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)(((^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. ------ 155224/16919445. ------ 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. ------ 155225/16919472. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a) a)(b a))) REDUCED to normal form. ------ 155226/16919499. ------ 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))(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. ------ 155227/16919526. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a (a a)) b)) REDUCED to normal form. ------ 155228/16919580. ------ 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)((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. ------ 155229/16919625. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.a)(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 155230/16919733. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 155231/16919805. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 155232/16919832. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 155233/16919859. ------ 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. ------ 155234/16919922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155235/16919976. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.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. ------ 155236/16920003. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (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. ------ 155237/16920030. ------ 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)((^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. ------ 155238/16920111. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 155239/16920246. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155240/16920273. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 155241/16920327. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 155242/16920381. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(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. ------ 155243/16920390. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((a a)(a a)))) REDUCED to normal form. ------ 155244/16920417. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b (b (^z.z)))) REDUCED to normal form. ------ 155245/16920444. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.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. ------ 155246/16920471. ------ 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. ------ 155247/16920498. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 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. ------ 155248/16920795. ------ 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)))) REDUCED to normal form. ------ 155249/16920822. ------ 1. ==[ start ]==> ((((a a) a) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a a)(b (^x.x)))) REDUCED to normal form. ------ 155250/16920921. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.b)((^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)((^y.y) a)) 10. ==[ alpha ]==> ((a a)((^x.x) a)) 11. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 155251/16921002. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 155252/16921020. ------ 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))) 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. ------ 155253/16921047. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.(a a)))) REDUCED to normal form. ------ 155254/16921128. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 155255/16921155. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) 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. ------ 155256/16921182. ------ 1. ==[ start ]==> ((a (a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 155257/16921191. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155258/16921380. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 155259/16921407. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.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. ------ 155260/16921542. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 155261/16921551. ------ 1. ==[ start ]==> (((a b)(^a.a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.x))(c ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.x))(c b)) REDUCED to normal form. ------ 155262/16921569. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 155263/16921668. ------ 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. ------ 155264/16921740. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((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. ------ 155265/16921947. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (b (b (^x1.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 155266/16921956. ------ 1. ==[ start ]==> (((a b) b)((a a)((a a)(a a)))) REDUCED to normal form. ------ 155267/16922028. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(a (^x1.x1)))) 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. ------ 155268/16922163. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 155269/16922262. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 155270/16922289. ------ 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))) REDUCED to normal form. ------ 155271/16922343. ------ 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. ------ 155272/16922370. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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)) 5. ==[ beta ]==> ((((a a) a) a)(b b)) REDUCED to normal form. ------ 155273/16922397. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 155274/16922487. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 155275/16922622. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 155276/16922631. ------ 1. ==[ start ]==> (((a b) c)(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 155277/16922658. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(b ((^y.y) b))) 3. ==[ beta ]==> (((a a) b)(b ((^y.y) b))) 4. ==[ alpha ]==> (((a a) b)(b ((^x.x) b))) 5. ==[ beta ]==> (((a a) b)(b b)) REDUCED to normal form. ------ 155278/16922685. ------ 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. ------ 155279/16922739. ------ 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)))(a (^y1.y1)))) REDUCED to normal form. ------ 155280/16922766. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b a)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.b))((b a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.b))((b a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.b))((b a) a)) REDUCED to normal form. ------ 155281/16922820. ------ 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)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155282/16922847. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a b)((a a) a))) REDUCED to normal form. ------ 155283/16922874. ------ 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. ------ 155284/16922901. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a a))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a a))) 9. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 155285/16922928. ------ 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)))) REDUCED to normal form. ------ 155286/16923045. ------ 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. ------ 155287/16923072. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 155288/16923099. ------ 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. ------ 155289/16923126. ------ 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))(^z.(z z)))) 3. ==[ beta ]==> (((a b) a)(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 155290/16923153. ------ 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. ------ 155291/16923180. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a b)(^y.a))) REDUCED to normal form. ------ 155292/16923207. ------ 1. ==[ start ]==> ((a (b a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((a (b a))(((a a) a)(^x.b))) REDUCED to normal form. ------ 155293/16923297. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(b a))) 5. ==[ beta ]==> (b ((^z.a)(b a))) 6. ==[ alpha ]==> (b ((^x.a)(b a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 155294/16923378. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 155295/16923486. ------ 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. ------ 155296/16923513. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.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. ------ 155297/16923567. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 155298/16923630. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (b a))) REDUCED to normal form. ------ 155299/16923648. ------ 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. ------ 155300/16923657. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 155301/16923684. ------ 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))) 5. ==[ beta ]==> (((a a)(^x.a))(a b)) REDUCED to normal form. ------ 155302/16923711. ------ 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 (^x1.(^y1.y1)))(a a))) REDUCED to normal form. ------ 155303/16923774. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y)) d)) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 155304/16924044. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 155305/16924134. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 155306/16924215. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((^y1.y1)(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. ------ 155307/16924323. ------ 1. ==[ start ]==> (((^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.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. ------ 155308/16924377. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 155309/16924431. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 155310/16924512. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(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. ------ 155311/16924575. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (b a))) REDUCED to normal form. ------ 155312/16924629. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a)(a a))) REDUCED to normal form. ------ 155313/16924935. ------ 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. ------ 155314/16924962. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) 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))) 5. ==[ beta ]==> ((a b)((a a)(^y.a))) 6. ==[ alpha ]==> ((a b)((a a)(^x.a))) REDUCED to normal form. ------ 155315/16924971. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a))((^a.a) 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. ------ 155316/16924998. ------ 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. ------ 155317/16925133. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 155318/16925241. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(a a))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155319/16925295. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.a)(^b.(^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)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 155320/16925322. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^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. ------ 155321/16925376. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 155322/16925412. ------ 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. ------ 155323/16925439. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(a (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(a (b a))) REDUCED to normal form. ------ 155324/16925466. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 155325/16925493. ------ 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. ------ 155326/16925520. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a b) a)) REDUCED to normal form. ------ 155327/16925574. ------ 1. ==[ start ]==> (((a (^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)(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.x2))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 155328/16925601. ------ 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. ------ 155329/16925718. ------ 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))(^z.z))) REDUCED to normal form. ------ 155330/16925745. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^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. ------ 155331/16925772. ------ 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. ------ 155332/16925799. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 155333/16925826. ------ 1. ==[ start ]==> ((((^a.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)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 155334/16925907. ------ 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 (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 155335/16925934. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a a)(^c.(^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. ------ 155336/16925961. ------ 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. ------ 155337/16925997. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 155338/16926132. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 155339/16926276. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((b b)(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> ((b b)(((a a) a)((^x.x) a))) 5. ==[ beta ]==> ((b b)(((a a) a) a)) REDUCED to normal form. ------ 155340/16926303. ------ 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. ------ 155341/16926357. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^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. ------ 155342/16926384. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (^y1.y1))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a b))) REDUCED to normal form. ------ 155343/16926402. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b (^y.(a a)))) 3. ==[ beta ]==> (((b a)(b a))(b (^y.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(b (^x.(a a)))) REDUCED to normal form. ------ 155344/16926483. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 155345/16926591. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.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. ------ 155346/16926690. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b) b)) REDUCED to normal form. ------ 155347/16926717. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a) c)) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a) c)) REDUCED to normal form. ------ 155348/16926879. ------ 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)) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 155349/16926906. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 155350/16927212. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 155351/16927428. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^a.a))(^c.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. ------ 155352/16927455. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.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. ------ 155353/16927491. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((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. ------ 155354/16927518. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 155355/16927590. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 155356/16927599. ------ 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. ------ 155357/16927626. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)((a a) a))) REDUCED to normal form. ------ 155358/16927698. ------ 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 (^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. ------ 155359/16927824. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 155360/16927851. ------ 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)(^z.z)) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 155361/16927878. ------ 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. ------ 155362/16927986. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a) a)) 3. ==[ beta ]==> (((a b)(a a))((^y.a) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.a) a)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 155363/16928013. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 155364/16928148. ------ 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))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.z))) 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. ------ 155365/16928202. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 155366/16928292. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(^a.a))) 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. ------ 155367/16928373. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^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. ------ 155368/16928481. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (^b.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. ------ 155369/16928616. ------ 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.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. ------ 155370/16928643. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 155371/16928697. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.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. ------ 155372/16928706. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (a (^y.y)))) REDUCED to normal form. ------ 155373/16928733. ------ 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 ((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b ((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b ((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b ((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.x1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155374/16928787. ------ 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. ------ 155375/16928814. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 155376/16928841. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a a) a)) REDUCED to normal form. ------ 155377/16928886. ------ 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. ------ 155378/16928895. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c b)) REDUCED to normal form. ------ 155379/16928922. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b c)) 3. ==[ beta ]==> ((b (^y.(y y)))(b c)) 4. ==[ alpha ]==> ((b (^x.(x x)))(b c)) REDUCED to normal form. ------ 155380/16929003. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 155381/16929021. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.a)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 155382/16929039. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 155383/16929066. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^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. ------ 155384/16929120. ------ 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)) b)((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 155385/16929147. ------ 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)(^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. ------ 155386/16929174. ------ 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. ------ 155387/16929201. ------ 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. ------ 155388/16929228. ------ 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.(^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)(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. ------ 155389/16929255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) b) REDUCED to normal form. ------ 155390/16929309. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a) a)) REDUCED to normal form. ------ 155391/16929336. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.y) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x) a)) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 155392/16929362. ------ 1. ==[ start ]==> (^a.(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (^x.(((x x)(x x))((^y.y) x))) 3. ==[ beta ]==> (^x.(((x x)(x x)) x)) REDUCED to normal form. ------ 155393/16929363. ------ 1. ==[ start ]==> (a (((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (a (((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> (a (((a a)(a a)) a)) REDUCED to normal form. ------ 155394/16939440. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a)) a) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a)) a) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 155395/16939446. ------ 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)) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 155396/16939473. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((((^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)))) 5. ==[ beta ]==> ((b (a (a a)))(((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> ((b (a (a a)))(((^x.x) b)(a (a a)))) 7. ==[ beta ]==> ((b (a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 155397/16939500. ------ 1. ==[ start ]==> ((^a.b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 155398/16939581. ------ 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)(a a)))) 3. ==[ beta ]==> ((((^z.z)(a a))((^x1.x1)(a a)))(^y.y)) 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. ------ 155399/16939770. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)((^z.(^x1.x1)) a))) 3. ==[ eta ]==> ((^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. ------ 155400/16939941. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 155401/16940196. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 155402/16940265. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a)) c)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155403/16940823. ------ 1. ==[ start ]==> ((^a.((a a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a b)((^y.y)(a a)))((a b)((^y.y)(a a))))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a b)((^x.x)(a a)))((a b)((^y.y)(a a))))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((((a b)(a a))((a b)((^y.y)(a a))))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a b)(a a))((a b)((^x.x)(a a))))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a b)(a a))((a b)(a a)))((a b)((^y.y)(a a)))) 8. ==[ alpha ]==> ((((a b)(a a))((a b)(a a)))((a b)((^x.x)(a a)))) 9. ==[ beta ]==> ((((a b)(a a))((a b)(a a)))((a b)(a a))) REDUCED to normal form. ------ 155404/16941156. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 155405/16941771. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 155406/16941930. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(a a))((a a) a))(((^z.z)(a a))((a a) a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(a a))((a a) a))(((^z.z)(a a))((a a) a)))) 5. ==[ beta ]==> ((((^y.y)(a a))((a a) a))(((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a))((a a) a))) 7. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a))((a a) a))) 8. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))((a a) a))) 9. ==[ beta ]==> (((a a)((a a) a))((a a)((a a) a))) REDUCED to normal form. ------ 155407/16942842. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.(a a)))) REDUCED to normal form. ------ 155408/16943175. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a (a b))(^y.((^z.z) b))) 4. ==[ alpha ]==> ((a (a b))(^x.((^y.y) b))) 5. ==[ beta ]==> ((a (a b))(^x.b)) REDUCED to normal form. ------ 155409/16943841. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 155410/16945848. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 155411/16946811. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^b.((^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))(^y.(a a))) REDUCED to normal form. ------ 155412/16947036. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> (((a a)((a a) a))(^x.(x x))) REDUCED to normal form. ------ 155413/16947195. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 155414/16948143. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.((y y) y))) 3. ==[ beta ]==> (((a b)(a a))(^y.((y y) y))) 4. ==[ alpha ]==> (((a b)(a a))(^x.((x x) x))) REDUCED to normal form. ------ 155415/16948278. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.((^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)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(^x.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 155416/16948800. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 155417/16949106. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 155418/16949196. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a a)((^x.(^y.y)) a))(^x1.x1)) 4. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 155419/16949331. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.c)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.c)) REDUCED to normal form. ------ 155420/16949385. ------ 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)(a a))(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 155421/16949412. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(a a))) REDUCED to normal form. ------ 155422/16949466. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.b)) REDUCED to normal form. ------ 155423/16949493. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(y y))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(y y))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(x x))) REDUCED to normal form. ------ 155424/16949520. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 155425/16949532. ------ 1. ==[ start ]==> ((a a)(((a a)(a a))((^a.a) 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. ------ 155426/16949559. ------ 1. ==[ start ]==> ((a (a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((a (a a))(b (a (a a)))) REDUCED to normal form. ------ 155427/16949586. ------ 1. ==[ start ]==> ((a b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 155428/16949640. ------ 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. ------ 155429/16949667. ------ 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. ------ 155430/16949802. ------ 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. ------ 155431/16949820. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 155432/16949829. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 155433/16949856. ------ 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. ------ 155434/16949892. ------ 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)(((^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. ------ 155435/16949946. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 155436/16949955. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 155437/16949973. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(y1 y1)))) 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. ------ 155438/16949982. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 155439/16950009. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 155440/16950027. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 155441/16950117. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 155442/16950162. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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. ------ 155443/16950198. ------ 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. ------ 155444/16950225. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 155445/16950252. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 155446/16950279. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 155447/16950324. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 155448/16950351. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a)) c)) REDUCED to normal form. ------ 155449/16950576. ------ 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. ------ 155450/16950603. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a a))(^b.b))) 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))) 7. ==[ beta ]==> (a ((^y.y)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 155451/16950630. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 155452/16950774. ------ 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.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. ------ 155453/16950801. ------ 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. ------ 155454/16950828. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 155455/16950855. ------ 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. ------ 155456/16950882. ------ 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. ------ 155457/16950909. ------ 1. ==[ start ]==> ((a ((a a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a b)(a a))) REDUCED to normal form. ------ 155458/16951035. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c (^z.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.(a a)))) 5. ==[ beta ]==> (b (c (^y.(a a)))) 6. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 155459/16951107. ------ 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)((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. ------ 155460/16951161. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(^z.a))) 7. ==[ beta ]==> ((a a)(((^y.y) b)(^z.a))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.a))) 9. ==[ beta ]==> ((a a)(b (^y.a))) 10. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 155461/16951170. ------ 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. ------ 155462/16951197. ------ 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.(^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. ------ 155463/16951242. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 155464/16951413. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 155465/16951431. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155466/16951512. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a)) b)) IRREDUCIBLE: cycle. ------ 155467/16951575. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 155468/16951629. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 155469/16951683. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 155470/16951764. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 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. ------ 155471/16951791. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 155472/16951827. ------ 1. ==[ start ]==> (((a a)(a b))(b ((a a)(a a)))) REDUCED to normal form. ------ 155473/16951854. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(a (b (^y.y)))) REDUCED to normal form. ------ 155474/16951881. ------ 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))(a a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))(a a))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(a a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(a a))) REDUCED to normal form. ------ 155475/16951908. ------ 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. ------ 155476/16951935. ------ 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)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (a ((a (^y.(^z.z)))((^x1.x1) a))) 8. ==[ alpha ]==> (a ((a (^x.(^y.y)))((^z.z) a))) 9. ==[ beta ]==> (a ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 155477/16951962. ------ 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. ------ 155478/16951989. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 155479/16952016. ------ 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))) 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. ------ 155480/16952196. ------ 1. ==[ start ]==> (((a b) b)(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b) b)(b (^x.(a a)))) REDUCED to normal form. ------ 155481/16952241. ------ 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))(^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. ------ 155482/16952250. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 155483/16952268. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 155484/16952277. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b)(a (^a.a)))) 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. ------ 155485/16952322. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.(x1 x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.(x1 x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(z z)))) 9. ==[ beta ]==> ((^y.y)((b a)(^z.(z z)))) 10. ==[ alpha ]==> ((^x.x)((b a)(^y.(y y)))) 11. ==[ beta ]==> ((b a)(^y.(y y))) 12. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 155486/16952385. ------ 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 a)) REDUCED to normal form. ------ 155487/16952403. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> (b ((a b)(^z.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 155488/16952412. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 155489/16952628. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 155490/16952871. ------ 1. ==[ start ]==> (((a b) c)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 155491/16952898. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 155492/16952970. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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) 7. ==[ beta ]==> b REDUCED to normal form. ------ 155493/16953204. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (b a))) REDUCED to normal form. ------ 155494/16953231. ------ 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.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))))) REDUCED to normal form. ------ 155495/16953258. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a a)((^y.y) b))) 3. ==[ beta ]==> ((a (a b))((a a)((^y.y) b))) 4. ==[ alpha ]==> ((a (a b))((a a)((^x.x) b))) 5. ==[ beta ]==> ((a (a b))((a a) b)) REDUCED to normal form. ------ 155496/16953618. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^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. ------ 155497/16953789. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.b))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 155498/16953816. ------ 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. ------ 155499/16953897. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 155500/16953924. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.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. ------ 155501/16954014. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))((^y.y) a))) 3. ==[ beta ]==> (((a a)(b a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 155502/16954041. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 155503/16954068. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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. ------ 155504/16954095. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 155505/16954122. ------ 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)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> (((a a) a)((^y.y)(a b))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(a b))) 9. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 155506/16954149. ------ 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.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. ------ 155507/16954176. ------ 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. ------ 155508/16954203. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.z))(b a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))(b a))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(b a))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(b a))) REDUCED to normal form. ------ 155509/16954230. ------ 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 (^z.(^x1.x1))))) REDUCED to normal form. ------ 155510/16954275. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^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. ------ 155511/16954293. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155512/16954374. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 155513/16954455. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 155514/16954563. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 155515/16954572. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1)))(^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. ------ 155516/16954590. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a) b)) REDUCED to normal form. ------ 155517/16954617. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a)(^z.z)) c)) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z)) 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. ------ 155518/16954680. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 155519/16954707. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.b)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(^z.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 155520/16954761. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 155521/16954788. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 155522/16954860. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 155523/16954905. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 155524/16954932. ------ 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))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x))(b a))((a a) a)) REDUCED to normal form. ------ 155525/16954959. ------ 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. ------ 155526/16954986. ------ 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)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a) a)((^x.x)(^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. ------ 155527/16955013. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 155528/16955040. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (a a))(a b))) REDUCED to normal form. ------ 155529/16955067. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)(^x.x))(a ((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)(^x.x))(a (a a))) REDUCED to normal form. ------ 155530/16955094. ------ 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 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)))) REDUCED to normal form. ------ 155531/16955121. ------ 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)(^x.x)) a)((a a)(b a))) REDUCED to normal form. ------ 155532/16955211. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(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. ------ 155533/16955238. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z1.(z1 z1)))) 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. ------ 155534/16955373. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 155535/16955490. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 155536/16955517. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((b a)((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((b a)((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 155537/16955544. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 155538/16955571. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.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. ------ 155539/16955652. ------ 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.(^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 a) REDUCED to normal form. ------ 155540/16955877. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)(a b))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)(a b))) 5. ==[ beta ]==> (((a a) b)(a (a b))) REDUCED to normal form. ------ 155541/16955904. ------ 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 (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 155542/16955931. ------ 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. ------ 155543/16956237. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(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. ------ 155544/16956480. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 155545/16956705. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 155546/16956723. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 155547/16956732. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 155548/16956786. ------ 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. ------ 155549/16956840. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 155550/16956867. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 155551/16956894. ------ 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)(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. ------ 155552/16957092. ------ 1. ==[ start ]==> (((a b)(a b))(b (a b))) REDUCED to normal form. ------ 155553/16957119. ------ 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.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. ------ 155554/16957146. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(a a))) REDUCED to normal form. ------ 155555/16957200. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^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. ------ 155556/16957227. ------ 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. ------ 155557/16957254. ------ 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)(^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. ------ 155558/16957281. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 155559/16957371. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a)(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155560/16957452. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 155561/16957560. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((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. ------ 155562/16957596. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 155563/16957623. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.(y y))(^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 155564/16957839. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 155565/16957866. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.a))) REDUCED to normal form. ------ 155566/16957938. ------ 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.(^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. ------ 155567/16957947. ------ 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 (^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. ------ 155568/16957974. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.a))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> ((b (^x.a))(a ((^z.z) a))) 8. ==[ alpha ]==> ((b (^x.a))(a ((^y.y) a))) 9. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 155569/16958001. ------ 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. ------ 155570/16958172. ------ 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. ------ 155571/16958199. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 155572/16958226. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a ((a a) a))) 3. ==[ beta ]==> (((a b)(a a))(a ((a a) a))) REDUCED to normal form. ------ 155573/16958253. ------ 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. ------ 155574/16958280. ------ 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. ------ 155575/16958334. ------ 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. ------ 155576/16958361. ------ 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 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. ------ 155577/16958532. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1)) 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. ------ 155578/16958613. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1)) d)) 3. ==[ beta ]==> (b ((a (^x1.x1)) d)) 4. ==[ alpha ]==> (b ((a (^x.x)) d)) REDUCED to normal form. ------ 155579/16958721. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.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. ------ 155580/16958838. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 155581/16958856. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((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. ------ 155582/16958883. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 x1)))) 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. ------ 155583/16958937. ------ 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. ------ 155584/16958946. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.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. ------ 155585/16958973. ------ 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))))((^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. ------ 155586/16959018. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> (b ((^z.(z z)) a)) 4. ==[ alpha ]==> (b ((^x.(x x)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 155587/16959027. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (^z.z))) REDUCED to normal form. ------ 155588/16959054. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^a.(^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. ------ 155589/16959081. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.a))) REDUCED to normal form. ------ 155590/16959126. ------ 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)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155591/16959135. ------ 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))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 155592/16959162. ------ 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 (^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. ------ 155593/16959189. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 155594/16959243. ------ 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)(^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. ------ 155595/16959279. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 155596/16959306. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 155597/16959333. ------ 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. ------ 155598/16959360. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c a)) 3. ==[ beta ]==> (((a (a a)) b)(c a)) REDUCED to normal form. ------ 155599/16959387. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 155600/16959414. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a c)) REDUCED to normal form. ------ 155601/16959441. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (a a))) REDUCED to normal form. ------ 155602/16959468. ------ 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. ------ 155603/16959495. ------ 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. ------ 155604/16959549. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a b)) REDUCED to normal form. ------ 155605/16959576. ------ 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. ------ 155606/16959603. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) 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. ------ 155607/16966284. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((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)))(^y.((a a)(^z.z))))) 4. ==[ alpha ]==> (((^x.((a a)(^y.y)))(^z.((a a)(^x1.x1))))((^y1.((a a)(^z1.z1)))(^x2.((a a)(^y2.y2))))) 5. ==[ beta ]==> (((a a)(^y.y))((^y1.((a a)(^z1.z1)))(^x2.((a a)(^y2.y2))))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.((a a)(^z.z)))(^x1.((a a)(^y1.y1))))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 155608/16969689. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a)) b) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a)) b) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 155609/16969713. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155610/16969794. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155611/16969956. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (^y.((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (^x.((a (a a))((^y.y) b))) 5. ==[ beta ]==> (^x.((a (a a)) b)) REDUCED to normal form. ------ 155612/16970040. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^c.((^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. ------ 155613/16970298. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.b)((a a)(^z.z)))(((^y.b)((a a)(^z.z)))((^y.b)((a a)(^z.z))))) 4. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.b)((a a)(^x1.x1)))((^y1.b)((a a)(^z1.z1))))) 5. ==[ beta ]==> (b (((^z.b)((a a)(^x1.x1)))((^y1.b)((a a)(^z1.z1))))) 6. ==[ alpha ]==> (b (((^x.b)((a a)(^y.y)))((^z.b)((a a)(^x1.x1))))) 7. ==[ beta ]==> (b (b ((^z.b)((a a)(^x1.x1))))) 8. ==[ alpha ]==> (b (b ((^x.b)((a a)(^y.y))))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 155614/16970877. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(x x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 155615/16971594. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((^y.a)((^z.z) b)) b) 4. ==[ alpha ]==> (((^x.a)((^y.y) b)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 155616/16971981. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c ((^z.z) b))) 3. ==[ beta ]==> (^y.((c ((^z.z) b))(c ((^z.z) b)))) 4. ==[ alpha ]==> (^x.((c ((^y.y) b))(c ((^z.z) b)))) 5. ==[ beta ]==> (^x.((c b)(c ((^z.z) b)))) 6. ==[ alpha ]==> (^x.((c b)(c ((^y.y) b)))) 7. ==[ beta ]==> (^x.((c b)(c b))) REDUCED to normal form. ------ 155617/16972758. ------ 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. ------ 155618/16973118. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((y y)(y y)))) REDUCED to normal form. ------ 155619/16973619. ------ 1. ==[ start ]==> ((^a.(b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.b)((a a) a))) 3. ==[ eta ]==> (b ((^y.b)((a a) a))) 4. ==[ alpha ]==> (b ((^x.b)((a a) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 155620/16974168. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 155621/16974456. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1)))(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^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. ------ 155622/16975035. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 155623/16975059. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155624/16975374. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155625/16975872. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(b y))) 3. ==[ eta ]==> (((^x.b)((a a) a)) b) 4. ==[ beta ]==> (b b) REDUCED to normal form. ------ 155626/16976373. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((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)))((^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)))((^x2.x2)((a a)(^y2.y2))))) 5. ==[ beta ]==> ((((a a)(^y.y))((^z.z)((a a)(^x1.x1))))(((^y1.y1)((a a)(^z1.z1)))((^x2.x2)((a a)(^y2.y2))))) 6. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)((a a)(^z.z))))(((^x1.x1)((a a)(^y1.y1)))((^z1.z1)((a a)(^x2.x2))))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^z.z)))(((^x1.x1)((a a)(^y1.y1)))((^z1.z1)((a a)(^x2.x2))))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)((a a)(^x1.x1)))((^y1.y1)((a a)(^z1.z1))))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^x1.x1))((^y1.y1)((a a)(^z1.z1))))) 10. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))((^x1.x1)((a a)(^y1.y1))))) 11. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))((a a)(^y1.y1)))) 12. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 155627/16976376. ------ 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. ------ 155628/16977294. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 155629/16977453. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c (^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c (^z.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 155630/16978239. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 155631/16978401. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.a))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.a))) REDUCED to normal form. ------ 155632/16978614. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155633/16979193. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(z (z z)))) 3. ==[ beta ]==> (b (^z.(z (z z)))) 4. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 155634/16979364. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 155635/16979433. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (a (^x1.x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 155636/16979454. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^b.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. ------ 155637/16979535. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^b.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. ------ 155638/16979589. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 155639/16979643. ------ 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.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 155640/16979724. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(a a))) REDUCED to normal form. ------ 155641/16979751. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 155642/16979778. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 155643/16979808. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((a (^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 155644/16979835. ------ 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. ------ 155645/16979862. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^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. ------ 155646/16979889. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 155647/16979943. ------ 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)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155648/16979970. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^x1.x1)))) 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. ------ 155649/16979997. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 155650/16980024. ------ 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 (^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. ------ 155651/16980051. ------ 1. ==[ start ]==> ((a (^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (^x.a))((a (a a)) b)) REDUCED to normal form. ------ 155652/16980132. ------ 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 REDUCED to normal form. ------ 155653/16980168. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.(^z.z)) a)(^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. ------ 155654/16980195. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((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. ------ 155655/16980222. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 155656/16980249. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 155657/16980276. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 155658/16980366. ------ 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. ------ 155659/16980384. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a 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. ------ 155660/16980393. ------ 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. ------ 155661/16980465. ------ 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. ------ 155662/16980573. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 155663/16980600. ------ 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. ------ 155664/16980663. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^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. ------ 155665/16980690. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 155666/16980969. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a ((^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. ------ 155667/16981212. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^y1.y1)))) 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. ------ 155668/16981266. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (a ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 155669/16981347. ------ 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. ------ 155670/16981383. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 155671/16981410. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 155672/16981437. ------ 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. ------ 155673/16981464. ------ 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 (^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. ------ 155674/16981491. ------ 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. ------ 155675/16981554. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(a b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 155676/16981581. ------ 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. ------ 155677/16981635. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 155678/16981662. ------ 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 (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 155679/16981680. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.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. ------ 155680/16981689. ------ 1. ==[ start ]==> ((a (a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((^y.y) b))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 155681/16982076. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c ((^y.y) b))) 3. ==[ beta ]==> ((a (^x.(a a)))(c b)) REDUCED to normal form. ------ 155682/16982094. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.a))(^c.(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. ------ 155683/16982292. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 155684/16982319. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 155685/16982373. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 9. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 10. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 155686/16982454. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (b ((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 155687/16982517. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 155688/16982544. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 155689/16982598. ------ 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. ------ 155690/16982625. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(^y.y))(^z.(^x1.x1)))(((a a)(^y.y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 155691/16982652. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 155692/16982679. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.b))) REDUCED to normal form. ------ 155693/16982706. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 155694/16982742. ------ 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)(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. ------ 155695/16982769. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((b a)(b a))) REDUCED to normal form. ------ 155696/16982796. ------ 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.(^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) REDUCED to normal form. ------ 155697/16982823. ------ 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. ------ 155698/16982850. ------ 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. ------ 155699/16982895. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 155700/16982904. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 155701/16982931. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 155702/16983210. ------ 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. ------ 155703/16983237. ------ 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)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 155704/16983246. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 155705/16983273. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1))) c)) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 155706/16983291. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)((^x.x) a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((b a) a)) REDUCED to normal form. ------ 155707/16983372. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 155708/16983525. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(b (^y.y))) 3. ==[ beta ]==> ((a (a b))(b (^y.y))) 4. ==[ alpha ]==> ((a (a b))(b (^x.x))) REDUCED to normal form. ------ 155709/16983579. ------ 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)(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. ------ 155710/16983606. ------ 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. ------ 155711/16983687. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 155712/16983714. ------ 1. ==[ start ]==> ((a (b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((a (b a))((^x.b)((a a) a))) 3. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 155713/16983948. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((b a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((b a) c)) REDUCED to normal form. ------ 155714/16984155. ------ 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. ------ 155715/16984218. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 155716/16984263. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)(a (^x1.x1)))) REDUCED to normal form. ------ 155717/16984497. ------ 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.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 155718/16984542. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((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. ------ 155719/16984551. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(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. ------ 155720/16984839. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 155721/16984866. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a) b)) REDUCED to normal form. ------ 155722/16985127. ------ 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 (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. ------ 155723/16985136. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.(^z1.z1))) a)) 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. ------ 155724/16985154. ------ 1. ==[ start ]==> ((a (^b.b))((b a)(a a))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(a a))) REDUCED to normal form. ------ 155725/16985433. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 155726/16985469. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 155727/16985757. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a) c)) REDUCED to normal form. ------ 155728/16985964. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(a (b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(a (b a))) 3. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 155729/16985973. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a) a)) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 155730/16986000. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.(^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)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 155731/16986027. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 155732/16986072. ------ 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. ------ 155733/16986198. ------ 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. ------ 155734/16986279. ------ 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. ------ 155735/16986306. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 155736/16986360. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 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. ------ 155737/16986414. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 155738/16986441. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 155739/16986468. ------ 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. ------ 155740/16986747. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^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. ------ 155741/16986783. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b) c)) 3. ==[ beta ]==> ((b b)((^y.b) c)) 4. ==[ alpha ]==> ((b b)((^x.b) c)) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 155742/16986828. ------ 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. ------ 155743/16986855. ------ 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. ------ 155744/16986909. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))(a b))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))(a b))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))(a b))) REDUCED to normal form. ------ 155745/16986972. ------ 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))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 155746/16986999. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 155747/16987053. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(y1 y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(x1 x1))) REDUCED to normal form. ------ 155748/16987107. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (^x1.a))) REDUCED to normal form. ------ 155749/16987134. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 155750/16987161. ------ 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)))) REDUCED to normal form. ------ 155751/16987197. ------ 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))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 155752/16987224. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 155753/16987278. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 155754/16987305. ------ 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 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 155755/16987332. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a 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. ------ 155756/16987359. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 155757/16987386. ------ 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)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.(a a))) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.(a a))) REDUCED to normal form. ------ 155758/16987548. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c (^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.a))) REDUCED to normal form. ------ 155759/16987863. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z)) c)) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y)) c)) 5. ==[ beta ]==> ((b c)((^y.y) c)) 6. ==[ alpha ]==> ((b c)((^x.x) c)) 7. ==[ beta ]==> ((b c) c) REDUCED to normal form. ------ 155760/16987935. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x))(c (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(c (^y.y))) REDUCED to normal form. ------ 155761/16987962. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 155762/16987998. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.b) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.b) a)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 155763/16988016. ------ 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)(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a)(a a))) REDUCED to normal form. ------ 155764/16988097. ------ 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. ------ 155765/16988214. ------ 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.(^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. ------ 155766/16988241. ------ 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. ------ 155767/16988268. ------ 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.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 155768/16988331. ------ 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. ------ 155769/16988385. ------ 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.(^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. ------ 155770/16988412. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 155771/16988439. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.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. ------ 155772/16988466. ------ 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.(^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. ------ 155773/16988493. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(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))) 5. ==[ beta ]==> (((a b)(a a))(^y.a)) 6. ==[ alpha ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 155774/16988628. ------ 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)))) 5. ==[ beta ]==> ((b a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 155775/16988709. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 155776/16988880. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((^x1.x1) a))) 3. ==[ beta ]==> (b (c ((^x1.x1) a))) 4. ==[ alpha ]==> (b (c ((^x.x) a))) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 155777/16988988. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155778/16989105. ------ 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)))) 7. ==[ beta ]==> (a (a (^y.(^z.z)))) 8. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 155779/16989213. ------ 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. ------ 155780/16989285. ------ 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. ------ 155781/16989294. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 155782/16989321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.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. ------ 155783/16989348. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^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. ------ 155784/16989402. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) REDUCED to normal form. ------ 155785/16989429. ------ 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))(^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. ------ 155786/16989456. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 155787/16989510. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 155788/16989528. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (a (^z.z)))) REDUCED to normal form. ------ 155789/16989546. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 155790/16989573. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.z))) REDUCED to normal form. ------ 155791/16989600. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (^a.(^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. ------ 155792/16989627. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^b.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. ------ 155793/16989654. ------ 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.(^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. ------ 155794/16989681. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(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. ------ 155795/16989708. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^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. ------ 155796/16989735. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^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. ------ 155797/16989762. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.y))) REDUCED to normal form. ------ 155798/16989816. ------ 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)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 155799/16989843. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 155800/16989870. ------ 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. ------ 155801/17000352. ------ 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)(^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. ------ 155802/17000484. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 155803/17000583. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a b)(^z.(^x1.x1)))((a b)(^y1.(^z1.z1))))) REDUCED to normal form. ------ 155804/17001171. ------ 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. ------ 155805/17001879. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)(^z.z))) 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. ------ 155806/17002266. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.x1))((^z.a)(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.z))((^x1.a)(^y1.y1)))) 5. ==[ beta ]==> (^x.(a ((^x1.a)(^y1.y1)))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.z)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 155807/17003403. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 155808/17003904. ------ 1. ==[ start ]==> ((^a.(b a))((a b)(^c.a))) 2. ==[ alpha ]==> ((^x.(b x))((a b)(^y.a))) 3. ==[ eta ]==> (b ((a b)(^y.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 155809/17004078. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.b)(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.z)) 5. ==[ beta ]==> (b (^z.z)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 155810/17004411. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^a.((^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)))(^x1.b)) REDUCED to normal form. ------ 155811/17004741. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x1.(^y1.y1)))(^z1.z1))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 155812/17005023. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 155813/17005320. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^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. ------ 155814/17005329. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(x1 (^y1.(^z1.z1))))) REDUCED to normal form. ------ 155815/17005659. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155816/17006166. ------ 1. ==[ start ]==> (((a b)(^c.a))(^a.(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(b y))) 3. ==[ eta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 155817/17008191. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^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))) REDUCED to normal form. ------ 155818/17008524. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 155819/17008899. ------ 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. ------ 155820/17008992. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.((^a.a)(^a.a)))) 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 ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155821/17009478. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 155822/17009487. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z (z z)))) REDUCED to normal form. ------ 155823/17009586. ------ 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.(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155824/17009718. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 155825/17009820. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.c)) 3. ==[ beta ]==> (((a (a a)) b)(^y.c)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.c)) REDUCED to normal form. ------ 155826/17009874. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 155827/17010036. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.a)) 2. ==[ alpha ]==> ((((^x.x) b)(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. ------ 155828/17010063. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.a)) REDUCED to normal form. ------ 155829/17010111. ------ 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))) 5. ==[ beta ]==> (a (((a a)(a a)) a)) REDUCED to normal form. ------ 155830/17010138. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (((a a) a)(b (a (a a)))) REDUCED to normal form. ------ 155831/17010165. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 155832/17010192. ------ 1. ==[ start ]==> (((^a.a) b)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)((b a)((a a) a))) 3. ==[ beta ]==> (b ((b a)((a a) a))) REDUCED to normal form. ------ 155833/17010219. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 155834/17010246. ------ 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. ------ 155835/17010273. ------ 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. ------ 155836/17010300. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 155837/17010327. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^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. ------ 155838/17010381. ------ 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)(((^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. ------ 155839/17010453. ------ 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)(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. ------ 155840/17010588. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 155841/17010606. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 155842/17010633. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 155843/17010660. ------ 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. ------ 155844/17010687. ------ 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. ------ 155845/17010696. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.b)((a a)(^z.z)))((^y.b)((a a)(^z.z)))) 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. ------ 155846/17010723. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 155847/17010777. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 9. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 10. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 11. ==[ beta ]==> (b ((^y.y) b)) 12. ==[ alpha ]==> (b ((^x.x) b)) 13. ==[ beta ]==> (b b) REDUCED to normal form. ------ 155848/17010804. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (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. ------ 155849/17010831. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 155850/17011047. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^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. ------ 155851/17011074. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 155852/17011182. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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. ------ 155853/17011209. ------ 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. ------ 155854/17011245. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(b (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.a))(b (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))(b (b (^y.y)))) REDUCED to normal form. ------ 155855/17011272. ------ 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. ------ 155856/17011299. ------ 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)) REDUCED to normal form. ------ 155857/17011596. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (b (((^y.y) a)((^z.z) b))) 6. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 7. ==[ beta ]==> (b (a ((^y.y) b))) 8. ==[ alpha ]==> (b (a ((^x.x) b))) 9. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 155858/17011623. ------ 1. ==[ start ]==> ((((a a) a) a)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 155859/17011848. ------ 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)(a a))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.b))) REDUCED to normal form. ------ 155860/17011875. ------ 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. ------ 155861/17011956. ------ 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. ------ 155862/17011983. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> ((a (a b))(a (^y.y))) 4. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 155863/17011992. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.b)((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((^z.z) b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 155864/17012154. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^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. ------ 155865/17012262. ------ 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. ------ 155866/17012343. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (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. ------ 155867/17012370. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 155868/17012496. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.b) 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)) 9. ==[ beta ]==> (a c) REDUCED to normal form. ------ 155869/17012541. ------ 1. ==[ start ]==> (((^a.b) b)((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b) b)((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 155870/17012748. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> (b (c (^x1.x1))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 155871/17012757. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> (((a b) b)((a (^x.x)) b)) REDUCED to normal form. ------ 155872/17012784. ------ 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. ------ 155873/17012829. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 155874/17012883. ------ 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)))((^x2.x2) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 11. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 12. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155875/17012964. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 155876/17013090. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)(^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. ------ 155877/17013117. ------ 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. ------ 155878/17013171. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(a a)) a)) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 155879/17013198. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b) b)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b b)) REDUCED to normal form. ------ 155880/17013288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 155881/17013432. ------ 1. ==[ start ]==> (((a b) c)(d (b a))) REDUCED to normal form. ------ 155882/17013459. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b)(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) b)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 155883/17013486. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(b ((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b b)) REDUCED to normal form. ------ 155884/17013540. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b (a a))) REDUCED to normal form. ------ 155885/17013567. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 155886/17013621. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155887/17013648. ------ 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)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((^y.y)(^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. ------ 155888/17013675. ------ 1. ==[ start ]==> (((a b)(^b.a))((a b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)((a a) a))) REDUCED to normal form. ------ 155889/17013702. ------ 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. ------ 155890/17013729. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 155891/17013873. ------ 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. ------ 155892/17013900. ------ 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. ------ 155893/17013927. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((b a)(^y.a))) 3. ==[ beta ]==> (((a b) a)((b a)(^y.a))) 4. ==[ alpha ]==> (((a b) a)((b a)(^x.a))) REDUCED to normal form. ------ 155894/17013954. ------ 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. ------ 155895/17013981. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a)(a a))(^b.(^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. ------ 155896/17014008. ------ 1. ==[ start ]==> ((a (b a))((a b)(^c.a))) 2. ==[ alpha ]==> ((a (b a))((a b)(^x.a))) REDUCED to normal form. ------ 155897/17014098. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (b ((^z.(z z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 155898/17014179. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 155899/17014287. ------ 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. ------ 155900/17014314. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(a a))(^b.(^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 a) REDUCED to normal form. ------ 155901/17014368. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 155902/17014458. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (b a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (b a))) REDUCED to normal form. ------ 155903/17014485. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.a))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 155904/17014512. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a b)) REDUCED to normal form. ------ 155905/17014845. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 155906/17014854. ------ 1. ==[ start ]==> (((^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 a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155907/17014935. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> ((a a)((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(a (a a)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 155908/17015016. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(^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. ------ 155909/17015124. ------ 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 (^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. ------ 155910/17015151. ------ 1. ==[ start ]==> (((^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.x2))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 155911/17015232. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.(z z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(y y)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 155912/17015313. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 155913/17015376. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(c ((a a)(^z.z)))) REDUCED to normal form. ------ 155914/17015421. ------ 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.(^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. ------ 155915/17015430. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 155916/17015493. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 155917/17015736. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a)(^z.z))) REDUCED to normal form. ------ 155918/17015763. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((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)))) REDUCED to normal form. ------ 155919/17015772. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^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. ------ 155920/17015799. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))((^x2.x2) 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. ------ 155921/17015934. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 155922/17016096. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.b)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(y y)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 155923/17016177. ------ 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 z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.b)(^x1.b))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 155924/17016213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c ((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(a a))(c ((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.(a a))(c ((^y.y)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 155925/17016240. ------ 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. ------ 155926/17016267. ------ 1. ==[ start ]==> (((a b)(^c.a))(a (b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (b a))) REDUCED to normal form. ------ 155927/17016294. ------ 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.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. ------ 155928/17016321. ------ 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. ------ 155929/17016375. ------ 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. ------ 155930/17016402. ------ 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. ------ 155931/17016546. ------ 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.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(((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))) REDUCED to normal form. ------ 155932/17016573. ------ 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. ------ 155933/17016600. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((a b)(^x.a))) REDUCED to normal form. ------ 155934/17016627. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 155935/17016654. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(^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)))) 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. ------ 155936/17016708. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.b))) REDUCED to normal form. ------ 155937/17016735. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((b (a a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((b (a a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 155938/17016798. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 155939/17016933. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 155940/17017077. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)(a (^y.y)))) 3. ==[ beta ]==> ((b b)((a b)(a (^y.y)))) 4. ==[ alpha ]==> ((b b)((a b)(a (^x.x)))) REDUCED to normal form. ------ 155941/17017104. ------ 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. ------ 155942/17017158. ------ 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. ------ 155943/17017185. ------ 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) a)((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a ((a a) a))) REDUCED to normal form. ------ 155944/17017203. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c (^y.b))) 3. ==[ beta ]==> (((b a)(b a))(c (^y.b))) 4. ==[ alpha ]==> (((b a)(b a))(c (^x.b))) REDUCED to normal form. ------ 155945/17017284. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 155946/17017392. ------ 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 y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155947/17017491. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(a a)) a)) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 155948/17017518. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((a b) b)) REDUCED to normal form. ------ 155949/17017707. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 155950/17017932. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b)(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155951/17018013. ------ 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. ------ 155952/17018121. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155953/17018229. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a)(^b.(^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. ------ 155954/17018292. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (a b))) 3. ==[ beta ]==> ((a (^y.y))(a (a b))) 4. ==[ alpha ]==> ((a (^x.x))(a (a b))) REDUCED to normal form. ------ 155955/17018319. ------ 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. ------ 155956/17018400. ------ 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. ------ 155957/17018427. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 155958/17018625. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 155959/17018652. ------ 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. ------ 155960/17018679. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 155961/17018814. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 155962/17018841. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z)) 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. ------ 155963/17019003. ------ 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. ------ 155964/17019093. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^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 ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155965/17019174. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.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. ------ 155966/17019417. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 155967/17019444. ------ 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))((^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. ------ 155968/17019498. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((b b)((^y.(y y))(^z.z))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(^y.y))) 9. ==[ beta ]==> ((b b)((^y.y)(^y.y))) 10. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 11. ==[ beta ]==> ((b b)(^y.y)) 12. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 155969/17019579. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^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. ------ 155970/17019588. ------ 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. ------ 155971/17019615. ------ 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. ------ 155972/17019642. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 155973/17019687. ------ 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 (^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 155974/17019723. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c b)) 3. ==[ beta ]==> ((b (^y.(y y)))(c b)) 4. ==[ alpha ]==> ((b (^x.(x x)))(c b)) REDUCED to normal form. ------ 155975/17019750. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b c)) REDUCED to normal form. ------ 155976/17019822. ------ 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))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 155977/17019867. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.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. ------ 155978/17019894. ------ 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)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 155979/17019921. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y) c)) 3. ==[ beta ]==> (((a (a a)) b)((^y.y) c)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x) c)) 5. ==[ beta ]==> (((a (a a)) b) c) REDUCED to normal form. ------ 155980/17019948. ------ 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 (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 155981/17019975. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 155982/17020002. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 155983/17020029. ------ 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. ------ 155984/17020056. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z)) 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. ------ 155985/17020110. ------ 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)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.x1))) REDUCED to normal form. ------ 155986/17020137. ------ 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. ------ 155987/17020164. ------ 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)) 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. ------ 155988/17020190. ------ 1. ==[ start ]==> (^a.((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (^x.((b (^y.y))(x (^z.z)))) REDUCED to normal form. ------ 155989/17020191. ------ 1. ==[ start ]==> (a ((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (a ((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 155990/17030301. ------ 1. ==[ start ]==> ((^a.a)((b (^a.a))(a (^a.a)))) 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. ------ 155991/17030328. ------ 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))((^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))) 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. ------ 155992/17030355. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 155993/17030436. ------ 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)(^z.z))(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 155994/17030625. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))(b (^x1.x1)))) 3. ==[ eta ]==> ((^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. ------ 155995/17030673. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 155996/17030796. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 155997/17031078. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 155998/17031120. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 155999/17031678. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((((^y.y)(a a))(a b))(((^y.y)(a a))(a b)))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (((((^x.x)(a a))(a b))(((^y.y)(a a))(a b)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((((a a)(a b))(((^y.y)(a a))(a b)))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((((a a)(a b))(((^x.x)(a a))(a b)))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> ((((a a)(a b))((a a)(a b)))(((^y.y)(a a))(a b))) 8. ==[ alpha ]==> ((((a a)(a b))((a a)(a b)))(((^x.x)(a a))(a b))) 9. ==[ beta ]==> ((((a a)(a b))((a a)(a b)))((a a)(a b))) REDUCED to normal form. ------ 156000/17032011. ------ 1. ==[ start ]==> ((^a.(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 156001/17032653. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(b (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(b (^z.z)))) REDUCED to normal form. ------ 156002/17032785. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((((a a)(^z.z))((^x1.x1)(^y1.y1)))(((a a)(^z.z))((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((((a a)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> ((((a a)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^y1.y1))) 10. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 156003/17034390. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 156004/17034723. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 156005/17034765. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 156006/17035047. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 156007/17035344. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 156008/17035641. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 156009/17035656. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^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. ------ 156010/17035938. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 156011/17036478. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 156012/17037477. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 156013/17037918. ------ 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)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 156014/17038050. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 156015/17038503. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.z))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 156016/17039025. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 156017/17039304. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(^b.(^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. ------ 156018/17039790. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.d)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.d)) 3. ==[ beta ]==> (b (^z.d)) 4. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 156019/17039799. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 156020/17039907. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) REDUCED to normal form. ------ 156021/17040030. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1)) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 156022/17040078. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 156023/17040132. ------ 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)))) REDUCED to normal form. ------ 156024/17040213. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.c)) REDUCED to normal form. ------ 156025/17040267. ------ 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. ------ 156026/17040348. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 156027/17040375. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 156028/17040414. ------ 1. ==[ start ]==> ((a a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 156029/17040441. ------ 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. ------ 156030/17040468. ------ 1. ==[ start ]==> ((a b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((a b)(b (a (a a)))) REDUCED to normal form. ------ 156031/17040522. ------ 1. ==[ start ]==> (((a a)(a a))((b a)((a a) a))) REDUCED to normal form. ------ 156032/17040549. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 156033/17040684. ------ 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. ------ 156034/17040711. ------ 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)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a ((a a)(a a)))) REDUCED to normal form. ------ 156035/17040738. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 156036/17040783. ------ 1. ==[ start ]==> (((a (^a.a)) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 156037/17040828. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 156038/17040855. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.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. ------ 156039/17040891. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 156040/17040909. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 156041/17040999. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 156042/17041017. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((a b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(^y.(^z.z)))((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 156043/17041080. ------ 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. ------ 156044/17041098. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(^z.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(^z.z))) 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. ------ 156045/17041107. ------ 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)(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a (a a)) a)(b ((^y.y) b))) 6. ==[ alpha ]==> (((a (a a)) a)(b ((^x.x) b))) 7. ==[ beta ]==> (((a (a a)) a)(b b)) REDUCED to normal form. ------ 156046/17041134. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 156047/17041161. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 156048/17041188. ------ 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.(^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. ------ 156049/17041206. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 156050/17041233. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) b)) REDUCED to normal form. ------ 156051/17041323. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 156052/17041458. ------ 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. ------ 156053/17041485. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 156054/17041512. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^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. ------ 156055/17041539. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 156056/17041656. ------ 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)(^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. ------ 156057/17041683. ------ 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. ------ 156058/17041710. ------ 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.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 156059/17041737. ------ 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. ------ 156060/17041764. ------ 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. ------ 156061/17041791. ------ 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. ------ 156062/17042043. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^y.(^z.z)))) 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. ------ 156063/17042052. ------ 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. ------ 156064/17042079. ------ 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)((^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. ------ 156065/17042106. ------ 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. ------ 156066/17042124. ------ 1. ==[ start ]==> ((a (^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 156067/17042295. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 156068/17042313. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156069/17042394. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z)) a)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b (^z.z)) a)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z)) a)) IRREDUCIBLE: cycle. ------ 156070/17042457. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.a))) 3. ==[ beta ]==> ((((a a) a) b)(^y.a)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.a)) REDUCED to normal form. ------ 156071/17042484. ------ 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. ------ 156072/17042565. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 156073/17042592. ------ 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. ------ 156074/17042619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 156075/17042673. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 156076/17042709. ------ 1. ==[ start ]==> (((a a)(a b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a b))(c ((^x.x) b))) 3. ==[ beta ]==> (((a a)(a b))(c b)) REDUCED to normal form. ------ 156077/17042736. ------ 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. ------ 156078/17042763. ------ 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 (^y.y))(a (b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 156079/17042790. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 156080/17042817. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> (a (((^y.y) b)(a (^z.z)))) 8. ==[ alpha ]==> (a (((^x.x) b)(a (^y.y)))) 9. ==[ beta ]==> (a (b (a (^y.y)))) 10. ==[ alpha ]==> (a (b (a (^x.x)))) REDUCED to normal form. ------ 156081/17042844. ------ 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. ------ 156082/17042871. ------ 1. ==[ start ]==> (((a b)(a a))((b a)(a (a a)))) REDUCED to normal form. ------ 156083/17042898. ------ 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)(^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)(^x.x))(^z.z))) 6. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 156084/17043078. ------ 1. ==[ start ]==> (((a b) b)(c (^b.b))) 2. ==[ alpha ]==> (((a b) b)(c (^x.x))) REDUCED to normal form. ------ 156085/17043105. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(b (^y.(a a)))) 3. ==[ beta ]==> (((a a) a)(b (^y.(a a)))) 4. ==[ alpha ]==> (((a a) a)(b (^x.(a a)))) REDUCED to normal form. ------ 156086/17043150. ------ 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)(((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. ------ 156087/17043159. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 156088/17043204. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 9. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.a))) 10. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 11. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 12. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 156089/17043213. ------ 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. ------ 156090/17043267. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))((^x1.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. ------ 156091/17043285. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 156092/17043294. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 156093/17043321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a b))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 156094/17043510. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 156095/17043753. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a))(^d.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(x x))(^y.a))) 3. ==[ beta ]==> (((a b) c)((^y.a)(^y.a))) 4. ==[ alpha ]==> (((a b) c)((^x.a)(^y.a))) 5. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 156096/17043780. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 156097/17043807. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.a))(^b.b))) 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. ------ 156098/17044086. ------ 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. ------ 156099/17044113. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (b a))) REDUCED to normal form. ------ 156100/17044140. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 156101/17044167. ------ 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. ------ 156102/17044419. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 156103/17044500. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a a)(^z.z))) 3. ==[ beta ]==> (b ((a a)(^z.z))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 156104/17044563. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 156105/17044671. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 156106/17044698. ------ 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. ------ 156107/17044752. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 156108/17044806. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 156109/17044833. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 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. ------ 156110/17044878. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 156111/17044896. ------ 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. ------ 156112/17044923. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 156113/17044950. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(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 (a a))(((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> ((a (a a))((a a)(a (a a)))) REDUCED to normal form. ------ 156114/17044977. ------ 1. ==[ start ]==> (((a (a a))(a b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a b)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a b))((a b)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a b))((a b)(^x.x))) REDUCED to normal form. ------ 156115/17045004. ------ 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 a) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a) a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 156116/17045031. ------ 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)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a b))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a b))) 7. ==[ beta ]==> ((((a a) a)(^x.x))(a b)) REDUCED to normal form. ------ 156117/17045058. ------ 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. ------ 156118/17045085. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) 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. ------ 156119/17045112. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 156120/17045157. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(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. ------ 156121/17045175. ------ 1. ==[ start ]==> (((^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.x2))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156122/17045256. ------ 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 a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a a)(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(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. ------ 156123/17045337. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.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. ------ 156124/17045445. ------ 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 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. ------ 156125/17045454. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(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. ------ 156126/17045472. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^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)) REDUCED to normal form. ------ 156127/17045481. ------ 1. ==[ start ]==> (((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.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. ------ 156128/17045499. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 156129/17045562. ------ 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 z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 156130/17045589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 156131/17045643. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 156132/17045670. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 156133/17045697. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 156134/17045751. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 156135/17045769. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^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. ------ 156136/17045787. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a)(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a)(a a))) REDUCED to normal form. ------ 156137/17045814. ------ 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 (^z.z)))) REDUCED to normal form. ------ 156138/17045841. ------ 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.x1) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)((^y.y) a))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 156139/17045868. ------ 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. ------ 156140/17045895. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 156141/17045922. ------ 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)(^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. ------ 156142/17045949. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))(a b))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))(a b))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 156143/17045976. ------ 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)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) 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)))(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. ------ 156144/17046003. ------ 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 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)))) REDUCED to normal form. ------ 156145/17046048. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(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. ------ 156146/17046093. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((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))) REDUCED to normal form. ------ 156147/17046120. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(a a))(^x2.a))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))(^x2.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. ------ 156148/17046255. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 156149/17046363. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a)(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156150/17046372. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 156151/17046399. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))(^b.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. ------ 156152/17046426. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 156153/17046534. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 156154/17046561. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^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. ------ 156155/17046588. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(^d.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. ------ 156156/17046759. ------ 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. ------ 156157/17046786. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (a b))) REDUCED to normal form. ------ 156158/17046813. ------ 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. ------ 156159/17046840. ------ 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. ------ 156160/17047119. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 156161/17047362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 156162/17047587. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 156163/17047605. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^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. ------ 156164/17047614. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 156165/17047668. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 156166/17047713. ------ 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. ------ 156167/17047722. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 156168/17047749. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)((a a) a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 156169/17047776. ------ 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)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 156170/17047974. ------ 1. ==[ start ]==> (((a b)(a b))(c ((a a) a))) REDUCED to normal form. ------ 156171/17048001. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(b (a b))) 3. ==[ beta ]==> (((a a)((a a) a))(b (a b))) REDUCED to normal form. ------ 156172/17048028. ------ 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 ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 156173/17048082. ------ 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. ------ 156174/17048109. ------ 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)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((b (a (^x.x)))((^z.z) a)) 8. ==[ alpha ]==> ((b (a (^x.x)))((^y.y) a)) 9. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 156175/17048136. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 156176/17048163. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 156177/17048253. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(^x2.x2))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x2.x2))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156178/17048334. ------ 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. ------ 156179/17048442. ------ 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. ------ 156180/17048478. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 156181/17048505. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^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. ------ 156182/17048613. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 156183/17048631. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 156184/17048748. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 156185/17048820. ------ 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. ------ 156186/17048856. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 156187/17048883. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a ((^z.z) a))) 7. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 156188/17049108. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 156189/17049135. ------ 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. ------ 156190/17049162. ------ 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. ------ 156191/17049216. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 156192/17049243. ------ 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. ------ 156193/17049270. ------ 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)(^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. ------ 156194/17049414. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(^z.(^x1.x1)))) 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. ------ 156195/17049495. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a) c)) 3. ==[ beta ]==> (b (((^x1.x1) a) c)) 4. ==[ alpha ]==> (b (((^x.x) a) c)) 5. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 156196/17049603. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156197/17049720. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(a a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(a a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(a a))) 5. ==[ beta ]==> (a ((^y.(y y))(a a))) 6. ==[ alpha ]==> (a ((^x.(x x))(a a))) 7. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 156198/17049738. ------ 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 ]==> (((^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. ------ 156199/17049765. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))(^b.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. ------ 156200/17049819. ------ 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. ------ 156201/17049828. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^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. ------ 156202/17049855. ------ 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)(^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. ------ 156203/17049909. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 156204/17049963. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 156205/17050017. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(y1 y1)))) REDUCED to normal form. ------ 156206/17050044. ------ 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))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 156207/17050071. ------ 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 (^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. ------ 156208/17050125. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 156209/17050143. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z)) b)) REDUCED to normal form. ------ 156210/17050161. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 156211/17050188. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a a)) REDUCED to normal form. ------ 156212/17050215. ------ 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.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))) REDUCED to normal form. ------ 156213/17050242. ------ 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. ------ 156214/17050296. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b b)) REDUCED to normal form. ------ 156215/17050323. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a c)) REDUCED to normal form. ------ 156216/17050350. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (a a))) 5. ==[ beta ]==> (((a a)(a a))(b (a a))) REDUCED to normal form. ------ 156217/17050377. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (a (^y.y)))) REDUCED to normal form. ------ 156218/17050431. ------ 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)))(^x1.x1))(b a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b a)) REDUCED to normal form. ------ 156219/17050458. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a b)) 3. ==[ beta ]==> ((b (a (a a)))(a b)) REDUCED to normal form. ------ 156220/17050485. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a (a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a (a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (a a))) REDUCED to normal form. ------ 156221/17055276. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^x1.(^y1.y1))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156222/17055879. ------ 1. ==[ start ]==> ((^a.(^b.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156223/17060649. ------ 1. ==[ start ]==> ((^a.(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156224/17060730. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156225/17060892. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(^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 ]==> (^x.((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (^x.((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (^x.(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> (^x.(a (^y.(^z.z)))) REDUCED to normal form. ------ 156226/17061234. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.(a a))((^z.z)(a a)))(((^y.(a a))((^z.z)(a a)))((^y.(a a))((^z.z)(a a))))) 4. ==[ alpha ]==> (((^x.(a a))((^y.y)(a a)))(((^z.(a a))((^x1.x1)(a a)))((^y1.(a a))((^z1.z1)(a a))))) 5. ==[ beta ]==> ((a a)(((^z.(a a))((^x1.x1)(a a)))((^y1.(a a))((^z1.z1)(a a))))) 6. ==[ alpha ]==> ((a a)(((^x.(a a))((^y.y)(a a)))((^z.(a a))((^x1.x1)(a a))))) 7. ==[ beta ]==> ((a a)((a a)((^z.(a a))((^x1.x1)(a a))))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a))((^y.y)(a a))))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 156227/17062530. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(y y))(a (^z.(^x1.x1)))) b) 4. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z)))) b) 5. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z)))) b) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 156228/17063721. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 156229/17063799. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((((^z.(^x1.(^y1.y1)))(^z1.a))((^z.(^x1.(^y1.y1)))(^z1.a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.(^x2.x2)))(^y2.a)))(^z2.z2)) 5. ==[ beta ]==> (((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.a)))(^z2.z2)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a)))(^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. ------ 156230/17064081. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.((x1 x1)(x1 x1)))) 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. ------ 156231/17064555. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ eta ]==> (b ((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 156232/17065104. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 156233/17065392. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a (^x1.x1))) 3. ==[ beta ]==> ((a (^x1.x1))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 156234/17065395. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 156235/17065995. ------ 1. ==[ start ]==> ((^a.(^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156236/17065998. ------ 1. ==[ start ]==> ((a (^b.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 156237/17066286. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 156238/17067309. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.(^z.z))((^x1.x1)(a a)))((^y.(^z.z))((^x1.x1)(a a))))(((^y.(^z.z))((^x1.x1)(a a)))((^y.(^z.z))((^x1.x1)(a a))))) 4. ==[ alpha ]==> ((((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(a a))))(((^x2.(^y2.y2))((^z2.z2)(a a)))((^x3.(^y3.y3))((^z3.z3)(a a))))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))((^z1.z1)(a a))))(((^x2.(^y2.y2))((^z2.z2)(a a)))((^x3.(^y3.y3))((^z3.z3)(a a))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1)(a a))))(((^y1.(^z1.z1))((^x2.x2)(a a)))((^y2.(^z2.z2))((^x3.x3)(a a))))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(a a)))(((^y1.(^z1.z1))((^x2.x2)(a a)))((^y2.(^z2.z2))((^x3.x3)(a a))))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.(^y1.y1))((^z1.z1)(a a)))((^x2.(^y2.y2))((^z2.z2)(a a))))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))((^z1.z1)(a a)))((^x2.(^y2.y2))((^z2.z2)(a a))))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1)(a a)))((^y1.(^z1.z1))((^x2.x2)(a a))))) 11. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(a a)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 12. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1)(a a)))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 15. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 16. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156239/17067591. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 156240/17068041. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^b.((^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)))(^x.(a a))) REDUCED to normal form. ------ 156241/17068257. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 156242/17068860. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(x1 b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(x1 b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(y1 b))) REDUCED to normal form. ------ 156243/17069202. ------ 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))) REDUCED to normal form. ------ 156244/17069364. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 156245/17069550. ------ 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. ------ 156246/17070138. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.d)) REDUCED to normal form. ------ 156247/17070417. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 156248/17070498. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^a.(^b.a))) 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. ------ 156249/17070552. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 156250/17070606. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 156251/17070660. ------ 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.(^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. ------ 156252/17070687. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(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. ------ 156253/17070714. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 156254/17070771. ------ 1. ==[ start ]==> ((a (^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 156255/17070798. ------ 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)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 156256/17070825. ------ 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)))) 5. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 156257/17070852. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 156258/17070906. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156259/17070933. ------ 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.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(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. ------ 156260/17070960. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 156261/17070987. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 156262/17071014. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^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. ------ 156263/17071095. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 156264/17071122. ------ 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.(^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. ------ 156265/17071158. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.(^a.a)) a)(^a.a))) 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))) 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. ------ 156266/17071185. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 156267/17071212. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 156268/17071239. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 156269/17071275. ------ 1. ==[ start ]==> (((a 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)(^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. ------ 156270/17071347. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 156271/17071356. ------ 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. ------ 156272/17071428. ------ 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. ------ 156273/17071455. ------ 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. ------ 156274/17071563. ------ 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. ------ 156275/17071653. ------ 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 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. ------ 156276/17071680. ------ 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. ------ 156277/17071932. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(b (b (^z.z)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(b (b (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 156278/17072175. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^y1.y1)(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. ------ 156279/17072229. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (a (((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(b a))) 7. ==[ beta ]==> (a ((^y.y)(b a))) 8. ==[ alpha ]==> (a ((^x.x)(b a))) 9. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 156280/17072310. ------ 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. ------ 156281/17072337. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^y1.y1)))) 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. ------ 156282/17072373. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(y y)))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 156283/17072400. ------ 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. ------ 156284/17072427. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^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. ------ 156285/17072454. ------ 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. ------ 156286/17072544. ------ 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. ------ 156287/17072571. ------ 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. ------ 156288/17072625. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^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. ------ 156289/17072643. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 156290/17072652. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 156291/17072805. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) b) c)) 3. ==[ beta ]==> ((((a a) a) b)(b c)) REDUCED to normal form. ------ 156292/17073057. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 156293/17073255. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 156294/17073282. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 156295/17073336. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a 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. ------ 156296/17073417. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) a)(a (^a.(^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. ------ 156297/17073471. ------ 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. ------ 156298/17073507. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 156299/17073561. ------ 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. ------ 156300/17073588. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.(y y))((b a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.(x x))((b a)(^y.(y y)))) 7. ==[ beta ]==> (((b a)(^y.(y y)))((b a)(^y.(y y)))) 8. ==[ alpha ]==> (((b a)(^x.(x x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 156301/17073615. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 156302/17073642. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 156303/17073669. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.b))) REDUCED to normal form. ------ 156304/17073732. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 156305/17073759. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(y y))(b a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(x x))(b a))) 5. ==[ beta ]==> ((a ((a a) a))((b a)(b a))) REDUCED to normal form. ------ 156306/17073786. ------ 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. ------ 156307/17073813. ------ 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. ------ 156308/17073840. ------ 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)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)((a a)(a a)))) 5. ==[ beta ]==> ((((a a) a) a)((a a)(a a))) REDUCED to normal form. ------ 156309/17073858. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(a a)) a)) 3. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 156310/17073867. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 156311/17073894. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b)(^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)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 156312/17073921. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.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. ------ 156313/17074173. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 156314/17074200. ------ 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)))) 4. ==[ alpha ]==> ((^x.x)(a ((a a)(a a)))) 5. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 156315/17074209. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 156316/17074236. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z) b)) 3. ==[ beta ]==> ((a (^y.b))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.b))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 156317/17074254. ------ 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 (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 156318/17074335. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1)(^y1.y1)))) 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. ------ 156319/17074488. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(c (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))(c (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 156320/17074515. ------ 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. ------ 156321/17074569. ------ 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. ------ 156322/17074596. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 156323/17074677. ------ 1. ==[ start ]==> ((a (b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 156324/17074911. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 156325/17075226. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.(^y1.y1)))(a a))) REDUCED to normal form. ------ 156326/17075514. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 156327/17075802. ------ 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. ------ 156328/17075829. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.(^y1.y1))) a)) REDUCED to normal form. ------ 156329/17076090. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a 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. ------ 156330/17076117. ------ 1. ==[ start ]==> ((a (^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 156331/17076405. ------ 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. ------ 156332/17076720. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z)) b)) REDUCED to normal form. ------ 156333/17076747. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((b a)(((^y.y)(a a)) c)) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a)) c)) 5. ==[ beta ]==> ((b a)((a a) c)) REDUCED to normal form. ------ 156334/17076927. ------ 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. ------ 156335/17077035. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 156336/17077161. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c (^y.(a a)))) 3. ==[ beta ]==> ((a (b a))(c (^y.(a a)))) 4. ==[ alpha ]==> ((a (b a))(c (^x.(a a)))) REDUCED to normal form. ------ 156337/17077188. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 156338/17077242. ------ 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. ------ 156339/17077269. ------ 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 a)) REDUCED to normal form. ------ 156340/17077296. ------ 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)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 156341/17077377. ------ 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 x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 156342/17077404. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(a b))) 3. ==[ beta ]==> ((b (a a))((^y.a)(a b))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(a b))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 156343/17077431. ------ 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)(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 156344/17077710. ------ 1. ==[ start ]==> (((^a.(^a.(^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))(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. ------ 156345/17077746. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a)) b)) 3. ==[ beta ]==> ((b b)((^y.(a a)) b)) 4. ==[ alpha ]==> ((b b)((^x.(a a)) b)) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 156346/17077773. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b) c)) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 156347/17077791. ------ 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. ------ 156348/17077818. ------ 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. ------ 156349/17077872. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)((a a) a))) 5. ==[ beta ]==> (((b a)(b a))(a ((a a) a))) REDUCED to normal form. ------ 156350/17077962. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 156351/17078016. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^x1.a))) REDUCED to normal form. ------ 156352/17078070. ------ 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. ------ 156353/17078097. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 156354/17078124. ------ 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))) REDUCED to normal form. ------ 156355/17078160. ------ 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)))((^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. ------ 156356/17078187. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(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))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 156357/17078214. ------ 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.(^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. ------ 156358/17078241. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 156359/17078268. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 156360/17078295. ------ 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 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. ------ 156361/17078322. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 156362/17078349. ------ 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.z))(^x1.b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 156363/17078376. ------ 1. ==[ start ]==> ((((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.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 156364/17078826. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a) b)) 3. ==[ beta ]==> ((b c)(((a a) a) b)) REDUCED to normal form. ------ 156365/17078853. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^y.y)) c)) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y) c)) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x) c)) 5. ==[ beta ]==> ((((a a)(a a)) b) c) REDUCED to normal form. ------ 156366/17078979. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a (a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a (a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (a b))) REDUCED to normal form. ------ 156367/17078988. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b) a)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 156368/17079060. ------ 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. ------ 156369/17079177. ------ 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. ------ 156370/17079204. ------ 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.(^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. ------ 156371/17079231. ------ 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. ------ 156372/17079294. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 156373/17079321. ------ 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. ------ 156374/17079348. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.y))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 156375/17079375. ------ 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.(^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. ------ 156376/17079402. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))(^b.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. ------ 156377/17079429. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 156378/17079456. ------ 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.(^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. ------ 156379/17079483. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(^c.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))) 5. ==[ beta ]==> (((a a)(a b))(^y.a)) 6. ==[ alpha ]==> (((a a)(a b))(^x.a)) REDUCED to normal form. ------ 156380/17079591. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c (^z.(z z)))) 3. ==[ beta ]==> ((b ((^y.y) a))(c (^z.(z z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c (^y.(y y)))) 5. ==[ beta ]==> ((b a)(c (^y.(y y)))) 6. ==[ alpha ]==> ((b a)(c (^x.(x x)))) REDUCED to normal form. ------ 156381/17079618. ------ 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)))) REDUCED to normal form. ------ 156382/17079672. ------ 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))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 156383/17079843. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (a (^x1.x1)))) 3. ==[ beta ]==> (b (d (a (^x1.x1)))) 4. ==[ alpha ]==> (b (d (a (^x.x)))) REDUCED to normal form. ------ 156384/17079951. ------ 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. ------ 156385/17080068. ------ 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. ------ 156386/17080113. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c c)) 3. ==[ beta ]==> ((^y.y)(c c)) 4. ==[ alpha ]==> ((^x.x)(c c)) 5. ==[ beta ]==> (c c) REDUCED to normal form. ------ 156387/17080176. ------ 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. ------ 156388/17080203. ------ 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. ------ 156389/17080248. ------ 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 (b ((^z.z) a))) 4. ==[ alpha ]==> (b (b ((^x.x) a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 156390/17080257. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a) d)) REDUCED to normal form. ------ 156391/17080284. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z)) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z)) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y)) a)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 156392/17080311. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 156393/17080356. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156394/17080392. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 156395/17080419. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 156396/17080473. ------ 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 ]==> (((^y.y) a) a) 8. ==[ alpha ]==> (((^x.x) a) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 156397/17080509. ------ 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)))) 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. ------ 156398/17080536. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^b.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. ------ 156399/17080590. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^a.(^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. ------ 156400/17080617. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a (^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a (^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 156401/17080644. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 156402/17080671. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 156403/17080698. ------ 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.(^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. ------ 156404/17080725. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 156405/17080779. ------ 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 (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 156406/17080806. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(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. ------ 156407/17080833. ------ 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))) 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. ------ 156408/17086236. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.(^a.(^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. ------ 156409/17091060. ------ 1. ==[ start ]==> ((^a.b)((^c.(a a)) d)) 2. ==[ alpha ]==> ((^x.b)((^y.(a a)) d)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 156410/17091378. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 156411/17091501. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 156412/17091600. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))(^z.(a a)))((((^y.y)(a a))(^z.(a a)))(((^y.y)(a a))(^z.(a a))))) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((((^z.z)(a a))(^x1.(a a)))(((^y1.y1)(a a))(^z1.(a a))))) 5. ==[ beta ]==> (((a a)(^y.(a a)))((((^z.z)(a a))(^x1.(a a)))(((^y1.y1)(a a))(^z1.(a a))))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((((^y.y)(a a))(^z.(a a)))(((^x1.x1)(a a))(^y1.(a a))))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(((a a)(^z.(a a)))(((^x1.x1)(a a))(^y1.(a a))))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.(a a)))(((^z.z)(a a))(^x1.(a a))))) 9. ==[ beta ]==> (((a a)(^x.(a a)))(((a a)(^y.(a a)))((a a)(^x1.(a a))))) 10. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.(a a)))((a a)(^z.(a a))))) REDUCED to normal form. ------ 156413/17091801. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 156414/17092215. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.z))(^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. ------ 156415/17092593. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(b (^y1.y1)))) REDUCED to normal form. ------ 156416/17092716. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 156417/17092896. ------ 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 ]==> (((a (a a))(^y.(^z.(^x1.x1)))) b) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 156418/17092989. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(z (^x1.x1)))) IRREDUCIBLE: cycle. ------ 156419/17093283. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(((^z.(z z))(^x1.(^y1.(^z1.z1))))((^z.(z z))(^x1.(^y1.(^z1.z1)))))) 4. ==[ alpha ]==> (^x.(((^y.(y y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(^y2.(^z2.z2)))))) 5. ==[ beta ]==> (^x.(((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(^y2.(^z2.z2)))))) 6. ==[ alpha ]==> (^x.(((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))((^y2.(y2 y2))(^z2.(^x3.(^y3.y3)))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))((^y2.(y2 y2))(^z2.(^x3.(^y3.y3)))))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2)))))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156420/17093727. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 156421/17094447. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^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. ------ 156422/17094456. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 156423/17094921. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(a a))(^b.(^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. ------ 156424/17095770. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.(^b.b))) 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. ------ 156425/17096067. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 156426/17096361. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.a)(^a.(^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. ------ 156427/17096364. ------ 1. ==[ start ]==> ((a (^b.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 156428/17096643. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156429/17096676. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(^z.z))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156430/17097183. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 156431/17097210. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 156432/17097675. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a (^y.y))(^z.(a a)))((a (^y.y))(^z.(a a))))(((a (^y.y))(^z.(a a)))((a (^y.y))(^z.(a a))))) 4. ==[ alpha ]==> ((((a (^x.x))(^y.(a a)))((a (^z.z))(^x1.(a a))))(((a (^y1.y1))(^z1.(a a)))((a (^x2.x2))(^y2.(a a))))) REDUCED to normal form. ------ 156433/17097714. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 156434/17097957. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 156435/17098182. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 156436/17098200. ------ 1. ==[ start ]==> (((^a.b)(a b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 156437/17098848. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.(^z1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.(^y2.(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.(^y2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156438/17099037. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(a y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1))) 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. ------ 156439/17099226. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.y1))) REDUCED to normal form. ------ 156440/17099235. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(x1 b))) REDUCED to normal form. ------ 156441/17099415. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156442/17099916. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ eta ]==> ((^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. ------ 156443/17100414. ------ 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. ------ 156444/17100504. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 156445/17100531. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(z (z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(z (z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(y (y y)))) REDUCED to normal form. ------ 156446/17100612. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.a)) REDUCED to normal form. ------ 156447/17100735. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 156448/17100783. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 156449/17100864. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.c)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.c)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 156450/17100918. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 156451/17100972. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.b)) REDUCED to normal form. ------ 156452/17101026. ------ 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)))(^x1.x1))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 156453/17101053. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 156454/17101155. ------ 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. ------ 156455/17101182. ------ 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. ------ 156456/17101191. ------ 1. ==[ start ]==> ((a b)((^c.(a a)) d)) 2. ==[ alpha ]==> ((a b)((^x.(a a)) d)) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 156457/17101209. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(b (a (a a)))) REDUCED to normal form. ------ 156458/17101236. ------ 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 ]==> (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. ------ 156459/17101263. ------ 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. ------ 156460/17101290. ------ 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. ------ 156461/17101317. ------ 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)(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. ------ 156462/17101344. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 156463/17101371. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(b a))) REDUCED to normal form. ------ 156464/17101425. ------ 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 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. ------ 156465/17101470. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)(c (^y.(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 156466/17101506. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a a)((^y.(^z.z)) 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. ------ 156467/17101632. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (a a))) REDUCED to normal form. ------ 156468/17101650. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 156469/17101677. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 156470/17101704. ------ 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. ------ 156471/17101731. ------ 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. ------ 156472/17101740. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.(a a))((^z.z)(a a)))((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (((^x.(a a))((^y.y)(a a)))((^z.(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a a)((^z.(a a))((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 156473/17101767. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((a a)(^y1.y1)))) 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. ------ 156474/17101821. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156475/17101848. ------ 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. ------ 156476/17101875. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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 REDUCED to normal form. ------ 156477/17101929. ------ 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 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. ------ 156478/17101974. ------ 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. ------ 156479/17102172. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 156480/17102226. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 156481/17102253. ------ 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. ------ 156482/17102289. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(c ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.a))(c ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(c ((a a)(a a)))) REDUCED to normal form. ------ 156483/17102316. ------ 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. ------ 156484/17102343. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)(a ((^z.(^x1.x1)) 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. ------ 156485/17102640. ------ 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.(^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. ------ 156486/17102667. ------ 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))) 5. ==[ beta ]==> ((((a a) a) a)(a b)) REDUCED to normal form. ------ 156487/17102721. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(b (^x1.x1)))) REDUCED to normal form. ------ 156488/17102847. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 156489/17102865. ------ 1. ==[ start ]==> (((a a)((a a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 156490/17102919. ------ 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. ------ 156491/17102946. ------ 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. ------ 156492/17103027. ------ 1. ==[ start ]==> ((a (a b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 156493/17103036. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156494/17103117. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(b (^x1.x1)))) IRREDUCIBLE: cycle. ------ 156495/17103198. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^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. ------ 156496/17103225. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 156497/17103306. ------ 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. ------ 156498/17103414. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 156499/17103567. ------ 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. ------ 156500/17103585. ------ 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 ((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. ------ 156501/17103801. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) b)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) b)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 156502/17103828. ------ 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. ------ 156503/17103846. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(a a)))) 5. ==[ beta ]==> ((a a)(b (^y.(a a)))) 6. ==[ alpha ]==> ((a a)(b (^x.(a a)))) REDUCED to normal form. ------ 156504/17103855. ------ 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. ------ 156505/17103927. ------ 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)(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. ------ 156506/17104008. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 156507/17104080. ------ 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)))) 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. ------ 156508/17104107. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^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. ------ 156509/17104161. ------ 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. ------ 156510/17104188. ------ 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. ------ 156511/17104242. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 156512/17104269. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))(b b)) REDUCED to normal form. ------ 156513/17104467. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 156514/17104548. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^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. ------ 156515/17104584. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 156516/17104611. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(a a))) 5. ==[ beta ]==> ((a (^x.b))(b (a a))) REDUCED to normal form. ------ 156517/17104665. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156518/17104692. ------ 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)(^y.y))(a (a a)))) REDUCED to normal form. ------ 156519/17104719. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y)(^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. ------ 156520/17104746. ------ 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)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 156521/17104773. ------ 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. ------ 156522/17104944. ------ 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. ------ 156523/17104971. ------ 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.(^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)))) REDUCED to normal form. ------ 156524/17104998. ------ 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. ------ 156525/17105025. ------ 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))(^z.(z z)))) REDUCED to normal form. ------ 156526/17105052. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(a a))(^b.(^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. ------ 156527/17105142. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 156528/17105223. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 156529/17105412. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a b)(a b))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 156530/17105493. ------ 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. ------ 156531/17105529. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (b a))) 3. ==[ beta ]==> (((a a)(^y.a))(c (b a))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (b a))) REDUCED to normal form. ------ 156532/17105556. ------ 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.(^y1.y1))))) REDUCED to normal form. ------ 156533/17105619. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z))) b)) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 156534/17105880. ------ 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 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. ------ 156535/17105898. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a (^b.b))) 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. ------ 156536/17105979. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 156537/17106060. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.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. ------ 156538/17106168. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 156539/17106195. ------ 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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 156540/17106222. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 156541/17106357. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 156542/17106474. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (b a))) REDUCED to normal form. ------ 156543/17106492. ------ 1. ==[ start ]==> ((a (^b.b))((^a.a)(^a.(^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. ------ 156544/17106510. ------ 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))) 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. ------ 156545/17106771. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 156546/17106807. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(^y.y))) 3. ==[ beta ]==> ((a b)((b a)(^y.y))) 4. ==[ alpha ]==> ((a b)((b a)(^x.x))) REDUCED to normal form. ------ 156547/17106978. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 156548/17107140. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.a))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 156549/17107167. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(z1 z1)))) 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. ------ 156550/17107221. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.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. ------ 156551/17107284. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(c (a a))) REDUCED to normal form. ------ 156552/17107302. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^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. ------ 156553/17107311. ------ 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. ------ 156554/17107338. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 156555/17107365. ------ 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.z))(a a))) REDUCED to normal form. ------ 156556/17107419. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b) a)) REDUCED to normal form. ------ 156557/17107446. ------ 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. ------ 156558/17107617. ------ 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. ------ 156559/17107644. ------ 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.(^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. ------ 156560/17107671. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 156561/17107698. ------ 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 y)))) REDUCED to normal form. ------ 156562/17107779. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((b (a a))(a (^y.b))) 6. ==[ alpha ]==> ((b (a a))(a (^x.b))) REDUCED to normal form. ------ 156563/17107806. ------ 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. ------ 156564/17107842. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 156565/17107977. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a))(^b.(^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. ------ 156566/17108085. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.a)(^c.(^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. ------ 156567/17108121. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))(a a))) 5. ==[ beta ]==> ((b b)((a a)(a a))) REDUCED to normal form. ------ 156568/17108148. ------ 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. ------ 156569/17108202. ------ 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. ------ 156570/17108229. ------ 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. ------ 156571/17108310. ------ 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)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 156572/17108328. ------ 1. ==[ start ]==> (((^a.b)(a b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 156573/17108436. ------ 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. ------ 156574/17108535. ------ 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. ------ 156575/17108562. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((a (^x.x)) b)((a a) a)) REDUCED to normal form. ------ 156576/17108589. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b) b)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b) b)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b) b)) REDUCED to normal form. ------ 156577/17108616. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a) a) c)) REDUCED to normal form. ------ 156578/17108805. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 156579/17108832. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a) c)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a) c)) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 156580/17108976. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a (^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a (^x2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156581/17109057. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 156582/17109165. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.y1)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156583/17109273. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.x))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 156584/17109300. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 156585/17109336. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(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. ------ 156586/17109354. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.b)) REDUCED to normal form. ------ 156587/17109363. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(a (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (a b))) REDUCED to normal form. ------ 156588/17109444. ------ 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. ------ 156589/17109471. ------ 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. ------ 156590/17109543. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(a (^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156591/17109669. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 156592/17109723. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a) a)) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a) a)) 5. ==[ beta ]==> ((a b)(((a a) a) a)) REDUCED to normal form. ------ 156593/17109750. ------ 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)(^x1.x1)) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z) b)) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 156594/17109777. ------ 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. ------ 156595/17110047. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 156596/17110137. ------ 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. ------ 156597/17110218. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(^a.(^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. ------ 156598/17110461. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 156599/17110488. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.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. ------ 156600/17110542. ------ 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. ------ 156601/17110623. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^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. ------ 156602/17110632. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 156603/17110659. ------ 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. ------ 156604/17110686. ------ 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. ------ 156605/17110731. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b (^b.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. ------ 156606/17110740. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) a)) REDUCED to normal form. ------ 156607/17110794. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c b)) REDUCED to normal form. ------ 156608/17110866. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 156609/17110884. ------ 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)(^y.y))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 156610/17110911. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a) c)) REDUCED to normal form. ------ 156611/17110938. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a) a)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a) a)) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 156612/17110965. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^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. ------ 156613/17111019. ------ 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. ------ 156614/17111046. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 156615/17111073. ------ 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.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)(a a))((a (^y.y)) a)) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x)) a)) REDUCED to normal form. ------ 156616/17111100. ------ 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. ------ 156617/17111154. ------ 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)))(^z.z)) b) REDUCED to normal form. ------ 156618/17111181. ------ 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. ------ 156619/17111208. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a a) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a a) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a) a)) REDUCED to normal form. ------ 156620/17111261. ------ 1. ==[ start ]==> (^a.(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (^x.(((^y.(^z.z)) x)(x x))) 3. ==[ beta ]==> (^x.((^z.z)(x x))) 4. ==[ alpha ]==> (^x.((^y.y)(x x))) 5. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 156621/17111262. ------ 1. ==[ start ]==> (a (((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (a ((^y.y)(a a))) 4. ==[ alpha ]==> (a ((^x.x)(a a))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 156622/17121393. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a)) a) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(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. ------ 156623/17121399. ------ 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. ------ 156624/17121426. ------ 1. ==[ start ]==> ((^a.(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((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)))) REDUCED to normal form. ------ 156625/17121453. ------ 1. ==[ start ]==> ((^a.b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.b)(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 156626/17121534. ------ 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 a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((b a)((a a) a))(^x.x)) REDUCED to normal form. ------ 156627/17121723. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) a)((a a)(a a)))) 3. ==[ eta ]==> ((^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. ------ 156628/17121798. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 156629/17121894. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 156630/17122203. ------ 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. ------ 156631/17122218. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156632/17122776. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (((((a a)(^y.y))((a a) a))(((a a)(^y.y))((a a) a)))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (((((a a)(^x.x))((a a) a))(((a a)(^y.y))((a a) a)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 156633/17123109. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 156634/17123778. ------ 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. ------ 156635/17123883. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((b a)(a (a a)))((b a)(a (a a))))) 4. ==[ alpha ]==> ((^x.x)(((b a)(a (a a)))((b a)(a (a a))))) 5. ==[ beta ]==> (((b a)(a (a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 156636/17124498. ------ 1. ==[ start ]==> (((^a.b) c)(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(^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. ------ 156637/17124849. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 156638/17125863. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b) 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. ------ 156639/17126151. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x1.(^y1.y1))))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 156640/17126469. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 156641/17126775. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 156642/17128107. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^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. ------ 156643/17128602. ------ 1. ==[ start ]==> (((a b)(^a.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 156644/17129148. ------ 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. ------ 156645/17129628. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.x1))) REDUCED to normal form. ------ 156646/17129817. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.b))) REDUCED to normal form. ------ 156647/17130150. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.((y y) y))) REDUCED to normal form. ------ 156648/17130708. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(^b.(^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. ------ 156649/17130807. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(z z)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(z z)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 156650/17130816. ------ 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. ------ 156651/17130924. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 156652/17131032. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 156653/17131113. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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 ]==> (^x.a) REDUCED to normal form. ------ 156654/17131128. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 156655/17131203. ------ 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) 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. ------ 156656/17131473. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.b)) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.b)) REDUCED to normal form. ------ 156657/17131527. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 156658/17131539. ------ 1. ==[ start ]==> ((a a)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> ((a a)((^y.y)(a a))) 4. ==[ alpha ]==> ((a a)((^x.x)(a a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 156659/17131566. ------ 1. ==[ start ]==> ((a (a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 156660/17131593. ------ 1. ==[ start ]==> ((a b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a b)(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> ((a b)(((a a)(a a)) a)) REDUCED to normal form. ------ 156661/17131647. ------ 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. ------ 156662/17131674. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b a)((a a) a))) REDUCED to normal form. ------ 156663/17131809. ------ 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. ------ 156664/17131836. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (a a)) b)) REDUCED to normal form. ------ 156665/17131863. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 5. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 156666/17131935. ------ 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. ------ 156667/17131953. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 156668/17131980. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.(^z1.z1)))) 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. ------ 156669/17132034. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.(x x)))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 156670/17132142. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((((^y.y)(a a))(^z.(a a)))(((^y.y)(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(a a))(^x1.(a a)))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))(^z.(a a)))) 9. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.(a a)))) 10. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 156671/17132169. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((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. ------ 156672/17132205. ------ 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. ------ 156673/17132223. ------ 1. ==[ start ]==> (((^a.(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.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 156674/17132232. ------ 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. ------ 156675/17132250. ------ 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. ------ 156676/17132259. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(b ((^y.y) b))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(b b)) REDUCED to normal form. ------ 156677/17132286. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.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) REDUCED to normal form. ------ 156678/17132313. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 156679/17132340. ------ 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. ------ 156680/17132358. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 156681/17132448. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((b b)(^y.(y y))) 6. ==[ alpha ]==> ((b b)(^x.(x x))) REDUCED to normal form. ------ 156682/17132583. ------ 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. ------ 156683/17132637. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 156684/17132664. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(^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. ------ 156685/17132691. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 156686/17132781. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 156687/17132808. ------ 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. ------ 156688/17132835. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 156689/17132862. ------ 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. ------ 156690/17132889. ------ 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. ------ 156691/17132916. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a) a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 156692/17133168. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)((b (^y.y))(^z.z))) 8. ==[ alpha ]==> ((a a)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 156693/17133231. ------ 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. ------ 156694/17133249. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 156695/17133420. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 156696/17133438. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.b)((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.b)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156697/17133582. ------ 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 a)) REDUCED to normal form. ------ 156698/17133600. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^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. ------ 156699/17133609. ------ 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. ------ 156700/17133636. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 156701/17133690. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 156702/17133717. ------ 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. ------ 156703/17133744. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.b)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.b)(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 156704/17133888. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 156705/17133915. ------ 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. ------ 156706/17133942. ------ 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 a))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) 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. ------ 156707/17133969. ------ 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. ------ 156708/17133996. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.(^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 (^x.(^y.y))) a)) REDUCED to normal form. ------ 156709/17134023. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a)(a (a a)))) 3. ==[ beta ]==> ((a (a a))((b a)(a (a a)))) REDUCED to normal form. ------ 156710/17134257. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 156711/17134329. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 11. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 12. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 13. ==[ beta ]==> (b (^y.(^z.z))) 14. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 156712/17134338. ------ 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. ------ 156713/17134365. ------ 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)))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((^y1.y1) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 9. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156714/17134410. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 156715/17134419. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(^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. ------ 156716/17134446. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 156717/17134635. ------ 1. ==[ start ]==> (((^a.b) c)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 156718/17134878. ------ 1. ==[ start ]==> (((a b) c)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 156719/17134932. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 156720/17134986. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(a a))) REDUCED to normal form. ------ 156721/17135031. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(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. ------ 156722/17135211. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 156723/17135238. ------ 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))((a a)(^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. ------ 156724/17135265. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((a (a b))(((^y.y) a)(b a))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) a)(b a))) 5. ==[ beta ]==> ((a (a b))(a (b a))) REDUCED to normal form. ------ 156725/17135292. ------ 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. ------ 156726/17135319. ------ 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)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z) b))) 7. ==[ beta ]==> ((^y.y)((a a)((^z.z) b))) 8. ==[ alpha ]==> ((^x.x)((a 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. ------ 156727/17135544. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 9. ==[ beta ]==> (b (^y.(a a))) 10. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 156728/17135625. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((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. ------ 156729/17135688. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b)(^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. ------ 156730/17135733. ------ 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. ------ 156731/17135796. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 156732/17135823. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 156733/17135877. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 156734/17135904. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 156735/17135958. ------ 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.y1))(^z1.(^x2.(^y2.y2))))) 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. ------ 156736/17136003. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 156737/17136021. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 156738/17136048. ------ 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)(a (^z.z)))) REDUCED to normal form. ------ 156739/17136075. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y)(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 (a a))(((a a)(^y.y))((^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. ------ 156740/17136102. ------ 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 (a a)))) 3. ==[ beta ]==> (((a (a a))(a b))((a a)(a (a a)))) REDUCED to normal form. ------ 156741/17136129. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 156742/17136156. ------ 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 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. ------ 156743/17136183. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(^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))) 5. ==[ beta ]==> (((a b)(a (a a)))(a b)) REDUCED to normal form. ------ 156744/17136210. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) 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. ------ 156745/17136237. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 156746/17136282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(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. ------ 156747/17136291. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 156748/17136381. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a a)(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 156749/17136462. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a) a)(^c.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. ------ 156750/17136579. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 156751/17136597. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 156752/17136606. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 156753/17136624. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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) REDUCED to normal form. ------ 156754/17136687. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a))(^b.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. ------ 156755/17136714. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(z z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 156756/17136768. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 156757/17136795. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 156758/17136822. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 156759/17136912. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 156760/17136939. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a)(a a))) REDUCED to normal form. ------ 156761/17136966. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 156762/17136993. ------ 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.z) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(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))((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. ------ 156763/17137020. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a b)(a (a a)))) 5. ==[ beta ]==> ((a b)((a b)(a (a a)))) REDUCED to normal form. ------ 156764/17137047. ------ 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)(^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. ------ 156765/17137074. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)((a a) a))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)((a a) a))) 7. ==[ beta ]==> (((a b)(^x.x))((a a) a)) REDUCED to normal form. ------ 156766/17137101. ------ 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))(a b))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (a a))(a b))) REDUCED to normal form. ------ 156767/17137128. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) 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. ------ 156768/17137182. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(b a))) REDUCED to normal form. ------ 156769/17137218. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(^a.a))) 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. ------ 156770/17137245. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))(^x2.(^y2.y2)))) 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. ------ 156771/17137380. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 156772/17137488. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((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. ------ 156773/17137524. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))(^a.(^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. ------ 156774/17137542. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a)) c)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a)) c)) 5. ==[ beta ]==> (b (((^y.y)(a a)) c)) 6. ==[ alpha ]==> (b (((^x.x)(a a)) c)) 7. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 156775/17137551. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 156776/17137578. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 156777/17137659. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 156778/17137686. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.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. ------ 156779/17137713. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 156780/17137812. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 156781/17137884. ------ 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))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) b)((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a) b)((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a) b)(^y.y)) 10. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 156782/17137911. ------ 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. ------ 156783/17137938. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)(a b))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) a)(a b))) 5. ==[ beta ]==> ((a (b a))(a (a b))) REDUCED to normal form. ------ 156784/17137965. ------ 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 (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 156785/17137992. ------ 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. ------ 156786/17138244. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a a)(^c.(^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. ------ 156787/17138568. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b) c)) 3. ==[ beta ]==> (((a a)(a a))((^y.b) c)) 4. ==[ alpha ]==> (((a a)(a a))((^x.b) c)) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 156788/17138595. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a) d)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a) d)) 3. ==[ beta ]==> ((^y.y)((^x1.a) d)) 4. ==[ alpha ]==> ((^x.x)((^y.a) d)) 5. ==[ beta ]==> ((^y.a) d) 6. ==[ alpha ]==> ((^x.a) d) 7. ==[ beta ]==> a REDUCED to normal form. ------ 156789/17138712. ------ 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. ------ 156790/17138739. ------ 1. ==[ start ]==> (((a b)(^a.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 156791/17138793. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 156792/17138838. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156793/17138847. ------ 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. ------ 156794/17138874. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^y1.y1))) 10. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.x1))) 11. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 12. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 156795/17138901. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 156796/17139153. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(b (a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b (a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (a b))) REDUCED to normal form. ------ 156797/17139207. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)(a a))) REDUCED to normal form. ------ 156798/17139234. ------ 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. ------ 156799/17139261. ------ 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)(^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. ------ 156800/17139288. ------ 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. ------ 156801/17139459. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^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. ------ 156802/17139567. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156803/17139603. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(^z.z))) 3. ==[ beta ]==> ((b c)((^y.b)(^z.z))) 4. ==[ alpha ]==> ((b c)((^x.b)(^y.y))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 156804/17139630. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)(^a.(^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. ------ 156805/17139738. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 156806/17139765. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.b)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 156807/17139837. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 156808/17139954. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.b))) REDUCED to normal form. ------ 156809/17139981. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(a a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(a a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(a a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 156810/17140008. ------ 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 (^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. ------ 156811/17140233. ------ 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. ------ 156812/17140260. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 156813/17140287. ------ 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. ------ 156814/17140341. ------ 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. ------ 156815/17140368. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> ((b a)(((^x.x) 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. ------ 156816/17140395. ------ 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. ------ 156817/17140539. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(^x1.(x1 x1)))) 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. ------ 156818/17140620. ------ 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. ------ 156819/17140728. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156820/17140845. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(a (^z.(^x1.x1)))) 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. ------ 156821/17140863. ------ 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. ------ 156822/17140890. ------ 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.(^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. ------ 156823/17140944. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(^z.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(^y.(y y)))) 7. ==[ beta ]==> ((b b)((a a)(^y.(y y)))) 8. ==[ alpha ]==> ((b b)((a a)(^x.(x x)))) REDUCED to normal form. ------ 156824/17140953. ------ 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. ------ 156825/17140980. ------ 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 z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156826/17141025. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z)) c)) 3. ==[ beta ]==> (b ((a (^z.z)) c)) 4. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 156827/17141034. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 156828/17141061. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 156829/17141142. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.a))) REDUCED to normal form. ------ 156830/17141169. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (^z.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.(y y)))) REDUCED to normal form. ------ 156831/17141196. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 156832/17141250. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 156833/17141268. ------ 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 (^y.y))))(a a)) REDUCED to normal form. ------ 156834/17141313. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 156835/17141340. ------ 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) 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. ------ 156836/17141367. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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))) REDUCED to normal form. ------ 156837/17141394. ------ 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. ------ 156838/17141421. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c a)) REDUCED to normal form. ------ 156839/17141448. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 156840/17141502. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (a a))) REDUCED to normal form. ------ 156841/17141556. ------ 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. ------ 156842/17141583. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b a)) 3. ==[ beta ]==> ((b (a (a a)))(b a)) REDUCED to normal form. ------ 156843/17141610. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a b)) 3. ==[ beta ]==> ((((a a)(a a)) a)(a b)) REDUCED to normal form. ------ 156844/17141664. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 156845/17146140. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 156846/17147346. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156847/17151804. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a)) b) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(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. ------ 156848/17151828. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156849/17151909. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156850/17152071. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a)(b a))) 3. ==[ beta ]==> (^y.(((a a) a)(b a))) 4. ==[ alpha ]==> (^x.(((a a) a)(b a))) REDUCED to normal form. ------ 156851/17152764. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156852/17153709. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(b a)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(b a)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 156853/17154558. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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))) REDUCED to normal form. ------ 156854/17154918. ------ 1. ==[ start ]==> (((^a.b) c)(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 156855/17154927. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 156856/17154978. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.b)(^a.(^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)(^z1.z1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156857/17155734. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(a (a a)))) 3. ==[ eta ]==> (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. ------ 156858/17156283. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 156859/17156286. ------ 1. ==[ start ]==> ((a (^a.(^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))))(^x1.b)) REDUCED to normal form. ------ 156860/17156571. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^x1.(^y1.(^z1.z1))))(^y.(^z.z))) 4. ==[ alpha ]==> ((b (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 156861/17157174. ------ 1. ==[ start ]==> ((^a.(^b.b))(b (b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156862/17157195. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 156863/17157489. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 156864/17157492. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 156865/17158488. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)(a b))) 3. ==[ beta ]==> ((((^y.a)(a b))((^y.a)(a b)))(((^y.a)(a b))((^y.a)(a b)))) 4. ==[ alpha ]==> ((((^x.a)(a b))((^y.a)(a b)))(((^z.a)(a b))((^x1.a)(a b)))) 5. ==[ beta ]==> ((a ((^y.a)(a b)))(((^z.a)(a b))((^x1.a)(a b)))) 6. ==[ alpha ]==> ((a ((^x.a)(a b)))(((^y.a)(a b))((^z.a)(a b)))) 7. ==[ beta ]==> ((a a)(((^y.a)(a b))((^z.a)(a b)))) 8. ==[ alpha ]==> ((a a)(((^x.a)(a b))((^y.a)(a b)))) 9. ==[ beta ]==> ((a a)(a ((^y.a)(a b)))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)(a b)))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 156866/17159013. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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 (^x.(a a))) REDUCED to normal form. ------ 156867/17159247. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.((^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)(^y.(a a))) REDUCED to normal form. ------ 156868/17160408. ------ 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))) REDUCED to normal form. ------ 156869/17160570. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.a))) REDUCED to normal form. ------ 156870/17161011. ------ 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)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156871/17161236. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 156872/17161344. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.d)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.d)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.d)) REDUCED to normal form. ------ 156873/17161623. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^b.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. ------ 156874/17161704. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.x))) REDUCED to normal form. ------ 156875/17161758. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 156876/17161866. ------ 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. ------ 156877/17161893. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(a a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(a a))) REDUCED to normal form. ------ 156878/17161947. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 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. ------ 156879/17161977. ------ 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))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 156880/17162004. ------ 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 ]==> ((^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. ------ 156881/17162031. ------ 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) 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. ------ 156882/17162058. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 156883/17162112. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 156884/17162139. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 156885/17162166. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 156886/17162193. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 156887/17162220. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a)(b a))) REDUCED to normal form. ------ 156888/17162301. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 156889/17162328. ------ 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))(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. ------ 156890/17162391. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a)(^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. ------ 156891/17162418. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 156892/17162445. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 156893/17162481. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 156894/17162508. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 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. ------ 156895/17162553. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 156896/17162661. ------ 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. ------ 156897/17162688. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 156898/17162715. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.(a a)))) REDUCED to normal form. ------ 156899/17162886. ------ 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. ------ 156900/17162913. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 156901/17163381. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(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. ------ 156902/17163435. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> (a (((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> (a (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 156903/17163516. ------ 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. ------ 156904/17163543. ------ 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 (^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))((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. ------ 156905/17163606. ------ 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. ------ 156906/17163633. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156907/17163660. ------ 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. ------ 156908/17163696. ------ 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. ------ 156909/17163777. ------ 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. ------ 156910/17163804. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 156911/17163858. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(b a))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 156912/17164011. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 156913/17164038. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b) a)(((^x.x) b) c)) 3. ==[ beta ]==> (((a b) a)(b c)) REDUCED to normal form. ------ 156914/17164263. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 156915/17164290. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 156916/17164416. ------ 1. ==[ start ]==> (((^a.b) b)((^b.b) c)) 2. ==[ alpha ]==> (((^x.b) b)((^y.y) c)) 3. ==[ beta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 156917/17164461. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(a (a a)))) 3. ==[ beta ]==> ((^y.(a a))((b a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))((b a)(a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 156918/17164488. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((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. ------ 156919/17164542. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(a b))) 5. ==[ beta ]==> ((^y.y)((a b)(a b))) 6. ==[ alpha ]==> ((^x.x)((a b)(a b))) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 156920/17164623. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 156921/17164677. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^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 (^x.x)) b)) REDUCED to normal form. ------ 156922/17164704. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 156923/17164767. ------ 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. ------ 156924/17164794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.a))((a (^y.(^z.z)))(^x1.a))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.(^y1.y1)))(^z1.a))) REDUCED to normal form. ------ 156925/17164821. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 156926/17164848. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 156927/17164911. ------ 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)(a a))((^y.b)(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(a b))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 156928/17164938. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 156929/17164965. ------ 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 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. ------ 156930/17164992. ------ 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. ------ 156931/17165019. ------ 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. ------ 156932/17165046. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 156933/17165064. ------ 1. ==[ start ]==> (((^a.b) c)((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 156934/17165073. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 156935/17165127. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.b)(^a.(^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. ------ 156936/17165406. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(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)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 156937/17165442. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a)) a)) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a)) a)) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 156938/17165460. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) b)(a a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b)(a a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b)(a a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b (a a))) REDUCED to normal form. ------ 156939/17165496. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156940/17165541. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((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. ------ 156941/17165748. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(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. ------ 156942/17165802. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)(a a))) 3. ==[ beta ]==> (((a b) a)((^y.y)(a a))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(a a))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 156943/17165829. ------ 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. ------ 156944/17165883. ------ 1. ==[ start ]==> ((a (b a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 156945/17166117. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b) a)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b a)) REDUCED to normal form. ------ 156946/17166432. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 156947/17166720. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 156948/17166729. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 156949/17167035. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 156950/17167116. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 156951/17167323. ------ 1. ==[ start ]==> ((a (^b.b))(b (b a))) 2. ==[ alpha ]==> ((a (^x.x))(b (b a))) REDUCED to normal form. ------ 156952/17167341. ------ 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.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 156953/17167638. ------ 1. ==[ start ]==> ((a ((^a.a) b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 156954/17167926. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a) a)) REDUCED to normal form. ------ 156955/17167953. ------ 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. ------ 156956/17167980. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.x))((a a) c)) REDUCED to normal form. ------ 156957/17168133. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(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. ------ 156958/17168241. ------ 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. ------ 156959/17168250. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 156960/17168421. ------ 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. ------ 156961/17168475. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 156962/17168502. ------ 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 a)) REDUCED to normal form. ------ 156963/17168529. ------ 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.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 156964/17168583. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 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. ------ 156965/17168610. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((b (a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 156966/17168637. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(a b))) 3. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 156967/17168916. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(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. ------ 156968/17168952. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z)) a)) 3. ==[ beta ]==> ((b b)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((b b)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 156969/17168979. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 156970/17168997. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(a (^x.x)))) REDUCED to normal form. ------ 156971/17169024. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((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. ------ 156972/17169033. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a) d)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) d)) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 156973/17169078. ------ 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. ------ 156974/17169159. ------ 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)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 156975/17169222. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 156976/17169276. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.(y1 y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(x1 x1))) REDUCED to normal form. ------ 156977/17169303. ------ 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. ------ 156978/17169366. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 156979/17169393. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 156980/17169420. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 156981/17169447. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 156982/17169501. ------ 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))(^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. ------ 156983/17169528. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^y.(^z.z)))) 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. ------ 156984/17169555. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) 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. ------ 156985/17169582. ------ 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.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 156986/17169807. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a a)(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a a)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 156987/17170032. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b) a)) 3. ==[ beta ]==> ((b c)((a b) a)) REDUCED to normal form. ------ 156988/17170059. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a) b)) REDUCED to normal form. ------ 156989/17170185. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b ((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b ((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b ((a a) a))) REDUCED to normal form. ------ 156990/17170266. ------ 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 (^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. ------ 156991/17170275. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 156992/17170374. ------ 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. ------ 156993/17170410. ------ 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. ------ 156994/17170437. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 156995/17170500. ------ 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. ------ 156996/17170527. ------ 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)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 156997/17170554. ------ 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. ------ 156998/17170608. ------ 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.(^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. ------ 156999/17170635. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 157000/17170662. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 157001/17170689. ------ 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.(^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. ------ 157002/17170968. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c d)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c d)) 3. ==[ beta ]==> (((^y.y)(^y.y))(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. ------ 157003/17171157. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157004/17171382. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 157005/17171409. ------ 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. ------ 157006/17171454. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (a (^z.z)))) 3. ==[ beta ]==> (b (c (a (^z.z)))) 4. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 157007/17171463. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z)) c)) REDUCED to normal form. ------ 157008/17171517. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 157009/17171562. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157010/17171571. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^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. ------ 157011/17171625. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.y))) REDUCED to normal form. ------ 157012/17171679. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 157013/17171715. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 157014/17171742. ------ 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))(^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. ------ 157015/17171769. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.a)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 157016/17171796. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (^y.y))) 3. ==[ beta ]==> (((a (a a)) b)(c (^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(c (^x.x))) REDUCED to normal form. ------ 157017/17171823. ------ 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 (^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. ------ 157018/17171850. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.a))) REDUCED to normal form. ------ 157019/17171877. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^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. ------ 157020/17171904. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(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. ------ 157021/17171931. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^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. ------ 157022/17171985. ------ 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)))(^x1.x1))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.x1))) REDUCED to normal form. ------ 157023/17172012. ------ 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. ------ 157024/17172039. ------ 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))) 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. ------ 157025/17172093. ------ 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)(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. ------ 157026/17172110. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z))) x)) 3. ==[ eta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 157027/17172111. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (a ((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (a (a (^y.y))) 4. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 157028/17172933. ------ 1. ==[ start ]==> ((^a.(^b.(^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. ------ 157029/17176578. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.(^b.b))) 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. ------ 157030/17181843. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 157031/17182260. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a) a) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a) a) 3. ==[ beta ]==> ((a (^y.y)) a) 4. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 157032/17182266. ------ 1. ==[ start ]==> ((^a.a)((^a.(a (^a.a))) 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 ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 157033/17182683. ------ 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 ]==> (((^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. ------ 157034/17182860. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a)(^y.y))(^z.b))((((a a)(^y.y))(^z.b))(((a a)(^y.y))(^z.b)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((((a a)(^z.z))(^x1.b))(((a a)(^y1.y1))(^z1.b)))) REDUCED to normal form. ------ 157035/17183085. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157036/17183088. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 157037/17183976. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.b)((^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. ------ 157038/17185014. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.((a a)(a a)))) REDUCED to normal form. ------ 157039/17185374. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 157040/17185425. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> (((((^z.z) b) b)(((^z.z) b) b))(^y.y)) 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)) 7. ==[ beta ]==> (((b b)(b b))(^y.y)) 8. ==[ alpha ]==> (((b b)(b b))(^x.x)) REDUCED to normal form. ------ 157041/17185743. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((a (^y.b))(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.((y y)(y y)))) REDUCED to normal form. ------ 157042/17186181. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(^y.y))(^z.(z z)))) 3. ==[ eta ]==> (b (((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 157043/17186730. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.a)(^b.b))) 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. ------ 157044/17186733. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 157045/17187354. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^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. ------ 157046/17187948. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^a.(^a.(^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. ------ 157047/17188218. ------ 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. ------ 157048/17188497. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(b z))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 157049/17188935. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((((^y.y) a)(^z.b))(((^y.y) a)(^z.b)))((((^y.y) a)(^z.b))(((^y.y) a)(^z.b)))) 4. ==[ alpha ]==> (((((^x.x) a)(^y.b))(((^z.z) a)(^x1.b)))((((^y1.y1) a)(^z1.b))(((^x2.x2) a)(^y2.b)))) 5. ==[ beta ]==> (((a (^y.b))(((^z.z) a)(^x1.b)))((((^y1.y1) a)(^z1.b))(((^x2.x2) a)(^y2.b)))) 6. ==[ alpha ]==> (((a (^x.b))(((^y.y) a)(^z.b)))((((^x1.x1) a)(^y1.b))(((^z1.z1) a)(^x2.b)))) 7. ==[ beta ]==> (((a (^x.b))(a (^z.b)))((((^x1.x1) a)(^y1.b))(((^z1.z1) a)(^x2.b)))) 8. ==[ alpha ]==> (((a (^x.b))(a (^y.b)))((((^z.z) a)(^x1.b))(((^y1.y1) a)(^z1.b)))) 9. ==[ beta ]==> (((a (^x.b))(a (^y.b)))((a (^x1.b))(((^y1.y1) a)(^z1.b)))) 10. ==[ alpha ]==> (((a (^x.b))(a (^y.b)))((a (^z.b))(((^x1.x1) a)(^y1.b)))) 11. ==[ beta ]==> (((a (^x.b))(a (^y.b)))((a (^z.b))(a (^y1.b)))) 12. ==[ alpha ]==> (((a (^x.b))(a (^y.b)))((a (^z.b))(a (^x1.b)))) REDUCED to normal form. ------ 157050/17189253. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 157051/17189469. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 157052/17189694. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(a a)))) REDUCED to normal form. ------ 157053/17190855. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.a))) 5. ==[ beta ]==> ((a b)(^y.(^z.a))) 6. ==[ alpha ]==> ((a b)(^x.(^y.a))) REDUCED to normal form. ------ 157054/17191458. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157055/17191593. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(^b.(^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)(^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. ------ 157056/17191818. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(z (z z)))) REDUCED to normal form. ------ 157057/17191899. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^y.a)) REDUCED to normal form. ------ 157058/17191995. ------ 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))) REDUCED to normal form. ------ 157059/17191998. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 157060/17192151. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.c)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.c)) REDUCED to normal form. ------ 157061/17192313. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 157062/17192394. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.a)) 3. ==[ beta ]==> (((^y.y)(a a))(^z.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. ------ 157063/17192412. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.z)) 3. ==[ beta ]==> ((a (^y.y))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 157064/17192417. ------ 1. ==[ start ]==> (^a.(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 157065/17192418. ------ 1. ==[ start ]==> (a (^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (a (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 157066/17192424. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) a)) 3. ==[ beta ]==> ((a a)(a (^y.y))) 4. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 157067/17192442. ------ 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))) 5. ==[ beta ]==> (a ((^y.y)(a a))) 6. ==[ alpha ]==> (a ((^x.x)(a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 157068/17192469. ------ 1. ==[ start ]==> (((a a) a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a) a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 157069/17192496. ------ 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. ------ 157070/17192523. ------ 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)))) 5. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 157071/17192550. ------ 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)((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. ------ 157072/17192577. ------ 1. ==[ start ]==> (((a a) b)((b a)((a a) a))) REDUCED to normal form. ------ 157073/17192604. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 157074/17192631. ------ 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)(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. ------ 157075/17192658. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 157076/17192712. ------ 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.(^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. ------ 157077/17192793. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 157078/17192820. ------ 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. ------ 157079/17192838. ------ 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. ------ 157080/17192937. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 157081/17192964. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 157082/17192991. ------ 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. ------ 157083/17193018. ------ 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. ------ 157084/17193054. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(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. ------ 157085/17193135. ------ 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. ------ 157086/17193162. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 157087/17193216. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 157088/17193243. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^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. ------ 157089/17193261. ------ 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. ------ 157090/17193288. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b (^z.z)) b)) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z)) b)) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y)) b)) REDUCED to normal form. ------ 157091/17193378. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 157092/17193459. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 157093/17193540. ------ 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. ------ 157094/17193594. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 157095/17193630. ------ 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. ------ 157096/17193927. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(b a))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 7. ==[ beta ]==> (b ((^y.y)(b a))) 8. ==[ alpha ]==> (b ((^x.x)(b a))) 9. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 157097/17193954. ------ 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. ------ 157098/17194008. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) REDUCED to normal form. ------ 157099/17194035. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 157100/17194134. ------ 1. ==[ start ]==> ((a (^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)((^z.z) 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. ------ 157101/17194152. ------ 1. ==[ start ]==> (((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 z)))) REDUCED to normal form. ------ 157102/17194179. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 157103/17194233. ------ 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. ------ 157104/17194260. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)(^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a b)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 157105/17194323. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(b a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157106/17194404. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) IRREDUCIBLE: cycle. ------ 157107/17194485. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 157108/17194512. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.b)(^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))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 157109/17194539. ------ 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.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 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. ------ 157110/17194674. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 157111/17194872. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (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. ------ 157112/17194881. ------ 1. ==[ start ]==> (((a b)(a a))((^b.b) c)) 2. ==[ alpha ]==> (((a b)(a a))((^x.x) c)) 3. ==[ beta ]==> (((a b)(a a)) c) REDUCED to normal form. ------ 157113/17195088. ------ 1. ==[ start ]==> (((a b) b)((a (a a))(b a))) REDUCED to normal form. ------ 157114/17195115. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) 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. ------ 157115/17195142. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 157116/17195160. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(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. ------ 157117/17195169. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 157118/17195367. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(^y.b))) 3. ==[ beta ]==> (((a a)(a a))((a b)(^y.b))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(^x.b))) REDUCED to normal form. ------ 157119/17195394. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 157120/17195475. ------ 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. ------ 157121/17195502. ------ 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))) REDUCED to normal form. ------ 157122/17195529. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 157123/17195556. ------ 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. ------ 157124/17195583. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b) b)) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 157125/17195619. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 157126/17195754. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 157127/17195835. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 157128/17195862. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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. ------ 157129/17195871. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b b)) REDUCED to normal form. ------ 157130/17195898. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(a ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(a ((a a)(a a)))) REDUCED to normal form. ------ 157131/17195952. ------ 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)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157132/17195979. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((b a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((b a) a)) REDUCED to normal form. ------ 157133/17196006. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 157134/17196033. ------ 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)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z)(^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. ------ 157135/17196060. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)((a a) a))) REDUCED to normal form. ------ 157136/17196258. ------ 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. ------ 157137/17196285. ------ 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. ------ 157138/17196312. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((b a)(^y.a))) REDUCED to normal form. ------ 157139/17196339. ------ 1. ==[ start ]==> ((a (b a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 157140/17196429. ------ 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) REDUCED to normal form. ------ 157141/17196510. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 157142/17196618. ------ 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. ------ 157143/17196699. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 157144/17196780. ------ 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. ------ 157145/17196888. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)(^b.b))) 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. ------ 157146/17196906. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b) a)) 2. ==[ alpha ]==> (((a a)(b a))((^x.x) a)) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 157147/17196933. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 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. ------ 157148/17196987. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y)) d)) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 157149/17197167. ------ 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))((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. ------ 157150/17197185. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157151/17197347. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 157152/17197455. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 157153/17197482. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 157154/17197509. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 157155/17197644. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 157156/17197752. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 157157/17197824. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 157158/17198058. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157159/17198103. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(a (^a.(^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. ------ 157160/17198265. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^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. ------ 157161/17198373. ------ 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. ------ 157162/17198427. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 157163/17198454. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.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. ------ 157164/17198589. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.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. ------ 157165/17198598. ------ 1. ==[ start ]==> (((a b)(^c.a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(c (a a))) REDUCED to normal form. ------ 157166/17198625. ------ 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. ------ 157167/17198652. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (b a))) REDUCED to normal form. ------ 157168/17198706. ------ 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. ------ 157169/17198733. ------ 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. ------ 157170/17198931. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 157171/17198958. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 157172/17198985. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a b)(^y.a))) REDUCED to normal form. ------ 157173/17199039. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^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 (^z.z)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 157174/17199066. ------ 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. ------ 157175/17199093. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) 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. ------ 157176/17199129. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 157177/17199264. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 157178/17199372. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 157179/17199408. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 157180/17199435. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)(a a))) REDUCED to normal form. ------ 157181/17199489. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((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. ------ 157182/17199516. ------ 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. ------ 157183/17199597. ------ 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. ------ 157184/17199615. ------ 1. ==[ start ]==> (((^a.b)(a b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(b (^y.(a a)))) 3. ==[ beta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 157185/17199624. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 157186/17199822. ------ 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. ------ 157187/17199849. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(a a)))) REDUCED to normal form. ------ 157188/17199876. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a)) a)) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 157189/17199903. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b) b)) REDUCED to normal form. ------ 157190/17200092. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 157191/17200119. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b) b)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b) b)) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 157192/17200263. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b (^y1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b (^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b (^x2.b))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157193/17200344. ------ 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)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 157194/17200452. ------ 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.(^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. ------ 157195/17200560. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^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. ------ 157196/17200587. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 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. ------ 157197/17200623. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(c (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(c (^y.y))) REDUCED to normal form. ------ 157198/17200650. ------ 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. ------ 157199/17200731. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(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. ------ 157200/17200758. ------ 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. ------ 157201/17200830. ------ 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))(b (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157202/17200839. ------ 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 a) a))) REDUCED to normal form. ------ 157203/17200956. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 157204/17200983. ------ 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 (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 157205/17201010. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.a))) 5. ==[ beta ]==> ((a b)((a a)(^y.a))) 6. ==[ alpha ]==> ((a b)((a a)(^x.a))) REDUCED to normal form. ------ 157206/17201037. ------ 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. ------ 157207/17201064. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z)) b)) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y)) b)) 7. ==[ beta ]==> ((b a)((^y.y) b)) 8. ==[ alpha ]==> ((b a)((^x.x) b)) 9. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 157208/17201226. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^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. ------ 157209/17201253. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z)) c)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z)) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y)) c)) 5. ==[ beta ]==> ((b a)((^y.(y y)) c)) 6. ==[ alpha ]==> ((b a)((^x.(x x)) c)) 7. ==[ beta ]==> ((b a)(c c)) REDUCED to normal form. ------ 157210/17201424. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.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. ------ 157211/17201505. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(^a.a))) 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. ------ 157212/17201613. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157213/17201730. ------ 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. ------ 157214/17201748. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^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 ]==> ((^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. ------ 157215/17201775. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(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. ------ 157216/17201829. ------ 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))((^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. ------ 157217/17201910. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.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. ------ 157218/17201919. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (a (^z.z)))) REDUCED to normal form. ------ 157219/17201946. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(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. ------ 157220/17201973. ------ 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. ------ 157221/17202027. ------ 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 (^z1.z1)))) REDUCED to normal form. ------ 157222/17202054. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((b (^x.(x x)))((a a) a)) REDUCED to normal form. ------ 157223/17202135. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 157224/17202153. ------ 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 (^x.(x (^y.y))))((^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. ------ 157225/17202171. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 157226/17202198. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 157227/17202252. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.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. ------ 157228/17202279. ------ 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.(^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. ------ 157229/17202306. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) c)) 3. ==[ beta ]==> ((((a a) a)(b a)) c) REDUCED to normal form. ------ 157230/17202333. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 157231/17202360. ------ 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)))) 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. ------ 157232/17202387. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y)) a)) REDUCED to normal form. ------ 157233/17202441. ------ 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.(^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. ------ 157234/17202468. ------ 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)) 5. ==[ beta ]==> ((b (a (a a))) b) REDUCED to normal form. ------ 157235/17202495. ------ 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))) 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. ------ 157236/17202549. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 157237/17202567. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a a)) 3. ==[ beta ]==> ((a (^y.y))(a a)) 4. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 157238/17202573. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a)))) a) 2. ==[ alpha ]==> ((^x.(x (x (^y.y)))) a) 3. ==[ beta ]==> (a (a (^y.y))) 4. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 157239/17202575. ------ 1. ==[ start ]==> (^a.(a (a (a (^a.a))))) 2. ==[ alpha ]==> (^x.(x (x (x (^y.y))))) REDUCED to normal form. ------ 157240/17202576. ------ 1. ==[ start ]==> (a (a (a (a (^a.a))))) 2. ==[ alpha ]==> (a (a (a (a (^x.x))))) REDUCED to normal form. ------ 157241/17202579. ------ 1. ==[ start ]==> ((^a.a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (^y.(y (y (^z.z)))) 4. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 157242/17208249. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157243/17212725. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a) b) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a) b) 3. ==[ beta ]==> ((a (^y.y)) b) 4. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 157244/17212731. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.z)) 3. ==[ beta ]==> ((^z.z)((^z.z)(^y.y))) 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. ------ 157245/17212734. ------ 1. ==[ start ]==> ((a (a (a (^a.a)))) a) 2. ==[ alpha ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 157246/17212740. ------ 1. ==[ start ]==> ((^a.a)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 3. ==[ beta ]==> (a (a (a (^y.y)))) 4. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 157247/17212743. ------ 1. ==[ start ]==> ((a a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 157248/17212749. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157249/17212767. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((((^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))) 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))) 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. ------ 157250/17212794. ------ 1. ==[ start ]==> ((^a.b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.b)((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 157251/17212875. ------ 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 (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))(^y.y)) 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)) REDUCED to normal form. ------ 157252/17213064. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (a a))((^z.z) b))) 3. ==[ eta ]==> ((^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. ------ 157253/17213166. ------ 1. ==[ start ]==> (((a a)(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 157254/17213235. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 157255/17213985. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a a)((^x.x)(^y.y)))(^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. ------ 157256/17214117. ------ 1. ==[ start ]==> ((^a.((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((b a)((^y.y)(^z.z)))((b a)((^y.y)(^z.z))))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((b a)((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1))))((b a)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((b a)(^y.y))((b a)((^z.z)(^x1.x1))))((b a)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((((b a)(^x.x))((b a)((^y.y)(^z.z))))((b a)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((((b a)(^x.x))((b a)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((((b a)(^x.x))((b a)(^y.y)))((b a)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((((b a)(^x.x))((b a)(^y.y)))((b a)(^x1.x1))) 10. ==[ alpha ]==> ((((b a)(^x.x))((b a)(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 157257/17214450. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 157258/17215146. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(b (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(b (^z.z)))) 7. ==[ beta ]==> (a (^y.(b (^z.z)))) 8. ==[ alpha ]==> (a (^x.(b (^y.y)))) REDUCED to normal form. ------ 157259/17215224. ------ 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)))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((a (^z.(^x1.x1)))((^y1.y1) a))((a (^z.(^x1.x1)))((^y1.y1) a)))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.(^z.z)))((^x1.x1) a))((a (^y1.(^z1.z1)))((^x2.x2) a)))) 5. ==[ beta ]==> (((a (^y.(^z.z)))((^x1.x1) a))((a (^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.(^y1.y1)))((^z1.z1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.(^y1.y1)))((^z1.z1) a))) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))((^y1.y1) a))) 9. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 157260/17216217. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 157261/17216892. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((^z.z) y))) 3. ==[ eta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 157262/17217225. ------ 1. ==[ start ]==> (((a a)(b a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a a)(b a))(^x.b)) REDUCED to normal form. ------ 157263/17217492. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x1.x1))(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 157264/17217828. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 157265/17218143. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 157266/17218410. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a a)(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157267/17218413. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(b a))) 3. ==[ beta ]==> ((a b)(^y.(b a))) 4. ==[ alpha ]==> ((a b)(^x.(b a))) REDUCED to normal form. ------ 157268/17218701. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(z a))) REDUCED to normal form. ------ 157269/17219223. ------ 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. ------ 157270/17219727. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 157271/17220411. ------ 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)(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^z.(z z))) REDUCED to normal form. ------ 157272/17220489. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 157273/17220807. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(a y))) 3. ==[ eta ]==> ((((^x.x) b) c) a) 4. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 157274/17221185. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.b))) REDUCED to normal form. ------ 157275/17221650. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 157276/17222184. ------ 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. ------ 157277/17222292. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 157278/17222400. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 157279/17222469. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)(^x1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 157280/17222571. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a a))((^x.x) b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.y)) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 157281/17222625. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 157282/17222706. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.c)) REDUCED to normal form. ------ 157283/17222760. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(x1 (^y1.y1)))) REDUCED to normal form. ------ 157284/17222787. ------ 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. ------ 157285/17222868. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(z z))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(z z))) 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. ------ 157286/17222886. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 157287/17222892. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a a)) 2. ==[ alpha ]==> ((^x.(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. ------ 157288/17222895. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 157289/17222900. ------ 1. ==[ start ]==> (^a.(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 157290/17222901. ------ 1. ==[ start ]==> (a (^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (a (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 157291/17222907. ------ 1. ==[ start ]==> ((a a)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 157292/17222916. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 157293/17222934. ------ 1. ==[ start ]==> ((a (a a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 157294/17222961. ------ 1. ==[ start ]==> ((a b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 157295/17223015. ------ 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. ------ 157296/17223042. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 157297/17223177. ------ 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. ------ 157298/17223204. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 157299/17223231. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) 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))) 5. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 157300/17223276. ------ 1. ==[ start ]==> (((a (^a.a)) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.(^z.z)))) REDUCED to normal form. ------ 157301/17223330. ------ 1. ==[ start ]==> (((a a)(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 157302/17223348. ------ 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)(^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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157303/17223402. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 157304/17223510. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> ((((a a)(^y.y))(^z.b))(((a a)(^y.y))(^z.b))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 157305/17223537. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(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. ------ 157306/17223573. ------ 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. ------ 157307/17223618. ------ 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. ------ 157308/17223627. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^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)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 157309/17223645. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((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. ------ 157310/17223654. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(b ((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(b ((^z.z) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.a))(b b)) REDUCED to normal form. ------ 157311/17223681. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 157312/17223708. ------ 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. ------ 157313/17223816. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 157314/17223951. ------ 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. ------ 157315/17223978. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 157316/17224005. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 157317/17224032. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 157318/17224059. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(^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. ------ 157319/17224086. ------ 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. ------ 157320/17224149. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 157321/17224176. ------ 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. ------ 157322/17224203. ------ 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. ------ 157323/17224230. ------ 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. ------ 157324/17224257. ------ 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. ------ 157325/17224284. ------ 1. ==[ start ]==> ((a ((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((b a)((^x.x)(^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. ------ 157326/17224491. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (^x1.(a a)))) REDUCED to normal form. ------ 157327/17224617. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a (^x.b))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.a))) REDUCED to normal form. ------ 157328/17224788. ------ 1. ==[ start ]==> (((^a.b) a)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 157329/17224968. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 157330/17224977. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 157331/17224995. ------ 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)) 5. ==[ beta ]==> ((a b)(b c)) REDUCED to normal form. ------ 157332/17225004. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.a)) REDUCED to normal form. ------ 157333/17225112. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.b))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 157334/17225139. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 157335/17225166. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 157336/17225283. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 157337/17225310. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(a (b (^z.z)))) 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. ------ 157338/17225337. ------ 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. ------ 157339/17225364. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) b)(a (^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. ------ 157340/17225391. ------ 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)))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))((^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. ------ 157341/17225625. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 157342/17225652. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.(a a)))) REDUCED to normal form. ------ 157343/17225697. ------ 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)(^z.z))((^y.y)(^z.z)))(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(^y1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.z))) 9. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.z))) 10. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.y))) 11. ==[ beta ]==> (((a a)(a a))(^y.y)) 12. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 157344/17225706. ------ 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. ------ 157345/17225733. ------ 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)(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. ------ 157346/17225760. ------ 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)))((^y1.y1) 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. ------ 157347/17225778. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 157348/17226003. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 157349/17226102. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) c)) 5. ==[ beta ]==> ((a (^y.(^z.z))) c) 6. ==[ alpha ]==> ((a (^x.(^y.y))) c) REDUCED to normal form. ------ 157350/17226246. ------ 1. ==[ start ]==> (((a b) c)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 157351/17226273. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 157352/17226354. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 157353/17226381. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.b))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(a a))) REDUCED to normal form. ------ 157354/17226579. ------ 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. ------ 157355/17226606. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(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 (^x.x))(a a))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^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. ------ 157356/17226633. ------ 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 a)(^y.y)))) 3. ==[ beta ]==> ((a (a b))((a (a a))((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (a b))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 157357/17226660. ------ 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. ------ 157358/17226687. ------ 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.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((^y.y)((a (^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 157359/17226714. ------ 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. ------ 157360/17226912. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(^z.b))) 5. ==[ beta ]==> (b (((a a) a)(^z.b))) 6. ==[ alpha ]==> (b (((a a) a)(^x.b))) REDUCED to normal form. ------ 157361/17227056. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z) b)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y) b)) 5. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 157362/17227101. ------ 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. ------ 157363/17227128. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((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. ------ 157364/17227164. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 157365/17227191. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 157366/17227245. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 157367/17227272. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 157368/17227299. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 157369/17227389. ------ 1. ==[ start ]==> (((a a)(b a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))(a ((^x.x) b))) 3. ==[ beta ]==> (((a a)(b a))(a b)) REDUCED to normal form. ------ 157370/17227416. ------ 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 (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 157371/17227443. ------ 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. ------ 157372/17227470. ------ 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))((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(a b))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 157373/17227497. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> (((a a) a)((a a)(a (a a)))) REDUCED to normal form. ------ 157374/17227524. ------ 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)(^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. ------ 157375/17227551. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 157376/17227578. ------ 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.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> (((a a) a)((^y.y)(a b))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(a b))) 9. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 157377/17227605. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 157378/17227659. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(b a))) REDUCED to normal form. ------ 157379/17227749. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 157380/17227830. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a b)(^b.(^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. ------ 157381/17227947. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 157382/17227974. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(b 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. ------ 157383/17227992. ------ 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)(^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. ------ 157384/17228046. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((b a) b)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a) b)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a) b)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a) b)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a) b)) 7. ==[ beta ]==> (((a a)(a a))((b a) b)) REDUCED to normal form. ------ 157385/17228082. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 157386/17228136. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.b)(^b.(^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. ------ 157387/17228190. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 157388/17228244. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 157389/17228280. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(b (b a))) REDUCED to normal form. ------ 157390/17228307. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 157391/17228334. ------ 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))) REDUCED to normal form. ------ 157392/17228361. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 157393/17228388. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))((^z.z) a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))((^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. ------ 157394/17228415. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a b)(a (a a)))) REDUCED to normal form. ------ 157395/17228442. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)((^y.y)(^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. ------ 157396/17228469. ------ 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 a) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(^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)))((^y.y)((a a) a))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)((a a) a))) 7. ==[ beta ]==> (((a a)(a (a a)))((a a) a)) REDUCED to normal form. ------ 157397/17228496. ------ 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))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))(a b))) REDUCED to normal form. ------ 157398/17228541. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157399/17228550. ------ 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)))) REDUCED to normal form. ------ 157400/17228577. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a a)(b a))) 3. ==[ beta ]==> ((a b)((a a)(b a))) REDUCED to normal form. ------ 157401/17228613. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((b a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 157402/17228748. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 157403/17228865. ------ 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. ------ 157404/17228910. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z)) b)) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y)) b)) 5. ==[ beta ]==> (b (((a a)(^y.y)) b)) 6. ==[ alpha ]==> (b (((a a)(^x.x)) b)) REDUCED to normal form. ------ 157405/17228919. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 157406/17228946. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 157407/17229027. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(^c.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. ------ 157408/17229054. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.b)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)(^z.b))) 5. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 157409/17229081. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 157410/17229108. ------ 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.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^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. ------ 157411/17229252. ------ 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. ------ 157412/17229279. ------ 1. ==[ start ]==> (((a (^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))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^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. ------ 157413/17229306. ------ 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. ------ 157414/17229333. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (a b))) REDUCED to normal form. ------ 157415/17229360. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^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 (^x.x))(a a))) REDUCED to normal form. ------ 157416/17229387. ------ 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. ------ 157417/17229612. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((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. ------ 157418/17229891. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.a)(^c.(^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)))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 157419/17229936. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a)) b)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a)) b)) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 157420/17229963. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.b) c)) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 157421/17230080. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(c (^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(c (^y.b))) REDUCED to normal form. ------ 157422/17230107. ------ 1. ==[ start ]==> (((a b)(^a.b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(b (^y.(a a)))) REDUCED to normal form. ------ 157423/17230161. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 157424/17230206. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a) a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157425/17230215. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 157426/17230242. ------ 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. ------ 157427/17230269. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 10. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 157428/17230575. ------ 1. ==[ start ]==> (((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)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (a a))) REDUCED to normal form. ------ 157429/17230602. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)(a a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)(a a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 157430/17230629. ------ 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. ------ 157431/17230656. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^x.x)))((^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. ------ 157432/17230827. ------ 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)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 157433/17230971. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(a b))) 3. ==[ beta ]==> ((b c)((^y.y)(a b))) 4. ==[ alpha ]==> ((b c)((^x.x)(a b))) 5. ==[ beta ]==> ((b c)(a b)) REDUCED to normal form. ------ 157434/17230998. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)(^y.y))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 157435/17231043. ------ 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 (^x.x))((^z.z) c)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) c)) 7. ==[ beta ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 157436/17231106. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 157437/17231205. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a) b)) 3. ==[ beta ]==> (b ((^z.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 157438/17231322. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (^x1.a))) REDUCED to normal form. ------ 157439/17231349. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a (^z.b))) 3. ==[ beta ]==> ((b (^y.a))(a (^z.b))) 4. ==[ alpha ]==> ((b (^x.a))(a (^y.b))) REDUCED to normal form. ------ 157440/17231628. ------ 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. ------ 157441/17231655. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.y))) REDUCED to normal form. ------ 157442/17231709. ------ 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. ------ 157443/17231736. ------ 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. ------ 157444/17231763. ------ 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.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 157445/17231817. ------ 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 (^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. ------ 157446/17231907. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)(^b.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. ------ 157447/17231988. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^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. ------ 157448/17232213. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b (^z.(z z)))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.(z z)))) 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. ------ 157449/17232258. ------ 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. ------ 157450/17232312. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))(^b.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. ------ 157451/17232321. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^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. ------ 157452/17232348. ------ 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. ------ 157453/17232393. ------ 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. ------ 157454/17232402. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.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. ------ 157455/17232429. ------ 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))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 157456/17232456. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(z z))) REDUCED to normal form. ------ 157457/17232501. ------ 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) 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. ------ 157458/17232510. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.(^z1.z1)))) REDUCED to normal form. ------ 157459/17232537. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^b.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. ------ 157460/17232564. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.(y y)))) REDUCED to normal form. ------ 157461/17232618. ------ 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 (^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. ------ 157462/17232636. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.a))) REDUCED to normal form. ------ 157463/17232681. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (a a))) REDUCED to normal form. ------ 157464/17232708. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b (a (^y.y)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b (a (^y.y)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 157465/17232735. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a ((^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. ------ 157466/17232762. ------ 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 (^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 157467/17232789. ------ 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. ------ 157468/17232816. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c a)) REDUCED to normal form. ------ 157469/17232843. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b b)) 5. ==[ beta ]==> (((a a)(a a))(b b)) REDUCED to normal form. ------ 157470/17232870. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a c)) REDUCED to normal form. ------ 157471/17232924. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (a (^x1.x1)))) REDUCED to normal form. ------ 157472/17232951. ------ 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. ------ 157473/17232978. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(b a)) REDUCED to normal form. ------ 157474/17233032. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 157475/17233050. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a (^z.z))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 157476/17233056. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a)))) b) 2. ==[ alpha ]==> ((^x.(x (x (^y.y)))) b) 3. ==[ beta ]==> (b (b (^y.y))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 157477/17233059. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 157478/17233067. ------ 1. ==[ start ]==> (^a.((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^x.(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 157479/17233068. ------ 1. ==[ start ]==> (a ((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (a ((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (a (^y.(y (^z.z)))) 4. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 157480/17233071. ------ 1. ==[ start ]==> ((^a.a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 157481/17233080. ------ 1. ==[ start ]==> ((^a.(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157482/17243223. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^z.(^x1.x1))((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157483/17243226. ------ 1. ==[ start ]==> ((a (a (a (^a.a)))) b) 2. ==[ alpha ]==> ((a (a (a (^x.x)))) b) REDUCED to normal form. ------ 157484/17243235. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a)))) 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 ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 157485/17243241. ------ 1. ==[ start ]==> ((^a.a)((^a.a)(^a.(a (^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))) REDUCED to normal form. ------ 157486/17243244. ------ 1. ==[ start ]==> ((a a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 157487/17243250. ------ 1. ==[ start ]==> ((^a.(^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (a (a (^z.z))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157488/17243253. ------ 1. ==[ start ]==> ((a (^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 157489/17243331. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157490/17243493. ------ 1. ==[ start ]==> ((^a.(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (^x.((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 157491/17244081. ------ 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. ------ 157492/17244186. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)(^y1.(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. ------ 157493/17245131. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.a)((a a)(^z.z))) b) 4. ==[ alpha ]==> (((^x.a)((a a)(^y.y))) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 157494/17246376. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(^y.((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))(^y.((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 157495/17246736. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(^y.((y y)(y y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.((y y)(y y)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 157496/17247078. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 157497/17247393. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 157498/17247705. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 157499/17247726. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 157500/17248596. ------ 1. ==[ start ]==> ((^a.(^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(c ((a a)(^z.z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157501/17248644. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 157502/17248923. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(b a))) 3. ==[ beta ]==> ((^y.y)(^z.(b a))) 4. ==[ alpha ]==> ((^x.x)(^y.(b a))) 5. ==[ beta ]==> (^y.(b a)) 6. ==[ alpha ]==> (^x.(b a)) REDUCED to normal form. ------ 157503/17249202. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(^d.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.a))) REDUCED to normal form. ------ 157504/17249910. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((((^y.(y y))((a a) a))((^y.(y y))((a a) a)))(((^y.(y y))((a a) a))((^y.(y y))((a a) a)))) 4. ==[ alpha ]==> ((((^x.(x x))((a a) a))((^y.(y y))((a a) a)))(((^z.(z z))((a a) a))((^x1.(x1 x1))((a a) a)))) 5. ==[ beta ]==> (((((a a) a)((a a) a))((^y.(y y))((a a) a)))(((^z.(z z))((a a) a))((^x1.(x1 x1))((a a) a)))) 6. ==[ alpha ]==> (((((a a) a)((a a) a))((^x.(x x))((a a) a)))(((^y.(y y))((a a) a))((^z.(z z))((a a) a)))) 7. ==[ beta ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))(((^y.(y y))((a a) a))((^z.(z z))((a a) a)))) 8. ==[ alpha ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))(((^x.(x x))((a a) a))((^y.(y y))((a a) a)))) 9. ==[ beta ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))((((a a) a)((a a) a))((^y.(y y))((a a) a)))) 10. ==[ alpha ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))((((a a) a)((a a) a))((^x.(x x))((a a) a)))) 11. ==[ 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. ------ 157505/17250696. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 157506/17250912. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.(a a)))) REDUCED to normal form. ------ 157507/17251308. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.b))) 3. ==[ beta ]==> ((b c)(^y.(^z.b))) 4. ==[ alpha ]==> ((b c)(^x.(^y.b))) REDUCED to normal form. ------ 157508/17251857. ------ 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. ------ 157509/17252151. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 157510/17252793. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.d)) REDUCED to normal form. ------ 157511/17252970. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b c)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b c)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 157512/17252991. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 157513/17253072. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^b.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. ------ 157514/17253153. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 157515/17253207. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(a (^z.z)))) REDUCED to normal form. ------ 157516/17253261. ------ 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.(^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. ------ 157517/17253315. ------ 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)))) 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. ------ 157518/17253369. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 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. ------ 157519/17253387. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.a)) 3. ==[ beta ]==> ((a (^y.y))(^z.a)) 4. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 157520/17253393. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.z))) 3. ==[ beta ]==> ((a (^z.z))((a (^z.z))(^y.y))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 157521/17253396. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 157522/17253405. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.z)(^y.y)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157523/17253417. ------ 1. ==[ start ]==> ((a a)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 157524/17253426. ------ 1. ==[ start ]==> ((a (^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a (a (a (^y.y))))) REDUCED to normal form. ------ 157525/17253435. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (a ((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> (a ((^x.(x (^y.y))) a)) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 157526/17253453. ------ 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)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 157527/17253480. ------ 1. ==[ start ]==> (((^a.a)(a a))((b (^a.a))(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)))) REDUCED to normal form. ------ 157528/17253507. ------ 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. ------ 157529/17253516. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.x) b)((^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. ------ 157530/17253561. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 157531/17253588. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 157532/17253615. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 157533/17253642. ------ 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))((^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. ------ 157534/17253669. ------ 1. ==[ start ]==> ((a (^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 157535/17253750. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.a)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.a)((a (a a))((^y.y) b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 157536/17253777. ------ 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) 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. ------ 157537/17253831. ------ 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. ------ 157538/17253867. ------ 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 (^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. ------ 157539/17253894. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a))(^a.(^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)))) REDUCED to normal form. ------ 157540/17253957. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a a))) REDUCED to normal form. ------ 157541/17253984. ------ 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. ------ 157542/17254002. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((b a)(^y.a))) 3. ==[ beta ]==> ((a a)((b a)(^y.a))) 4. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 157543/17254083. ------ 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. ------ 157544/17254137. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 157545/17254164. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a a))(^z.z))) REDUCED to normal form. ------ 157546/17254254. ------ 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. ------ 157547/17254326. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(a a)) c)) 3. ==[ beta ]==> ((b b)(((a a)(a a)) c)) REDUCED to normal form. ------ 157548/17254362. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 157549/17254830. ------ 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)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((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. ------ 157550/17254884. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> (a ((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((a b)((^x.x)(a a)))) 7. ==[ beta ]==> (a ((a b)(a a))) REDUCED to normal form. ------ 157551/17254965. ------ 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. ------ 157552/17254992. ------ 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) a)((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1) 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. ------ 157553/17255046. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)(b (^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a a)(b (^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((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. ------ 157554/17255082. ------ 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.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157555/17255109. ------ 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. ------ 157556/17255145. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^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. ------ 157557/17255172. ------ 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.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 157558/17255253. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))(a b))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a b))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 157559/17255280. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 157560/17255298. ------ 1. ==[ start ]==> (((^a.b) a)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.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. ------ 157561/17255307. ------ 1. ==[ start ]==> ((a (a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 157562/17255460. ------ 1. ==[ start ]==> ((((a a) a) b)((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a) b)((b (^x.x)) a)) REDUCED to normal form. ------ 157563/17255487. ------ 1. ==[ start ]==> (((a b) a)(((a a)(a a)) b)) REDUCED to normal form. ------ 157564/17255514. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(^x.b))(b c)) REDUCED to normal form. ------ 157565/17255739. ------ 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))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 157566/17255766. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 157567/17255865. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b) b)((^y.(a a)) b)) 3. ==[ beta ]==> (b ((^y.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 157568/17255910. ------ 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)))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 157569/17255937. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 157570/17255991. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(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. ------ 157571/17256072. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 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. ------ 157572/17256126. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^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))))) 7. ==[ beta ]==> ((a a)(a (a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 157573/17256153. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 157574/17256216. ------ 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. ------ 157575/17256243. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((((^y.y) b)(^z.(^x1.x1)))(((^y.y) b)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 9. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 10. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 11. ==[ beta ]==> ((b (^x.(^y.y)))(b (^x1.(^y1.y1)))) 12. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 157576/17256270. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 157577/17256297. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(^z.(z z)))) REDUCED to normal form. ------ 157578/17256324. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 157579/17256360. ------ 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)(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 a)) REDUCED to normal form. ------ 157580/17256387. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a b)) b) REDUCED to normal form. ------ 157581/17256441. ------ 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. ------ 157582/17256468. ------ 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. ------ 157583/17256495. ------ 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 (^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) REDUCED to normal form. ------ 157584/17256513. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 157585/17256522. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 157586/17256549. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 157587/17256909. ------ 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)))) REDUCED to normal form. ------ 157588/17256945. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 157589/17256990. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((b a)((^z.z) a))) 3. ==[ beta ]==> (b ((b a)((^z.z) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 157590/17257224. ------ 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. ------ 157591/17257251. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(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. ------ 157592/17257278. ------ 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. ------ 157593/17257305. ------ 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 (^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. ------ 157594/17257566. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 157595/17257881. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 157596/17257899. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 157597/17258178. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157598/17258565. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((b a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((b a) b)) REDUCED to normal form. ------ 157599/17258592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z)) c)) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z)) c)) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y)) c)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 157600/17258772. ------ 1. ==[ start ]==> ((a (^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 157601/17258817. ------ 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 (^x.x))(b a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 157602/17259096. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 157603/17259402. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a) a)) 3. ==[ beta ]==> ((b a)((b a) a)) REDUCED to normal form. ------ 157604/17259429. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 157605/17259690. ------ 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))(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. ------ 157606/17259726. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(a a)) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a)) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a)) c)) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 157607/17259897. ------ 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. ------ 157608/17259978. ------ 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 a)) REDUCED to normal form. ------ 157609/17260059. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 157610/17260086. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 157611/17260365. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c (a b))) 3. ==[ beta ]==> ((^y.(^z.z))(c (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157612/17260446. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 157613/17260473. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (^x1.x1)))) 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. ------ 157614/17260482. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 157615/17260527. ------ 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. ------ 157616/17260608. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (^y.y))(a b))) 3. ==[ beta ]==> (b ((a (^y.y))(a b))) 4. ==[ alpha ]==> (b ((a (^x.x))(a b))) REDUCED to normal form. ------ 157617/17260671. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 157618/17260725. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)(^x1.a))) REDUCED to normal form. ------ 157619/17260752. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 157620/17260779. ------ 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. ------ 157621/17260815. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.a)((a a) a))) 3. ==[ beta ]==> (((a a)((a a)(a a))) a) REDUCED to normal form. ------ 157622/17260842. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 157623/17260869. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^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. ------ 157624/17260896. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 157625/17260923. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 157626/17260977. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 157627/17261004. ------ 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 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. ------ 157628/17261031. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 157629/17261085. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^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. ------ 157630/17261256. ------ 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 (^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157631/17261481. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)(^y.b))) 3. ==[ beta ]==> ((b c)((a a)(^y.b))) 4. ==[ alpha ]==> ((b c)((a a)(^x.b))) REDUCED to normal form. ------ 157632/17261508. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b) a)) REDUCED to normal form. ------ 157633/17261715. ------ 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))) REDUCED to normal form. ------ 157634/17261724. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a) b)) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 157635/17261751. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 157636/17261823. ------ 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 (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157637/17261886. ------ 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. ------ 157638/17261949. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 157639/17261976. ------ 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. ------ 157640/17262003. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 157641/17262030. ------ 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. ------ 157642/17262057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.y))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 157643/17262084. ------ 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.(^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. ------ 157644/17262111. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(^b.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. ------ 157645/17262138. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 157646/17262165. ------ 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.(^y1.y1)))) 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. ------ 157647/17262327. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 157648/17262606. ------ 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. ------ 157649/17262741. ------ 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. ------ 157650/17262822. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c c)) 5. ==[ beta ]==> ((b ((^y.y) b))(c c)) 6. ==[ alpha ]==> ((b ((^x.x) b))(c c)) 7. ==[ beta ]==> ((b b)(c c)) REDUCED to normal form. ------ 157651/17262831. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 157652/17262858. ------ 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)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157653/17262912. ------ 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. ------ 157654/17262939. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y)) c)) REDUCED to normal form. ------ 157655/17263011. ------ 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. ------ 157656/17263020. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.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. ------ 157657/17263047. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^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. ------ 157658/17263128. ------ 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)(^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. ------ 157659/17263146. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b c)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b c)) REDUCED to normal form. ------ 157660/17263164. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 157661/17263191. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.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. ------ 157662/17263218. ------ 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.(^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. ------ 157663/17263245. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(^b.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. ------ 157664/17263299. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 157665/17263326. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 157666/17263353. ------ 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.(^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. ------ 157667/17263380. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(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. ------ 157668/17263434. ------ 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.(^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. ------ 157669/17263461. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (^y.y))) 3. ==[ beta ]==> ((b (a (a a)))(b (^y.y))) 4. ==[ alpha ]==> ((b (a (a a)))(b (^x.x))) REDUCED to normal form. ------ 157670/17263488. ------ 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)))) 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. ------ 157671/17263542. ------ 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))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 157672/17263560. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 157673/17263569. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.y))) REDUCED to normal form. ------ 157674/17263578. ------ 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. ------ 157675/17263599. ------ 1. ==[ start ]==> ((^a.(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157676/17273742. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.a)) 3. ==[ beta ]==> ((^z.a)((^z.a)(^y.y))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 157677/17273754. ------ 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. ------ 157678/17273778. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157679/17273781. ------ 1. ==[ start ]==> ((a (^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 157680/17273790. ------ 1. ==[ start ]==> (((^a.a) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (a (^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (a (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 157681/17273796. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((^y.(y (^z.z))) a)((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^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))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 157682/17274195. ------ 1. ==[ start ]==> (((a a)(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 157683/17274213. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 157684/17274363. ------ 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. ------ 157685/17274588. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 157686/17275410. ------ 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. ------ 157687/17275479. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 157688/17275659. ------ 1. ==[ start ]==> ((^a.(a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^y.(^z.z))) b) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 157689/17276046. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.(^y1.y1)))((^z.a)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.(a ((^y1.a)(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.(^x1.x1))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 157690/17276253. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z) c)) 3. ==[ beta ]==> ((^y.y)(((^z.z) c)((^z.z) c))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) c)((^z.z) c))) 5. ==[ beta ]==> (((^y.y) c)((^z.z) c)) 6. ==[ alpha ]==> (((^x.x) c)((^y.y) c)) 7. ==[ beta ]==> (c ((^y.y) c)) 8. ==[ alpha ]==> (c ((^x.x) c)) 9. ==[ beta ]==> (c c) REDUCED to normal form. ------ 157691/17276928. ------ 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. ------ 157692/17277264. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 157693/17277684. ------ 1. ==[ start ]==> ((^a.(b a))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.(b x))((b a)(^y.a))) 3. ==[ eta ]==> (b ((b a)(^y.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 157694/17278233. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 157695/17279124. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157696/17279478. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)(^z1.(^x2.(^y2.(^z2.z2))))) 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. ------ 157697/17280783. ------ 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. ------ 157698/17281518. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 157699/17282214. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(^z.((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((a a) a))) REDUCED to normal form. ------ 157700/17282853. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 157701/17283123. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^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. ------ 157702/17283429. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 157703/17283498. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^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. ------ 157704/17283600. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.y)) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 157705/17283681. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.c)) REDUCED to normal form. ------ 157706/17283735. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 157707/17283843. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 157708/17283915. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(z z))) 3. ==[ beta ]==> ((a (^y.y))(^z.(z z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 157709/17283921. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z) a)) 3. ==[ beta ]==> (((^z.z) a)(((^z.z) a)(^y.y))) 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))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 157710/17283924. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.a)) REDUCED to normal form. ------ 157711/17283933. ------ 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. ------ 157712/17283963. ------ 1. ==[ start ]==> ((a (^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 157713/17283972. ------ 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. ------ 157714/17283981. ------ 1. ==[ start ]==> ((a (a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> ((a (a a))(a (^y.y))) 4. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 157715/17283999. ------ 1. ==[ start ]==> (((a a) a)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 157716/17284026. ------ 1. ==[ start ]==> (((a a)(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 157717/17284053. ------ 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 ]==> (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. ------ 157718/17284080. ------ 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. ------ 157719/17284107. ------ 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. ------ 157720/17284134. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b a)((a a) a))) REDUCED to normal form. ------ 157721/17284161. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 157722/17284188. ------ 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.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 157723/17284242. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((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. ------ 157724/17284323. ------ 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 (^x.x)) b)(a ((a a)(a a)))) REDUCED to normal form. ------ 157725/17284350. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a))(b (^a.a)))) 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. ------ 157726/17284377. ------ 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. ------ 157727/17284395. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 157728/17284467. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 157729/17284494. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 157730/17284521. ------ 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. ------ 157731/17284548. ------ 1. ==[ start ]==> ((a (a (a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 157732/17284584. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157733/17284638. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 157734/17284692. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157735/17284746. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 157736/17284773. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 157737/17284818. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a) 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. ------ 157738/17284845. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b (^z.z)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y)) b)) REDUCED to normal form. ------ 157739/17284908. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 157740/17284935. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 157741/17285043. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(^z1.z1)))) 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. ------ 157742/17285124. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^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. ------ 157743/17285457. ------ 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. ------ 157744/17285484. ------ 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)((^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. ------ 157745/17285538. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a ((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a b)) REDUCED to normal form. ------ 157746/17285565. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 157747/17285592. ------ 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. ------ 157748/17285664. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 157749/17285682. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) 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. ------ 157750/17285709. ------ 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 (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 157751/17285736. ------ 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. ------ 157752/17285790. ------ 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)(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.b))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 157753/17285817. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 157754/17285844. ------ 1. ==[ start ]==> ((a (a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 157755/17285853. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157756/17285934. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((^x1.x1) b))) IRREDUCIBLE: cycle. ------ 157757/17286042. ------ 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 a)) REDUCED to normal form. ------ 157758/17286069. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 157759/17286204. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 157760/17286231. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 157761/17286402. ------ 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 a))) REDUCED to normal form. ------ 157762/17286411. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a)) b)) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 157763/17286438. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y) c)) 3. ==[ beta ]==> ((a (a a))((^y.y) c)) 4. ==[ alpha ]==> ((a (a a))((^x.x) c)) 5. ==[ beta ]==> ((a (a a)) c) REDUCED to normal form. ------ 157764/17286618. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b) b)((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b) b)((^x.x)((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. ------ 157765/17286645. ------ 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. ------ 157766/17286672. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 157767/17286690. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c (^z.z))) 3. ==[ beta ]==> ((^y.y)(c (^z.z))) 4. ==[ alpha ]==> ((^x.x)(c (^y.y))) 5. ==[ beta ]==> (c (^y.y)) 6. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 157768/17286699. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a (^z.z)) b)) REDUCED to normal form. ------ 157769/17286825. ------ 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)))((^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. ------ 157770/17286924. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a b)(^y.b))) REDUCED to normal form. ------ 157771/17286951. ------ 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.(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. ------ 157772/17287032. ------ 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)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)(^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. ------ 157773/17287059. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 157774/17287113. ------ 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. ------ 157775/17287149. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 157776/17287284. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(^x1.b))) 3. ==[ beta ]==> (b ((^z.b)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 157777/17287392. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 157778/17287401. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(c (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 157779/17287428. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(b ((^z.z) b))) 3. ==[ beta ]==> ((a (^y.b))(b ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.b))(b ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.b))(b b)) REDUCED to normal form. ------ 157780/17287482. ------ 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)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157781/17287509. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 157782/17287536. ------ 1. ==[ start ]==> (((a b)(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.a))((b a) a)) REDUCED to normal form. ------ 157783/17287563. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 157784/17287590. ------ 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))(^y.y))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)((^z.z)(^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. ------ 157785/17287815. ------ 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. ------ 157786/17287842. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 157787/17287869. ------ 1. ==[ start ]==> ((a (b a))((b a)(^b.a))) 2. ==[ alpha ]==> ((a (b a))((b a)(^x.a))) REDUCED to normal form. ------ 157788/17287959. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.b)((a a) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)((a a) a))) 5. ==[ beta ]==> (b ((^z.b)((a a) a))) 6. ==[ alpha ]==> (b ((^x.b)((a a) a))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 157789/17288040. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 157790/17288148. ------ 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. ------ 157791/17288175. ------ 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.(^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. ------ 157792/17288229. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 157793/17288310. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (b ((^y.a)(^z.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 157794/17288418. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 157795/17288463. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b) 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. ------ 157796/17288490. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 157797/17288697. ------ 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 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. ------ 157798/17288796. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 157799/17288877. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 157800/17288985. ------ 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))((^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. ------ 157801/17289012. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 157802/17289039. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 157803/17289093. ------ 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.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.x1))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 157804/17289174. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 157805/17289282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 157806/17289309. ------ 1. ==[ start ]==> ((a (^b.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 157807/17289381. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1))) 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. ------ 157808/17289435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) c)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) c)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 157809/17289588. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1)(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. ------ 157810/17289660. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(a (^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(a (^z1.(^x2.(^y2.y2))))) 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. ------ 157811/17289795. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 157812/17289903. ------ 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))((a a)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((a a)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157813/17290038. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 157814/17290119. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 157815/17290128. ------ 1. ==[ start ]==> (((a b)(^c.a))(d (a b))) 2. ==[ alpha ]==> (((a b)(^x.a))(d (a b))) REDUCED to normal form. ------ 157816/17290155. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 157817/17290182. ------ 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. ------ 157818/17290236. ------ 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.y1))(a a))) REDUCED to normal form. ------ 157819/17290263. ------ 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. ------ 157820/17290488. ------ 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.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 157821/17290515. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 157822/17290569. ------ 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) a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 157823/17290596. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((b (a a))(^x.(^y.y))) REDUCED to normal form. ------ 157824/17290659. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 157825/17290794. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 157826/17290902. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 157827/17290938. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((b b)(b ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b b)(b ((^x.x)(a a)))) 5. ==[ beta ]==> ((b b)(b (a a))) REDUCED to normal form. ------ 157828/17290965. ------ 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. ------ 157829/17291019. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(a (^z.z)))) REDUCED to normal form. ------ 157830/17291046. ------ 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) a)((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((a a) a) a)) REDUCED to normal form. ------ 157831/17291127. ------ 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))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a ((a a) a))) REDUCED to normal form. ------ 157832/17291145. ------ 1. ==[ start ]==> (((^a.b)(a b))(c (^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))(c (^y.b))) 3. ==[ beta ]==> (b (c (^y.b))) 4. ==[ alpha ]==> (b (c (^x.b))) REDUCED to normal form. ------ 157833/17291154. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))(a b))) REDUCED to normal form. ------ 157834/17291253. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157835/17291379. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(^z.b))) REDUCED to normal form. ------ 157836/17291406. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(a a)))) REDUCED to normal form. ------ 157837/17291433. ------ 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. ------ 157838/17291460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b) b)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b) b)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b) b)) 5. ==[ beta ]==> (((a a)(^y.y))((a b) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((a b) b)) REDUCED to normal form. ------ 157839/17291649. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a)) a)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a)) a)) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 157840/17291676. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b) b)) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 157841/17291703. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a) c)) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 157842/17291874. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 157843/17291982. ------ 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)((^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. ------ 157844/17292090. ------ 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)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 157845/17292117. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 157846/17292171. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 157847/17292261. ------ 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. ------ 157848/17292288. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 157849/17292369. ------ 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 (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 157850/17292396. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)((a a) a))) 3. ==[ beta ]==> ((b (^y.a))((a a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))((a a)((a a) a))) REDUCED to normal form. ------ 157851/17292486. ------ 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. ------ 157852/17292513. ------ 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)(^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. ------ 157853/17292540. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^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)))) REDUCED to normal form. ------ 157854/17292594. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 157855/17292621. ------ 1. ==[ start ]==> ((((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)) b)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z) b)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y) b)) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 157856/17292648. ------ 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. ------ 157857/17292783. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b a)((^y.(^z.z)) b)) 6. ==[ alpha ]==> ((b a)((^x.(^y.y)) b)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 157858/17292954. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(a (^x1.x1)))) 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. ------ 157859/17293035. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1)(^z1.z1)))) 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. ------ 157860/17293143. ------ 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))(^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. ------ 157861/17293260. ------ 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 (^x.x)) a)) REDUCED to normal form. ------ 157862/17293278. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(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. ------ 157863/17293305. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 157864/17293359. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.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. ------ 157865/17293368. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c c)) REDUCED to normal form. ------ 157866/17293440. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 157867/17293449. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (a a))) REDUCED to normal form. ------ 157868/17293476. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (a (^y.y)))) REDUCED to normal form. ------ 157869/17293503. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(b a)) REDUCED to normal form. ------ 157870/17293557. ------ 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. ------ 157871/17293584. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 157872/17293611. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a a) a)) REDUCED to normal form. ------ 157873/17293683. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^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. ------ 157874/17293701. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 157875/17293728. ------ 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 (^y.y)))(a a)) REDUCED to normal form. ------ 157876/17293755. ------ 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. ------ 157877/17293782. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a) c)) 3. ==[ beta ]==> (((a (a a)) b)((a a) c)) REDUCED to normal form. ------ 157878/17293809. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 157879/17293836. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 157880/17293863. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) c) REDUCED to normal form. ------ 157881/17293890. ------ 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))(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^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))) REDUCED to normal form. ------ 157882/17293917. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 157883/17293971. ------ 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. ------ 157884/17293998. ------ 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)) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 157885/17294025. ------ 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)) 5. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 157886/17294079. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 157887/17294097. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a (a a))) 3. ==[ beta ]==> ((a (^y.y))(a (a a))) 4. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 157888/17294106. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y) a)) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 157889/17294115. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a (^x1.x1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.z))) 5. ==[ beta ]==> ((a (^z.z))(^y.y)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 157890/17294132. ------ 1. ==[ start ]==> (^a.(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (^x.(b ((^y.(^z.z)) x))) 3. ==[ beta ]==> (^x.(b (^z.z))) 4. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 157891/17294133. ------ 1. ==[ start ]==> (a (b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (a (b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (a (b (^y.y))) 4. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 157892/17294163. ------ 1. ==[ start ]==> ((^a.(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((^y.(y (y (^z.z))))(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> ((^z.(z (z (^x1.x1))))((^z.(z (z (^x1.x1))))(^y.y))) 6. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z (z (^x1.x1))))(^y1.y1))) 7. ==[ beta ]==> (((^z.(z (z (^x1.x1))))(^y1.y1))(((^z.(z (z (^x1.x1))))(^y1.y1))(^y.y))) 8. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 9. ==[ beta ]==> (((^z.z)((^z.z)(^y.y)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 10. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 11. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1))) 13. ==[ beta ]==> ((^y.y)(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1))) 14. ==[ alpha ]==> ((^x.x)(((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1))) 15. ==[ beta ]==> (((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1)) 16. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.z))(^x1.x1)) 17. ==[ beta ]==> (((^z.z)((^z.z)(^y.y)))(^x1.x1)) 18. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 19. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 20. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 21. ==[ beta ]==> ((^y.y)(^z.z)) 22. ==[ alpha ]==> ((^x.x)(^y.y)) 23. ==[ beta ]==> (^y.y) 24. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 157893/17304288. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(z z))) 3. ==[ beta ]==> ((^z.(z z))((^z.(z z))(^y.y))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((^y.(y y))(^z.z))((^y.(y y))(^z.z))) 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. ------ 157894/17304324. ------ 1. ==[ start ]==> ((^a.a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.x)(b ((^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. ------ 157895/17304345. ------ 1. ==[ start ]==> (((^a.a) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^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. ------ 157896/17304351. ------ 1. ==[ start ]==> ((^a.(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(a (a (a (^y.y))))) 3. ==[ beta ]==> ((a (a (a (^y.y))))(a (a (a (^y.y))))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a (a (^y.y))))) REDUCED to normal form. ------ 157897/17304354. ------ 1. ==[ start ]==> ((a (a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 157898/17304378. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 157899/17304459. ------ 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) b)(a (a a)))(^y.y)) 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. ------ 157900/17304648. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^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. ------ 157901/17304777. ------ 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))))) REDUCED to normal form. ------ 157902/17304819. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 157903/17305596. ------ 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. ------ 157904/17305701. ------ 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. ------ 157905/17306034. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 157906/17306370. ------ 1. ==[ start ]==> ((((a a) a) b)(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 157907/17306757. ------ 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. ------ 157908/17306808. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((((^z.z) b)(a (^x1.x1)))(((^z.z) b)(a (^x1.x1))))) 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 (^x.x)))(b (a (^z.z)))) 10. ==[ alpha ]==> ((b (a (^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 157909/17308161. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b) a)(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a b) a)(^x.((^y.y) b))) 5. ==[ beta ]==> (((a b) a)(^x.b)) REDUCED to normal form. ------ 157910/17308836. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^z.b)) REDUCED to normal form. ------ 157911/17309076. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((^x1.x1) a)((a a)(^y1.y1)))(^y.(^z.z))) 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. ------ 157912/17309754. ------ 1. ==[ start ]==> ((((^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.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))))) REDUCED to normal form. ------ 157913/17309994. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157914/17310312. ------ 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))) REDUCED to normal form. ------ 157915/17310834. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 157916/17311338. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 157917/17311581. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 157918/17312022. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 157919/17312073. ------ 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. ------ 157920/17312418. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(a x))) 3. ==[ eta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 157921/17312796. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 157922/17313129. ------ 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. ------ 157923/17313234. ------ 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. ------ 157924/17313408. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 157925/17314053. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 157926/17314182. ------ 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) y1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.y1)) 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. ------ 157927/17314236. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 157928/17314371. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) 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)))) REDUCED to normal form. ------ 157929/17314452. ------ 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. ------ 157930/17314470. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 157931/17314476. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (a a))) 2. ==[ alpha ]==> ((^x.(x (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. ------ 157932/17314479. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(y y))) REDUCED to normal form. ------ 157933/17314488. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.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 ]==> ((^z.a)(^y.y)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 157934/17314518. ------ 1. ==[ start ]==> ((a a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a a)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a a)(b (^y.y))) 4. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 157935/17314536. ------ 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))))) 5. ==[ beta ]==> (a (^y.(y (^z.z)))) 6. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 157936/17314545. ------ 1. ==[ start ]==> ((a (a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 157937/17314554. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 157938/17314572. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(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. ------ 157939/17314626. ------ 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. ------ 157940/17314653. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 157941/17314788. ------ 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. ------ 157942/17314815. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(b a))) REDUCED to normal form. ------ 157943/17314842. ------ 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 (^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)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 157944/17314968. ------ 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))))) REDUCED to normal form. ------ 157945/17315013. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 157946/17315103. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 157947/17315121. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.(y y))((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.(x x))((b a)(^y.a))) 5. ==[ beta ]==> (((b a)(^y.a))((b a)(^y.a))) 6. ==[ alpha ]==> (((b a)(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 157948/17315148. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.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. ------ 157949/17315184. ------ 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. ------ 157950/17315202. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a b)(^c.(^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. ------ 157951/17315211. ------ 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. ------ 157952/17315256. ------ 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)(^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. ------ 157953/17315265. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^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)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 157954/17315292. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 157955/17315319. ------ 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. ------ 157956/17315562. ------ 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. ------ 157957/17315589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (a ((^y.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 157958/17315616. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 157959/17315670. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 157960/17315697. ------ 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. ------ 157961/17315724. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(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. ------ 157962/17315760. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 157963/17315787. ------ 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. ------ 157964/17315814. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(a a))) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(a a))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 157965/17315841. ------ 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. ------ 157966/17315868. ------ 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. ------ 157967/17315895. ------ 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. ------ 157968/17316228. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 157969/17316399. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 157970/17316417. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 157971/17316498. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)(^x1.x1))) IRREDUCIBLE: cycle. ------ 157972/17316561. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(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. ------ 157973/17316579. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b (^z.z)) a)) 3. ==[ beta ]==> (b ((b (^z.z)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 157974/17316606. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a b)(((a a)(a a)) b)) REDUCED to normal form. ------ 157975/17316615. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 157976/17316633. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^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. ------ 157977/17316669. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 157978/17316723. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 157979/17316750. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 157980/17316777. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 157981/17316921. ------ 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)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(b ((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)(b ((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)(b ((a a)(a a)))) 7. ==[ beta ]==> (a (b ((a a)(a a)))) REDUCED to normal form. ------ 157982/17316948. ------ 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. ------ 157983/17316975. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 157984/17317002. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> ((a (a a))(b (a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(b (a (^x.x)))) REDUCED to normal form. ------ 157985/17317011. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z) c)) 3. ==[ beta ]==> ((^y.(a a))((^z.z) c)) 4. ==[ alpha ]==> ((^x.(a a))((^y.y) c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 157986/17317263. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c (^z.z))) REDUCED to normal form. ------ 157987/17317371. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.b)(a (^a.a)))) 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. ------ 157988/17317389. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 157989/17317398. ------ 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)))((^z1.z1) 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. ------ 157990/17317614. ------ 1. ==[ start ]==> (((^a.b) c)((^b.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) REDUCED to normal form. ------ 157991/17317713. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^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. ------ 157992/17317857. ------ 1. ==[ start ]==> (((a b) c)((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b) c)((^x.b)(^y.b))) 3. ==[ beta ]==> (((a b) c) b) REDUCED to normal form. ------ 157993/17317884. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 157994/17317911. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(^a.a))(^c.(^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. ------ 157995/17317965. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 157996/17317992. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 157997/17318091. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) 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. ------ 157998/17318190. ------ 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))) REDUCED to normal form. ------ 157999/17318217. ------ 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. ------ 158000/17318244. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a b))((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (a b))((^x.x)((^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. ------ 158001/17318271. ------ 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. ------ 158002/17318298. ------ 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)))(((^y1.y1) a)(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(b a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(b a))) 7. ==[ beta ]==> ((^y.y)(((^z.z) a)(b a))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b a))) 9. ==[ beta ]==> (((^y.y) a)(b a)) 10. ==[ alpha ]==> (((^x.x) a)(b a)) 11. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 158003/17318325. ------ 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. ------ 158004/17318352. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 158005/17318523. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a b)(^z.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a b)(^z.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(^z.a))) 5. ==[ beta ]==> (b ((a b)(^z.a))) 6. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 158006/17318604. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 158007/17318667. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(a (^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. ------ 158008/17318712. ------ 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. ------ 158009/17318739. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1))) 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. ------ 158010/17318802. ------ 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 x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 158011/17318856. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 158012/17318883. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 158013/17318910. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 158014/17319000. ------ 1. ==[ start ]==> (((a a)(b a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 158015/17319027. ------ 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 (^x.x))((a a)(^y.y)))(a b)) REDUCED to normal form. ------ 158016/17319054. ------ 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 (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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))) REDUCED to normal form. ------ 158017/17319081. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((b a)(a (^x.x)))) REDUCED to normal form. ------ 158018/17319108. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((^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. ------ 158019/17319135. ------ 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 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. ------ 158020/17319162. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a b)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b)(a (a a)))((a b)(^y.y))) 4. ==[ alpha ]==> (((a b)(a (a a)))((a b)(^x.x))) REDUCED to normal form. ------ 158021/17319189. ------ 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. ------ 158022/17319216. ------ 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.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a b)) REDUCED to normal form. ------ 158023/17319270. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 158024/17319360. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 158025/17319441. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.(y1 y1)))) 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. ------ 158026/17319549. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 158027/17319558. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a a))) REDUCED to normal form. ------ 158028/17319585. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 158029/17319657. ------ 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 a))((^y.y)(a a)))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1))) a)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z))) a)) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z))) a)) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 158030/17319666. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1)))(^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. ------ 158031/17319747. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 158032/17319774. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 158033/17319801. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 158034/17319855. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 158035/17319918. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(b (b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(b (b a))) REDUCED to normal form. ------ 158036/17319945. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 158037/17319972. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a)(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((b a)(a a))) REDUCED to normal form. ------ 158038/17319999. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))(a (^z.z)))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 158039/17320026. ------ 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.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. ------ 158040/17320053. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a b)(a (a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((a b)(a (a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 158041/17320080. ------ 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)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a) a)((^x.x)(^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. ------ 158042/17320107. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)((a a) a))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((a a) a))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)((a a) a)) REDUCED to normal form. ------ 158043/17320161. ------ 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)((^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. ------ 158044/17320188. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^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)))) REDUCED to normal form. ------ 158045/17320359. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a) a)(^b.(^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. ------ 158046/17320476. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 158047/17320503. ------ 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. ------ 158048/17320521. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a) a)) 3. ==[ beta ]==> (((^y.y) b)((b a) a)) 4. ==[ alpha ]==> (((^x.x) b)((b a) a)) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 158049/17320548. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((a a)(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1)) 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. ------ 158050/17320638. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)(^b.(^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. ------ 158051/17320665. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(^c.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. ------ 158052/17320692. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 158053/17320719. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 158054/17320863. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)((^y.y) a))) 3. ==[ beta ]==> (((a a) b)((a b)((^y.y) a))) 4. ==[ alpha ]==> (((a a) b)((a b)((^x.x) a))) 5. ==[ beta ]==> (((a a) b)((a b) a)) REDUCED to normal form. ------ 158055/17320890. ------ 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. ------ 158056/17320917. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (b a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (b a))((^x.x)((^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. ------ 158057/17320944. ------ 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. ------ 158058/17320971. ------ 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)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)(a b))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a b))) 7. ==[ beta ]==> ((a a)(((^y.y) a)(a b))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)(a b))) 9. ==[ beta ]==> ((a a)(a (a b))) REDUCED to normal form. ------ 158059/17320998. ------ 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. ------ 158060/17321025. ------ 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. ------ 158061/17321223. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.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. ------ 158062/17321358. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a b) c)) 3. ==[ beta ]==> (b ((a b) c)) REDUCED to normal form. ------ 158063/17321502. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 158064/17321574. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(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. ------ 158065/17321628. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a) d)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a) d)) 3. ==[ beta ]==> (((b a)(b a))((^y.a) d)) 4. ==[ alpha ]==> (((b a)(b a))((^x.a) d)) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 158066/17321718. ------ 1. ==[ start ]==> (((a b)(^a.b))(c (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))(c (^y.b))) REDUCED to normal form. ------ 158067/17321772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 158068/17321817. ------ 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.(^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. ------ 158069/17321826. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 158070/17321853. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 158071/17321880. ------ 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. ------ 158072/17322186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b (a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (a b))) REDUCED to normal form. ------ 158073/17322213. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (a a))) REDUCED to normal form. ------ 158074/17322240. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b)(a a))) REDUCED to normal form. ------ 158075/17322267. ------ 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. ------ 158076/17322438. ------ 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 b)(^z.z))) 4. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 158077/17322546. ------ 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.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. ------ 158078/17322582. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 158079/17322609. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(a b))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a b)) REDUCED to normal form. ------ 158080/17322654. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.x)(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)) REDUCED to normal form. ------ 158081/17322717. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 158082/17322744. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)(^b.(^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. ------ 158083/17322816. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b) a)) 3. ==[ beta ]==> (b ((^z.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 158084/17322960. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (^z.a))) 3. ==[ beta ]==> ((b (^y.a))(b (^z.a))) 4. ==[ alpha ]==> ((b (^x.a))(b (^y.a))) REDUCED to normal form. ------ 158085/17322987. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 158086/17323320. ------ 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. ------ 158087/17323347. ------ 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. ------ 158088/17323374. ------ 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. ------ 158089/17323428. ------ 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. ------ 158090/17323518. ------ 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. ------ 158091/17323599. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 158092/17323923. ------ 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.(^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. ------ 158093/17323932. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.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. ------ 158094/17323959. ------ 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))((^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. ------ 158095/17324004. ------ 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. ------ 158096/17324013. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(^a.a))) 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. ------ 158097/17324040. ------ 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.(^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. ------ 158098/17324067. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^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. ------ 158099/17324112. ------ 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)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158100/17324148. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^a.(^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. ------ 158101/17324175. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.a))) REDUCED to normal form. ------ 158102/17324229. ------ 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)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 158103/17324247. ------ 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)))) REDUCED to normal form. ------ 158104/17324265. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b c)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b c)) 3. ==[ beta ]==> (((a a)(^y.y))(b c)) 4. ==[ alpha ]==> (((a a)(^x.x))(b c)) REDUCED to normal form. ------ 158105/17324346. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b (a (^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. ------ 158106/17324373. ------ 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.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a ((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a ((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 158107/17324400. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(a a))) REDUCED to normal form. ------ 158108/17324427. ------ 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. ------ 158109/17324481. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b b)) REDUCED to normal form. ------ 158110/17324535. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b (a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a a))) REDUCED to normal form. ------ 158111/17324562. ------ 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. ------ 158112/17324589. ------ 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. ------ 158113/17324643. ------ 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. ------ 158114/17324661. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 158115/17324670. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a a))) REDUCED to normal form. ------ 158116/17324679. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> (((^z.z) a)(^y.y)) 6. ==[ alpha ]==> (((^x.x) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 158117/17324736. ------ 1. ==[ start ]==> ((^a.(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.(z (^x1.x1))))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 158118/17327868. ------ 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 a)(a a))(^z.z)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 158119/17334861. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^z.(^x1.x1))((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158120/17334915. ------ 1. ==[ start ]==> ((^a.(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158121/17334933. ------ 1. ==[ start ]==> ((^a.(a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^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))))) 5. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> (((^z.z)(^x1.(x1 (^y1.y1))))(^y.y)) 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 ]==> ((^z.z)(^y.y)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158122/17334936. ------ 1. ==[ start ]==> ((a (a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 158123/17334945. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^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. ------ 158124/17334996. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158125/17335158. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^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 ]==> (^x.((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (^x.((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 158126/17335500. ------ 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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158127/17335773. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 158128/17336796. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.b)((^z.z)(a a))) b) 4. ==[ alpha ]==> (((^x.b)((^y.y)(a a))) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 158129/17336952. ------ 1. ==[ start ]==> ((((a a) a) b)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 158130/17338065. ------ 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. ------ 158131/17338068. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 158132/17338821. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ eta ]==> (b ((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 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. ------ 158133/17339418. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 158134/17340336. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 158135/17340576. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 158136/17340894. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.a))) 3. ==[ beta ]==> ((b a)(^y.(^z.a))) 4. ==[ alpha ]==> ((b a)(^x.(^y.a))) REDUCED to normal form. ------ 158137/17341182. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 158138/17341575. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x 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))))(((^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))))(((^z2.(^x3.x3))((^y3.y3)(^z3.z3)))((^x4.(^y4.y4))((^z4.z4)(^x5.x5))))) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2))))(((^z2.(^x3.x3))((^y3.y3)(^z3.z3)))((^x4.(^y4.y4))((^z4.z4)(^x5.x5))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1))))(((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))((^x3.(^y3.y3))((^z3.z3)(^x4.x4))))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.y1)))(((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))((^x3.(^y3.y3))((^z3.z3)(^x4.x4))))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))((^z2.(^x3.x3))((^y3.y3)(^z3.z3))))) 9. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))((^z2.(^x3.x3))((^y3.y3)(^z3.z3))))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((^y2.y2)(^z2.z2))))) 11. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 12. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 13. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 15. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 16. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158139/17341938. ------ 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. ------ 158140/17342388. ------ 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))(^x.(a a))) REDUCED to normal form. ------ 158141/17342604. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 158142/17343000. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.b))) REDUCED to normal form. ------ 158143/17343207. ------ 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 (^z.(z b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 158144/17343549. ------ 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))) REDUCED to normal form. ------ 158145/17343711. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.a))) REDUCED to normal form. ------ 158146/17343990. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.e)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.e)) 3. ==[ beta ]==> (b (^x1.e)) 4. ==[ alpha ]==> (b (^x.e)) REDUCED to normal form. ------ 158147/17344260. ------ 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. ------ 158148/17344503. ------ 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. ------ 158149/17344683. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^z.a)) REDUCED to normal form. ------ 158150/17344764. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(^b.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. ------ 158151/17344845. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.(^b.a))) 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. ------ 158152/17344953. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^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. ------ 158153/17345034. ------ 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. ------ 158154/17345058. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(^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 ]==> ((^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. ------ 158155/17345061. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 158156/17345070. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> ((^z.(z z))(^y.y)) 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. ------ 158157/17345118. ------ 1. ==[ start ]==> ((a (^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 158158/17345136. ------ 1. ==[ start ]==> ((a (a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.x)(^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. ------ 158159/17345145. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(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. ------ 158160/17345154. ------ 1. ==[ start ]==> (((a a) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a a) a)(a (^y.y))) 4. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 158161/17345172. ------ 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))) 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. ------ 158162/17345199. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 158163/17345253. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 158164/17345280. ------ 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)((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. ------ 158165/17345307. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 158166/17345334. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 158167/17345361. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.a))((a a)(a a))) REDUCED to normal form. ------ 158168/17345442. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 158169/17345469. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 158170/17345523. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> (a ((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> (a ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 158171/17345550. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.(^y1.y1)) 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. ------ 158172/17345586. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^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)(^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. ------ 158173/17345676. ------ 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. ------ 158174/17345694. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 158175/17345703. ------ 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. ------ 158176/17345775. ------ 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. ------ 158177/17345802. ------ 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. ------ 158178/17345856. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 158179/17345883. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 158180/17345946. ------ 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. ------ 158181/17345973. ------ 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)) 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)((^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. ------ 158182/17346018. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y)) b)) 3. ==[ beta ]==> ((b b)((b (^y.y)) b)) 4. ==[ alpha ]==> ((b b)((b (^x.x)) b)) REDUCED to normal form. ------ 158183/17346522. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^y1.y1)(^z1.z1)))) 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. ------ 158184/17346576. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> (a (((^z.z)(a a))(a b))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(a b))) 7. ==[ beta ]==> (a ((a a)(a b))) REDUCED to normal form. ------ 158185/17346657. ------ 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. ------ 158186/17346684. ------ 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.(^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. ------ 158187/17346738. ------ 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))((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> ((a a)((a (^y.y))((a a)(a a)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 158188/17346801. ------ 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. ------ 158189/17346864. ------ 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) 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. ------ 158190/17346891. ------ 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. ------ 158191/17346972. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 158192/17346990. ------ 1. ==[ start ]==> (((^a.b) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 158193/17346999. ------ 1. ==[ start ]==> ((a (a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 158194/17347179. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b) a)((b (^x.x)) a)) REDUCED to normal form. ------ 158195/17347206. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a)) b)) REDUCED to normal form. ------ 158196/17347404. ------ 1. ==[ start ]==> (((a a)(a b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 158197/17347458. ------ 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)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 9. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 158198/17347485. ------ 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. ------ 158199/17347602. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158200/17347629. ------ 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)))((^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. ------ 158201/17347683. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(((a 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)(^x.x))(^z.z)) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 158202/17347764. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 158203/17347818. ------ 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. ------ 158204/17347845. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 158205/17347899. ------ 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)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((a a)((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((a a)((a a)(a a)))) 11. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 158206/17347935. ------ 1. ==[ start ]==> ((((^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.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(^z.z))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(^z.z))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.y))) 7. ==[ beta ]==> ((((a a)(a a))(^y.y))(((a a)(a a))(^y.y))) 8. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 158207/17347962. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 158208/17347989. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 158209/17348016. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(y y)))) REDUCED to normal form. ------ 158210/17348079. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 158211/17348106. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.b)(a b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.b)(a b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.b)(a b))) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 158212/17348160. ------ 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. ------ 158213/17348187. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(y y))(b a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(x x))(b a))) 5. ==[ beta ]==> ((((a a) a) a)((b a)(b a))) REDUCED to normal form. ------ 158214/17348205. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 158215/17348214. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.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) REDUCED to normal form. ------ 158216/17348241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(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. ------ 158217/17348268. ------ 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. ------ 158218/17348601. ------ 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))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b b)) REDUCED to normal form. ------ 158219/17348637. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 158220/17348664. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 158221/17348682. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 158222/17348691. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 158223/17348943. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b (^b.b))) 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. ------ 158224/17348997. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b)(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. ------ 158225/17349024. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 158226/17349258. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 158227/17349366. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((b a) c)) 3. ==[ beta ]==> ((a (^y.(a a)))((b a) c)) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a) c)) REDUCED to normal form. ------ 158228/17349591. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 158229/17349618. ------ 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)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 158230/17349870. ------ 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)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158231/17350149. ------ 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. ------ 158232/17350257. ------ 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)) REDUCED to normal form. ------ 158233/17350284. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a) b)) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a) b)) 5. ==[ beta ]==> ((^y.b)((b a) b)) 6. ==[ alpha ]==> ((^x.b)((b a) b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 158234/17350482. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 158235/17350536. ------ 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)(^x.x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 158236/17350779. ------ 1. ==[ start ]==> ((a ((^a.a) b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 158237/17350788. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((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))) REDUCED to normal form. ------ 158238/17350815. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((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. ------ 158239/17351067. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 158240/17351121. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((b a) a)) REDUCED to normal form. ------ 158241/17351148. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) b)) REDUCED to normal form. ------ 158242/17351382. ------ 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))(a (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158243/17351418. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^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))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 158244/17351589. ------ 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. ------ 158245/17351616. ------ 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. ------ 158246/17351724. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 158247/17351751. ------ 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. ------ 158248/17351778. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^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)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 158249/17352138. ------ 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. ------ 158250/17352165. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^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. ------ 158251/17352174. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 158252/17352201. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.b) c)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b) c)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b) c)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 158253/17352219. ------ 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 a)(b a))(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)((^x.x) a))) 5. ==[ beta ]==> (((b a)(b a))(((a a) a) a)) REDUCED to normal form. ------ 158254/17352300. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^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. ------ 158255/17352417. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 158256/17352444. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 158257/17352471. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^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. ------ 158258/17352507. ------ 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.y)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a)(a a)))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)((a a)(a a)))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 10. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 158259/17352534. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.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. ------ 158260/17352561. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(^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. ------ 158261/17352588. ------ 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. ------ 158262/17352615. ------ 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)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 158263/17352642. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 158264/17352669. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 158265/17352696. ------ 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.(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. ------ 158266/17352723. ------ 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 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 158267/17352777. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 158268/17352804. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.(a a))) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 158269/17352948. ------ 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)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2) a)((^y2.y2)(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2) a)((^y2.y2)(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158270/17353173. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))(^z.a))) 3. ==[ beta ]==> ((b c)((a (^y.y))(^z.a))) 4. ==[ alpha ]==> ((b c)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 158271/17353200. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.b))) REDUCED to normal form. ------ 158272/17353407. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a (a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 158273/17353416. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b) a)) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 158274/17353443. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a) b)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a) b)) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 158275/17353515. ------ 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. ------ 158276/17353641. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 158277/17353668. ------ 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 y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 158278/17353695. ------ 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. ------ 158279/17353722. ------ 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)(^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. ------ 158280/17353749. ------ 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. ------ 158281/17353803. ------ 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.(^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. ------ 158282/17353830. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(^b.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. ------ 158283/17353857. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 158284/17354298. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c ((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158285/17354415. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a) c)) 3. ==[ beta ]==> (((^y.y) a)((^z.a) c)) 4. ==[ alpha ]==> (((^x.x) a)((^y.a) c)) 5. ==[ beta ]==> (a ((^y.a) c)) 6. ==[ alpha ]==> (a ((^x.a) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158286/17354433. ------ 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) 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)((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. ------ 158287/17354460. ------ 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. ------ 158288/17354523. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(^a.(^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. ------ 158289/17354550. ------ 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 (^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158290/17354604. ------ 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. ------ 158291/17354631. ------ 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. ------ 158292/17354658. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z)) c)) REDUCED to normal form. ------ 158293/17354703. ------ 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. ------ 158294/17354712. ------ 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)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 158295/17354739. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.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. ------ 158296/17354766. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^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. ------ 158297/17354820. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 158298/17354856. ------ 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)))) 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. ------ 158299/17354883. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^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. ------ 158300/17354910. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.y))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 158301/17354937. ------ 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))(^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. ------ 158302/17354964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 158303/17354991. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.x))) REDUCED to normal form. ------ 158304/17355018. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 158305/17355045. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(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))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.a))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.a))) REDUCED to normal form. ------ 158306/17355072. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^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. ------ 158307/17355126. ------ 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))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 158308/17355153. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^a.(^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. ------ 158309/17355180. ------ 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. ------ 158310/17355234. ------ 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. ------ 158311/17355252. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a) a)) 3. ==[ beta ]==> ((a (^y.y))((a a) a)) 4. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 158312/17355261. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.z))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 158313/17355270. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 158314/17365554. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^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)))) REDUCED to normal form. ------ 158315/17365563. ------ 1. ==[ start ]==> (((a a) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 158316/17365569. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z))) a)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 158317/17366109. ------ 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. ------ 158318/17366334. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.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. ------ 158319/17367405. ------ 1. ==[ start ]==> ((^a.(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(^y.(a a))) b) 4. ==[ alpha ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 158320/17367579. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 158321/17367792. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((^z.b)(^x1.(a a)))((^z.b)(^x1.(a a))))) 4. ==[ alpha ]==> (^x.(((^y.b)(^z.(a a)))((^x1.b)(^y1.(a a))))) 5. ==[ beta ]==> (^x.(b ((^x1.b)(^y1.(a a))))) 6. ==[ alpha ]==> (^x.(b ((^y.b)(^z.(a a))))) 7. ==[ beta ]==> (^x.(b b)) REDUCED to normal form. ------ 158322/17367966. ------ 1. ==[ start ]==> (((^a.b) b)(^a.(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. ------ 158323/17368317. ------ 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. ------ 158324/17369046. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((y1 y1)(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((y1 y1)(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1)(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158325/17369430. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ eta ]==> (b ((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 158326/17369712. ------ 1. ==[ start ]==> (((^a.a)(b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.x)(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. ------ 158327/17370360. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 158328/17370657. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(a a))(^y.(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 158329/17370870. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158330/17371521. ------ 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))) REDUCED to normal form. ------ 158331/17371800. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(b y1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 158332/17372184. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x 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))))((((^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))))((((^z2.z2)(^x3.x3))(^y3.(^z3.z3)))(((^x4.x4)(^y4.y4))(^z4.(^x5.x5))))) 5. ==[ beta ]==> ((((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2))))((((^z2.z2)(^x3.x3))(^y3.(^z3.z3)))(((^x4.x4)(^y4.y4))(^z4.(^x5.x5))))) 6. ==[ alpha ]==> ((((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))((((^y2.y2)(^z2.z2))(^x3.(^y3.y3)))(((^z3.z3)(^x4.x4))(^y4.(^z4.z4))))) 7. ==[ beta ]==> (((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))((((^y2.y2)(^z2.z2))(^x3.(^y3.y3)))(((^z3.z3)(^x4.x4))(^y4.(^z4.z4))))) 8. ==[ alpha ]==> (((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1))))((((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))(((^y3.y3)(^z3.z3))(^x4.(^y4.y4))))) 9. ==[ beta ]==> ((^y.y)((((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))(((^y3.y3)(^z3.z3))(^x4.(^y4.y4))))) 10. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2))))) 11. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2)))) 12. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 13. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 14. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 15. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 16. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158333/17372547. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^b.(^c.(^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. ------ 158334/17372772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(a a))) REDUCED to normal form. ------ 158335/17372997. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 158336/17373264. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 158337/17373438. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^z.(^x1.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 158338/17373816. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> (b (^z.(^x1.z))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 158339/17373825. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(y b))) REDUCED to normal form. ------ 158340/17374158. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.a))) 5. ==[ beta ]==> ((b a)(^y.(^z.a))) 6. ==[ alpha ]==> ((b a)(^x.(^y.a))) REDUCED to normal form. ------ 158341/17375004. ------ 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. ------ 158342/17375112. ------ 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.(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158343/17375121. ------ 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. ------ 158344/17375244. ------ 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. ------ 158345/17375292. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 158346/17375454. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.c)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.c)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.c)) 5. ==[ beta ]==> (((a a)(a a))(^y.c)) 6. ==[ alpha ]==> (((a a)(a a))(^x.c)) REDUCED to normal form. ------ 158347/17375562. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 158348/17375661. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.b)) 3. ==[ beta ]==> ((a (^y.y))(^z.b)) 4. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 158349/17375667. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a) a)) 2. ==[ alpha ]==> ((^x.(x (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. ------ 158350/17375679. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.(^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. ------ 158351/17375745. ------ 1. ==[ start ]==> (((^a.a) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) a)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (a (b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (a (b ((^x.(^y.y)) a))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 158352/17375763. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 158353/17375772. ------ 1. ==[ start ]==> (((a a) a)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 158354/17375781. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y))) a)) 3. ==[ beta ]==> ((a b)(a (^y.y))) 4. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 158355/17375799. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 158356/17375826. ------ 1. ==[ start ]==> (((^a.a) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (b ((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (b ((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 158357/17375853. ------ 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. ------ 158358/17375880. ------ 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. ------ 158359/17375907. ------ 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 (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 158360/17375934. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 158361/17375961. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 158362/17376015. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 158363/17376096. ------ 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. ------ 158364/17376123. ------ 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)))) 5. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 158365/17376150. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 158366/17376177. ------ 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.(^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. ------ 158367/17376240. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 158368/17376267. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 158369/17376294. ------ 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. ------ 158370/17376321. ------ 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. ------ 158371/17376330. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3)))) 7. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3)))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158372/17376411. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158373/17376438. ------ 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. ------ 158374/17376519. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 158375/17376546. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 158376/17376618. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.(^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) a)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 158377/17376645. ------ 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. ------ 158378/17376681. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 158379/17376708. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 158380/17376816. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(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. ------ 158381/17376843. ------ 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. ------ 158382/17376897. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 158383/17377230. ------ 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. ------ 158384/17377257. ------ 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. ------ 158385/17377311. ------ 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.(^y1.y1))))) REDUCED to normal form. ------ 158386/17377338. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(x x)))(a ((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a ((^y.y) b))) 7. ==[ beta ]==> ((a (^x.(x x)))(a b)) REDUCED to normal form. ------ 158387/17377365. ------ 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. ------ 158388/17377392. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a a)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(b (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158389/17377455. ------ 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. ------ 158390/17377482. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.a))) REDUCED to normal form. ------ 158391/17377509. ------ 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. ------ 158392/17377536. ------ 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. ------ 158393/17377590. ------ 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))) 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. ------ 158394/17377617. ------ 1. ==[ start ]==> ((a (a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (a b))((a b)(^x.(a a)))) REDUCED to normal form. ------ 158395/17377626. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 158396/17377707. ------ 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 z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(a (^x1.(^y1.y1))))) IRREDUCIBLE: cycle. ------ 158397/17377788. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 158398/17377896. ------ 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. ------ 158399/17377977. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 158400/17378004. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 158401/17378175. ------ 1. ==[ start ]==> (((^a.b) b)(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(a (b (^y.y)))) 3. ==[ beta ]==> (b (a (b (^y.y)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 158402/17378391. ------ 1. ==[ start ]==> (((a b) b)(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) b)(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b) b)(((a a) a)(a a))) REDUCED to normal form. ------ 158403/17378418. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)((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. ------ 158404/17378445. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(b a))) REDUCED to normal form. ------ 158405/17378472. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 158406/17378517. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (^y1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (^y1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (^x1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(a a)))) 9. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 10. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 11. ==[ beta ]==> (b (^y.(a a))) 12. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 158407/17378526. ------ 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. ------ 158408/17378598. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.b)(a (^a.a)))) 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. ------ 158409/17378670. ------ 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)))) 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. ------ 158410/17378697. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(^y.a))) REDUCED to normal form. ------ 158411/17378724. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a b)(^y.b))) 3. ==[ beta ]==> ((a ((a a) a))((a b)(^y.b))) 4. ==[ alpha ]==> ((a ((a a) a))((a b)(^x.b))) REDUCED to normal form. ------ 158412/17378751. ------ 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. ------ 158413/17378832. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 158414/17378859. ------ 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))) REDUCED to normal form. ------ 158415/17378922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158416/17379057. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 158417/17379138. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(^a.a))(^c.(^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. ------ 158418/17379201. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.b))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.b))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 158419/17379219. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.a))(^b.b))) 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))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 158420/17379255. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 158421/17379282. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) b)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b (a a))) REDUCED to normal form. ------ 158422/17379309. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 158423/17379336. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 158424/17379363. ------ 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)))) REDUCED to normal form. ------ 158425/17379615. ------ 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)(^x.x))(a a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 158426/17379642. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 158427/17379732. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 158428/17379813. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 158429/17379921. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(b 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)((^y.y) b)) 6. ==[ alpha ]==> ((b a)((^x.x) b)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 158430/17379948. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^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)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158431/17380083. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (b ((^y.b)(^z.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 158432/17380263. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b) 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)) 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. ------ 158433/17380290. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.(^z.z))) 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. ------ 158434/17380470. ------ 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 (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. ------ 158435/17380569. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(a (^z.z))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(a (^z.z))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(a (^z.z))) 5. ==[ beta ]==> ((a a)(a (^z.z))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 158436/17380650. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^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. ------ 158437/17380758. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 158438/17380785. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(a a)))) 9. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 158439/17380812. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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 REDUCED to normal form. ------ 158440/17380866. ------ 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)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 10. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 158441/17380947. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 158442/17381055. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^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. ------ 158443/17381082. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.x))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 158444/17381181. ------ 1. ==[ start ]==> (((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)) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 158445/17381361. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 158446/17381406. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 158447/17381568. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 158448/17381676. ------ 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)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((^x2.x2)(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. ------ 158449/17381730. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(b a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(b a))) 4. ==[ alpha ]==> (((^x.x) b)((^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. ------ 158450/17381811. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 158451/17381892. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(^c.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. ------ 158452/17382009. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (b a))) REDUCED to normal form. ------ 158453/17382036. ------ 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))) REDUCED to normal form. ------ 158454/17382072. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a) b)((^y.(a a)) c)) 4. ==[ alpha ]==> (((a a) b)((^x.(a a)) c)) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 158455/17382288. ------ 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))(^z.z))) REDUCED to normal form. ------ 158456/17382342. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(^x1.a))) REDUCED to normal form. ------ 158457/17382369. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> ((b (a a))(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> ((b (a a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 158458/17382396. ------ 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.(^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. ------ 158459/17382432. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 158460/17382567. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 158461/17382675. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158462/17382711. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c (a b))) 3. ==[ beta ]==> ((b b)(c (a b))) REDUCED to normal form. ------ 158463/17382738. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(b ((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (a a))) REDUCED to normal form. ------ 158464/17382792. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^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. ------ 158465/17382819. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(a (^x1.x1)))) REDUCED to normal form. ------ 158466/17382900. ------ 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. ------ 158467/17382927. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b))(a ((a a) a))) REDUCED to normal form. ------ 158468/17382981. ------ 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)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a a))) REDUCED to normal form. ------ 158469/17383026. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(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. ------ 158470/17383125. ------ 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. ------ 158471/17383152. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (^z.a))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.a))) REDUCED to normal form. ------ 158472/17383179. ------ 1. ==[ start ]==> ((((^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.b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 158473/17383206. ------ 1. ==[ start ]==> (((a (a a))(b a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 158474/17383233. ------ 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.x1)(a a)) a)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a)) a)) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a)) a)) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a)) a)) 7. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 158475/17383260. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b) b)) 3. ==[ beta ]==> ((((a a) a)(a a))((a b) b)) REDUCED to normal form. ------ 158476/17383287. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a) c)) REDUCED to normal form. ------ 158477/17383449. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 158478/17383476. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b) b)) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 158479/17383647. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> (b (a (^z.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 158480/17383755. ------ 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. ------ 158481/17383863. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(^z.z))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 158482/17383944. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.(z1 z1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(z1 z1)))) IRREDUCIBLE: cycle. ------ 158483/17384025. ------ 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 ((^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. ------ 158484/17384034. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a (a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a (a b))) REDUCED to normal form. ------ 158485/17384061. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a)(a a))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)(a a))) REDUCED to normal form. ------ 158486/17384142. ------ 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. ------ 158487/17384169. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 158488/17384196. ------ 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 a) a))) REDUCED to normal form. ------ 158489/17384259. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 158490/17384286. ------ 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. ------ 158491/17384313. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a b)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((a b)(a (^y.(y y)))) 8. ==[ alpha ]==> ((a b)(a (^x.(x x)))) REDUCED to normal form. ------ 158492/17384340. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 158493/17384367. ------ 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. ------ 158494/17384394. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 158495/17384421. ------ 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))((^y.y) b)) 6. ==[ alpha ]==> (((a b)(a a))((^x.x) b)) 7. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 158496/17384448. ------ 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. ------ 158497/17384556. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x) 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)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 158498/17384583. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z)) 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. ------ 158499/17384727. ------ 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 ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158500/17384808. ------ 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. ------ 158501/17384916. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.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. ------ 158502/17385033. ------ 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)))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 158503/17385078. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 158504/17385132. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(a a))) 7. ==[ beta ]==> ((b b)((^y.(y y))(a a))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(a a))) 9. ==[ beta ]==> ((b b)((a a)(a a))) REDUCED to normal form. ------ 158505/17385213. ------ 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. ------ 158506/17385276. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (a (^z.z)))) REDUCED to normal form. ------ 158507/17385321. ------ 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)(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158508/17385330. ------ 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. ------ 158509/17385357. ------ 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. ------ 158510/17385384. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 158511/17385456. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(a a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 158512/17385474. ------ 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.(^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. ------ 158513/17385501. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 158514/17385528. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) 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. ------ 158515/17385555. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y)) b)) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y)) b)) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x)) b)) REDUCED to normal form. ------ 158516/17385609. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a) a)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 158517/17385636. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^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. ------ 158518/17385690. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 158519/17385744. ------ 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 (^y1.y1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1)) a)) REDUCED to normal form. ------ 158520/17385771. ------ 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. ------ 158521/17385798. ------ 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)) 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. ------ 158522/17385852. ------ 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. ------ 158523/17385870. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a b)) 3. ==[ beta ]==> ((a (^y.y))(a b)) 4. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 158524/17385879. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a) a)) REDUCED to normal form. ------ 158525/17385888. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> (((^z.z)(^x1.x1))(^y.y)) 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. ------ 158526/17385990. ------ 1. ==[ start ]==> ((^a.b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 158527/17396088. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.b)) 3. ==[ beta ]==> ((^z.b)((^z.b)(^y.y))) 4. ==[ alpha ]==> ((^x.b)((^y.b)(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 158528/17396178. ------ 1. ==[ start ]==> ((^a.(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((b ((^y.(^z.z)) a))(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((b ((^x.(^y.y)) a))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((b (^y.y))(b ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((b (^x.x))(b ((^y.(^z.z)) a))) 7. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 158529/17396199. ------ 1. ==[ start ]==> (((a a) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 158530/17396205. ------ 1. ==[ start ]==> ((^a.b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(a (a (a (^y.y))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 158531/17396208. ------ 1. ==[ start ]==> ((a b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 158532/17396286. ------ 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)(a a))((^z.z) a))(^y.y)) 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. ------ 158533/17396475. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a) a)(b a))) 3. ==[ eta ]==> ((^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. ------ 158534/17396631. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(^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))))) REDUCED to normal form. ------ 158535/17396646. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 158536/17396970. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158537/17397450. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x) a)((^y.y) 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. ------ 158538/17397528. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((((^y.y) b)((^z.z) a))(((^y.y) b)((^z.z) a)))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((((^x.x) b)((^y.y) a))(((^z.z) b)((^x1.x1) a)))(((^y1.y1) b)((^z1.z1) a))) 5. ==[ beta ]==> (((b ((^y.y) a))(((^z.z) b)((^x1.x1) a)))(((^y1.y1) b)((^z1.z1) a))) 6. ==[ alpha ]==> (((b ((^x.x) a))(((^y.y) b)((^z.z) a)))(((^x1.x1) b)((^y1.y1) a))) 7. ==[ beta ]==> (((b a)(((^y.y) b)((^z.z) a)))(((^x1.x1) b)((^y1.y1) a))) 8. ==[ alpha ]==> (((b a)(((^x.x) b)((^y.y) a)))(((^z.z) b)((^x1.x1) a))) 9. ==[ beta ]==> (((b a)(b ((^y.y) a)))(((^z.z) b)((^x1.x1) a))) 10. ==[ alpha ]==> (((b a)(b ((^x.x) a)))(((^y.y) b)((^z.z) a))) 11. ==[ beta ]==> (((b a)(b a))(((^y.y) b)((^z.z) a))) 12. ==[ alpha ]==> (((b a)(b a))(((^x.x) b)((^y.y) a))) 13. ==[ beta ]==> (((b a)(b a))(b ((^y.y) a))) 14. ==[ alpha ]==> (((b a)(b a))(b ((^x.x) a))) 15. ==[ beta ]==> (((b a)(b a))(b a)) REDUCED to normal form. ------ 158539/17397861. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 158540/17398215. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 158541/17398224. ------ 1. ==[ start ]==> (((a b) a)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 158542/17398611. ------ 1. ==[ start ]==> (((a b)(a a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 158543/17398635. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((^y.y)((((a a)(a a))(a a))(((a a)(a a))(a a)))) 4. ==[ alpha ]==> ((^x.x)((((a a)(a a))(a a))(((a a)(a a))(a a)))) 5. ==[ beta ]==> ((((a a)(a a))(a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 158544/17399682. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158545/17400348. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.(^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. ------ 158546/17400690. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a (a a))(^y.((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))(^x.((^y.y) b))) 7. ==[ beta ]==> ((a (a a))(^x.b)) REDUCED to normal form. ------ 158547/17400903. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))((^x1.x1)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((^x.x)(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. ------ 158548/17401302. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 158549/17401608. ------ 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 (^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))))) REDUCED to normal form. ------ 158550/17401821. ------ 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) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 158551/17402157. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 158552/17402166. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y a))) REDUCED to normal form. ------ 158553/17403876. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^x.(x x))) REDUCED to normal form. ------ 158554/17403900. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)(a a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 158555/17404461. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.y))) REDUCED to normal form. ------ 158556/17404983. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.((z z) z))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.((z z) z))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.((y y) y))) 5. ==[ beta ]==> ((b a)(^y.((y y) y))) 6. ==[ alpha ]==> ((b a)(^x.((x x) x))) REDUCED to normal form. ------ 158557/17405061. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158558/17405640. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 158559/17405649. ------ 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. ------ 158560/17405757. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) REDUCED to normal form. ------ 158561/17405865. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 158562/17405880. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 158563/17406036. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y) x))) 3. ==[ eta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 158564/17406225. ------ 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)))) 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. ------ 158565/17406297. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(a a))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a a))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 158566/17406303. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a b)) 3. ==[ beta ]==> ((a b)((a b)(^y.y))) 4. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 158567/17406306. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.b)) REDUCED to normal form. ------ 158568/17406399. ------ 1. ==[ start ]==> ((a (a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a a))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a (a a))(b (^y.y))) 4. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 158569/17406417. ------ 1. ==[ start ]==> (((a a) a)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.x)(^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. ------ 158570/17406426. ------ 1. ==[ start ]==> ((a b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)(a (a (a (^x.x))))) REDUCED to normal form. ------ 158571/17406435. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^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)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 158572/17406480. ------ 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. ------ 158573/17406507. ------ 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. ------ 158574/17406642. ------ 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. ------ 158575/17406669. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 158576/17406696. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(b a))) 3. ==[ beta ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 158577/17406795. ------ 1. ==[ start ]==> (((a a)(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 158578/17406849. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(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))))) REDUCED to normal form. ------ 158579/17406867. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(^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. ------ 158580/17406957. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 158581/17406975. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) REDUCED to normal form. ------ 158582/17407002. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.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. ------ 158583/17407038. ------ 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. ------ 158584/17407056. ------ 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))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 158585/17407065. ------ 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. ------ 158586/17407083. ------ 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. ------ 158587/17407092. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 158588/17407119. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 158589/17407146. ------ 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))(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. ------ 158590/17407164. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a (a a))(^b.b))) 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. ------ 158591/17407173. ------ 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. ------ 158592/17407191. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 158593/17407326. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158594/17407470. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 158595/17407497. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 158596/17407524. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 158597/17407551. ------ 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. ------ 158598/17407578. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a a))(^b.b))) 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. ------ 158599/17407641. ------ 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. ------ 158600/17407668. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 158601/17407695. ------ 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. ------ 158602/17407722. ------ 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. ------ 158603/17407749. ------ 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))(b ((^y.y) a))) 4. ==[ alpha ]==> ((a ((a a) a))(b ((^x.x) a))) 5. ==[ beta ]==> ((a ((a a) a))(b a)) REDUCED to normal form. ------ 158604/17408010. ------ 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. ------ 158605/17408082. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 158606/17408253. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 158607/17408271. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((^y.b)((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.b)((a b)(^y.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 158608/17408352. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) IRREDUCIBLE: cycle. ------ 158609/17408415. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 158610/17408442. ------ 1. ==[ start ]==> (((a b) a)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)(b (^y.y)))) 3. ==[ beta ]==> (((a b) a)(b (^y.y))) 4. ==[ alpha ]==> (((a b) a)(b (^x.x))) REDUCED to normal form. ------ 158611/17408460. ------ 1. ==[ start ]==> (((^a.a)(a b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(a b))((b (^y.y)) a)) 3. ==[ beta ]==> ((a b)((b (^y.y)) a)) 4. ==[ alpha ]==> ((a b)((b (^x.x)) a)) REDUCED to normal form. ------ 158612/17408487. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a 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. ------ 158613/17408523. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 158614/17408550. ------ 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. ------ 158615/17408631. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 158616/17408802. ------ 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. ------ 158617/17408829. ------ 1. ==[ start ]==> (((a b)(a a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(a (b (^x.x)))) REDUCED to normal form. ------ 158618/17408856. ------ 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. ------ 158619/17408865. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a)) b)) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a)) b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158620/17408892. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 158621/17409171. ------ 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. ------ 158622/17409225. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 158623/17409243. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 158624/17409252. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.b)(a (^a.a)))) 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. ------ 158625/17409279. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 158626/17409468. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 158627/17409567. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 158628/17409711. ------ 1. ==[ start ]==> (((a b) c)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 158629/17409738. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.b)(^z.b))) 3. ==[ beta ]==> (((a a) b)((^y.b)(^z.b))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(^y.b))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 158630/17409846. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 158631/17409900. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158632/17409945. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z) b)) 3. ==[ beta ]==> (b ((^z.z) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 158633/17410044. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)((^y.y)(^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. ------ 158634/17410071. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a b)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a b)((a a) a))) REDUCED to normal form. ------ 158635/17410098. ------ 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. ------ 158636/17410125. ------ 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. ------ 158637/17410152. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.y)((a (a a))((a a)(^z.z)))) 8. ==[ alpha ]==> ((^x.x)((a (a 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. ------ 158638/17410179. ------ 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. ------ 158639/17410206. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a)((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 158640/17410233. ------ 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. ------ 158641/17410377. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(a a))(^b.(^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. ------ 158642/17410458. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^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. ------ 158643/17410521. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 158644/17410566. ------ 1. ==[ start ]==> (((^a.a)(b a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(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. ------ 158645/17410593. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^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. ------ 158646/17410629. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 158647/17410647. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a) c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a) c)) 3. ==[ beta ]==> (((a b)(a b))((b a) c)) REDUCED to normal form. ------ 158648/17410710. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 158649/17410737. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 158650/17410764. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 158651/17410791. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(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. ------ 158652/17410854. ------ 1. ==[ start ]==> (((a a)(b a))(c (b a))) REDUCED to normal form. ------ 158653/17410881. ------ 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.(^x1.x1))))) REDUCED to normal form. ------ 158654/17410908. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(a ((^z.z) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(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. ------ 158655/17410935. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 158656/17410962. ------ 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. ------ 158657/17410989. ------ 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))((^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. ------ 158658/17411016. ------ 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 (a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 158659/17411043. ------ 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. ------ 158660/17411070. ------ 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 a) a))) REDUCED to normal form. ------ 158661/17411124. ------ 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)(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a (a a))(a a))) REDUCED to normal form. ------ 158662/17411295. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a)(^a.a))(^b.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. ------ 158663/17411403. ------ 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))(((^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. ------ 158664/17411412. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 158665/17411430. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 158666/17411439. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(((^y1.y1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 158667/17411457. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^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. ------ 158668/17411511. ------ 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)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(^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. ------ 158669/17411520. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 158670/17411547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 158671/17411592. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> (b (((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 158672/17411601. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(^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. ------ 158673/17411628. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 158674/17411655. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 158675/17411709. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 158676/17411772. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 158677/17411799. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(b (b a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(b (b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (b a))) REDUCED to normal form. ------ 158678/17411826. ------ 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))))) 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. ------ 158679/17411853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a)(a a))) 3. ==[ beta ]==> (((^y.y)(a b))((b a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a b))((b a)(a a))) 5. ==[ beta ]==> ((a b)((b a)(a a))) REDUCED to normal form. ------ 158680/17411880. ------ 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. ------ 158681/17411907. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)((^z.z) a))) 6. ==[ alpha ]==> (((a b)(^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> (((a b)(^x.x))((a a) a)) REDUCED to normal form. ------ 158682/17411934. ------ 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)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a b)(a (a a)))) REDUCED to normal form. ------ 158683/17411961. ------ 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)(^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. ------ 158684/17412015. ------ 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. ------ 158685/17412042. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 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. ------ 158686/17412213. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 158687/17412321. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.(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. ------ 158688/17412330. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 158689/17412357. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^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. ------ 158690/17412384. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b a))) 3. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 158691/17412402. ------ 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)((b a) a)) 4. ==[ alpha ]==> ((^x.x)((b a) a)) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 158692/17412492. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(z z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158693/17412519. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)(^b.(^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. ------ 158694/17412546. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^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. ------ 158695/17412573. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 158696/17412600. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 158697/17412717. ------ 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. ------ 158698/17412744. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a b) a)) REDUCED to normal form. ------ 158699/17412771. ------ 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. ------ 158700/17412798. ------ 1. ==[ start ]==> (((a (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)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^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)(^x.x)))((^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. ------ 158701/17412825. ------ 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. ------ 158702/17412852. ------ 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. ------ 158703/17412879. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))((a (^x.x))(a a))) REDUCED to normal form. ------ 158704/17412906. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 158705/17413077. ------ 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. ------ 158706/17413212. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 158707/17413356. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.b))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.b))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.b))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 158708/17413383. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 158709/17413428. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 158710/17413482. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b) c)) 3. ==[ beta ]==> (((b a)(b a))((^y.b) c)) 4. ==[ alpha ]==> (((b a)(b a))((^x.b) c)) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 158711/17413626. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.(a a)))) REDUCED to normal form. ------ 158712/17413671. ------ 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 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. ------ 158713/17413680. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 158714/17413707. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 158715/17414067. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b (a b))) 3. ==[ beta ]==> ((b (a (^y.y)))(b (a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b (a b))) REDUCED to normal form. ------ 158716/17414094. ------ 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. ------ 158717/17414121. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 158718/17414400. ------ 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. ------ 158719/17414436. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 158720/17414463. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 158721/17414508. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b) a)) 3. ==[ beta ]==> ((b (^y.y))((a b) a)) 4. ==[ alpha ]==> ((b (^x.x))((a b) a)) REDUCED to normal form. ------ 158722/17414535. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 158723/17414571. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 158724/17414598. ------ 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.(y1 y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.(y1 y1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.(y1 y1)))) IRREDUCIBLE: cycle. ------ 158725/17414679. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.b)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.b)) REDUCED to normal form. ------ 158726/17414814. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 158727/17414841. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 158728/17415174. ------ 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. ------ 158729/17415201. ------ 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 ]==> ((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. ------ 158730/17415228. ------ 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. ------ 158731/17415282. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 158732/17415372. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^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 ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158733/17415453. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 158734/17415561. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158735/17415696. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a) c)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a) c)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 158736/17415777. ------ 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. ------ 158737/17415786. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 158738/17415813. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158739/17415858. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)(^z.(z z)))) 3. ==[ beta ]==> (b ((a a)(^z.(z z)))) 4. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 158740/17415867. ------ 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. ------ 158741/17415894. ------ 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 z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 158742/17415921. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 158743/17415975. ------ 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)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(z1 z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 y1))) REDUCED to normal form. ------ 158744/17416029. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 158745/17416083. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 158746/17416101. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 158747/17416146. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b c)) REDUCED to normal form. ------ 158748/17416200. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (a a))) 3. ==[ beta ]==> (((a (a a)) b)(c (a a))) REDUCED to normal form. ------ 158749/17416227. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 158750/17416254. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a ((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 158751/17416281. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 158752/17416308. ------ 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. ------ 158753/17416335. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c a)) REDUCED to normal form. ------ 158754/17416416. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (a a))) 3. ==[ beta ]==> ((b (a (a a)))(b (a a))) REDUCED to normal form. ------ 158755/17416443. ------ 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)))) 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. ------ 158756/17416497. ------ 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. ------ 158757/17416515. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^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 (^x.x))(a a)) REDUCED to normal form. ------ 158758/17416524. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a b)) REDUCED to normal form. ------ 158759/17416533. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 158760/17416644. ------ 1. ==[ start ]==> ((^a.b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 158761/17426742. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(a a))) 3. ==[ beta ]==> ((^z.(a a))((^z.(a a))(^y.y))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158762/17426868. ------ 1. ==[ start ]==> ((^a.b)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 158763/17426871. ------ 1. ==[ start ]==> ((a b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 158764/17426880. ------ 1. ==[ start ]==> (((^a.a)(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 158765/17426904. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 158766/17427066. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (^y.(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (^x.(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 158767/17427408. ------ 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. ------ 158768/17427708. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 158769/17428704. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(a b))) 3. ==[ beta ]==> (((^y.(a a))(a b)) b) 4. ==[ alpha ]==> (((^x.(a a))(a b)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 158770/17428887. ------ 1. ==[ start ]==> (((a b) a)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 158771/17429973. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((^z.(^x1.x1))((^y1.y1) b))((^z.(^x1.x1))((^y1.y1) b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))((^z1.z1) b)))(^x2.x2)) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))((^z1.z1) b)))(^x2.x2)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1) b)))(^y1.y1)) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) b))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 158772/17430729. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b)(a a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(a a))) 3. ==[ eta ]==> (b ((^y.y)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 158773/17431353. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.(^b.b))) 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))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 158774/17431659. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 158775/17431965. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 158776/17432271. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 158777/17432829. ------ 1. ==[ start ]==> (((a a)(^b.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 158778/17433873. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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))) REDUCED to normal form. ------ 158779/17434323. ------ 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)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 158780/17434539. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 158781/17434737. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(a b))) 3. ==[ beta ]==> (b (^z.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 158782/17435484. ------ 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))) REDUCED to normal form. ------ 158783/17435646. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.a))) 5. ==[ beta ]==> ((b a)(^y.(^z.a))) 6. ==[ alpha ]==> ((b a)(^x.(^y.a))) REDUCED to normal form. ------ 158784/17436312. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 158785/17436420. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.d)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.d)) REDUCED to normal form. ------ 158786/17436618. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.((^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)))(^x.a)) REDUCED to normal form. ------ 158787/17436699. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 158788/17436780. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.y))) REDUCED to normal form. ------ 158789/17436834. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(a (^y1.y1)))) REDUCED to normal form. ------ 158790/17436888. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^a.(^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. ------ 158791/17436942. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^a.(^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. ------ 158792/17436966. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> (((^z.z)(a a))(((^z.z)(a a))(^y.y))) 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. ------ 158793/17436969. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(a a))) REDUCED to normal form. ------ 158794/17436978. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.b)) 5. ==[ beta ]==> ((^z.b)(^y.y)) 6. ==[ alpha ]==> ((^x.b)(^y.y)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 158795/17437080. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(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. ------ 158796/17437098. ------ 1. ==[ start ]==> ((a b)((^a.a)(^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)))) REDUCED to normal form. ------ 158797/17437107. ------ 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. ------ 158798/17437116. ------ 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))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 158799/17437134. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 158800/17437188. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158801/17437197. ------ 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. ------ 158802/17437215. ------ 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)(((^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. ------ 158803/17437242. ------ 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.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. ------ 158804/17437269. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 158805/17437296. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 158806/17437377. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.a)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.a)(((a a) a)(b a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 158807/17437404. ------ 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)(^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. ------ 158808/17437458. ------ 1. ==[ start ]==> (((^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 a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (a (((^y.y) 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. ------ 158809/17437485. ------ 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))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(b (^y1.y1)))) 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. ------ 158810/17437629. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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)))) 5. ==[ beta ]==> ((a a)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 158811/17437638. ------ 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. ------ 158812/17437710. ------ 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. ------ 158813/17437737. ------ 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. ------ 158814/17437764. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 158815/17437818. ------ 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.(^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. ------ 158816/17437845. ------ 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. ------ 158817/17437881. ------ 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. ------ 158818/17437908. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 158819/17437935. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^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. ------ 158820/17437953. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((b b)(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> ((b b)((^y.y) a)) 6. ==[ alpha ]==> ((b b)((^x.x) a)) 7. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 158821/17438286. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 158822/17438457. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^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. ------ 158823/17438511. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> (a (((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> (a (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 158824/17438592. ------ 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. ------ 158825/17438619. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(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. ------ 158826/17438673. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z) b))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) b))) 9. ==[ beta ]==> ((a a)(a ((^y.y) b))) 10. ==[ alpha ]==> ((a a)(a ((^x.x) b))) 11. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 158827/17438826. ------ 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. ------ 158828/17438853. ------ 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. ------ 158829/17438925. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 158830/17438934. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(a b))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 158831/17439087. ------ 1. ==[ start ]==> ((((a a) a) b)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 158832/17439141. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y)) a)) REDUCED to normal form. ------ 158833/17439195. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b) c)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b c)) REDUCED to normal form. ------ 158834/17439339. ------ 1. ==[ start ]==> (((a a)(a b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 158835/17439420. ------ 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. ------ 158836/17439447. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.z))) 7. ==[ beta ]==> (a ((^y.a)(^z.z))) 8. ==[ alpha ]==> (a ((^x.a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158837/17439537. ------ 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 a) REDUCED to normal form. ------ 158838/17439564. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 158839/17439618. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^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. ------ 158840/17439699. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 158841/17439753. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^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. ------ 158842/17439780. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 158843/17439834. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1) b))) 9. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1) b))) 10. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) b))) 11. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 12. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 13. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 158844/17439897. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 158845/17439924. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 158846/17439951. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 158847/17440014. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 158848/17440041. ------ 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 a)) REDUCED to normal form. ------ 158849/17440068. ------ 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. ------ 158850/17440122. ------ 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 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. ------ 158851/17440140. ------ 1. ==[ start ]==> (((^a.b) c)((a (a a))(^d.a))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 158852/17440149. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((b a)(b a))) REDUCED to normal form. ------ 158853/17440176. ------ 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.(^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) REDUCED to normal form. ------ 158854/17440203. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^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. ------ 158855/17440617. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (b (((^z.z) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 158856/17440626. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y) b)) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 158857/17440878. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(c (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a)(c (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) a)(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 158858/17440905. ------ 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. ------ 158859/17440959. ------ 1. ==[ start ]==> ((a (b a))((^b.b)(a a))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(a a))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 158860/17441301. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 158861/17441328. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a) c)) REDUCED to normal form. ------ 158862/17441553. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 158863/17441580. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)(^b.b))) 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))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 158864/17441805. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158865/17441886. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)((a a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 158866/17442084. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.b)) REDUCED to normal form. ------ 158867/17442111. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (a a))(^x1.(a a)))) REDUCED to normal form. ------ 158868/17442192. ------ 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. ------ 158869/17442219. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1))) a)) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z))) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 158870/17442273. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z)) c)) REDUCED to normal form. ------ 158871/17442417. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 158872/17442444. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 158873/17442498. ------ 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.(^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. ------ 158874/17442723. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a) 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))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 158875/17442750. ------ 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))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^z1.z1))((a a)(^x2.x2)))) 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. ------ 158876/17443002. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.(a a)))) REDUCED to normal form. ------ 158877/17443029. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.a))(^c.(^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. ------ 158878/17443083. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a) a)) REDUCED to normal form. ------ 158879/17443317. ------ 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. ------ 158880/17443551. ------ 1. ==[ start ]==> (((a b)((a a) a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(c (^x.(a a)))) REDUCED to normal form. ------ 158881/17443578. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(b (^c.(^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)(^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 158882/17443659. ------ 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 a)) REDUCED to normal form. ------ 158883/17443686. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((b (a a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> ((b (a a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 158884/17444073. ------ 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. ------ 158885/17444100. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 158886/17444109. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 158887/17444136. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a)) b)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 158888/17444154. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((b a)(b a))((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))((a b)(a (^x.x)))) REDUCED to normal form. ------ 158889/17444235. ------ 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. ------ 158890/17444352. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.x1))) REDUCED to normal form. ------ 158891/17444379. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 158892/17444406. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 158893/17444442. ------ 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. ------ 158894/17444469. ------ 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 z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.z))) 11. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 12. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 158895/17444496. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.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. ------ 158896/17444523. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 158897/17444550. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^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))((^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. ------ 158898/17444577. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 158899/17444604. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 158900/17444658. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.(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. ------ 158901/17444712. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 158902/17444739. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 158903/17444766. ------ 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)))) 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. ------ 158904/17444883. ------ 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. ------ 158905/17444964. ------ 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 b))) REDUCED to normal form. ------ 158906/17445108. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b c)(a (^x.(^y.y)))) REDUCED to normal form. ------ 158907/17445135. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 158908/17445243. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) c)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) c)) 7. ==[ beta ]==> ((a (^x.x)) c) REDUCED to normal form. ------ 158909/17445342. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 158910/17445378. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b) a)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b) a)) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 158911/17445450. ------ 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. ------ 158912/17445576. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(a a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 158913/17445603. ------ 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 (^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. ------ 158914/17445630. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a b)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((a b)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((a b)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a b)(a ((^y.y) a))) 10. ==[ alpha ]==> ((a b)(a ((^x.x) a))) 11. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 158915/17445657. ------ 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. ------ 158916/17445684. ------ 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)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 158917/17445711. ------ 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. ------ 158918/17445738. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.y))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 158919/17445765. ------ 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.(^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. ------ 158920/17445792. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 158921/17445846. ------ 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.(^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. ------ 158922/17445873. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.a))) 7. ==[ beta ]==> ((b a)(^y.a)) 8. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 158923/17446125. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c d)) 3. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 158924/17446350. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z)) b)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y)) b)) 5. ==[ beta ]==> (a ((^y.(y y)) b)) 6. ==[ alpha ]==> (a ((^x.(x x)) b)) 7. ==[ beta ]==> (a (b b)) REDUCED to normal form. ------ 158925/17446368. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 158926/17446395. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.y1) 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. ------ 158927/17446458. ------ 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. ------ 158928/17446485. ------ 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.(^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. ------ 158929/17446539. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 158930/17446566. ------ 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. ------ 158931/17446593. ------ 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. ------ 158932/17446638. ------ 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 ((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158933/17446674. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z)) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z)) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y)) a)) 5. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 158934/17446701. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 158935/17446791. ------ 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))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 158936/17446818. ------ 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 (^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. ------ 158937/17446845. ------ 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)((^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. ------ 158938/17446872. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.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. ------ 158939/17446899. ------ 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))(^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. ------ 158940/17446926. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^b.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. ------ 158941/17446953. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.y))) REDUCED to normal form. ------ 158942/17446980. ------ 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 (^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. ------ 158943/17447007. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.a))) REDUCED to normal form. ------ 158944/17447061. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a (^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. ------ 158945/17447088. ------ 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)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 158946/17447115. ------ 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)))) 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. ------ 158947/17447169. ------ 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)(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. ------ 158948/17447187. ------ 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 (^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 158949/17447196. ------ 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. ------ 158950/17447205. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a b)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 158951/17447766. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 158952/17457000. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 158953/17457570. ------ 1. ==[ start ]==> (((^a.a)(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 158954/17457579. ------ 1. ==[ start ]==> (((a a)(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 158955/17457999. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 158956/17458002. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 158957/17458098. ------ 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. ------ 158958/17458323. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 158959/17458449. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b (^x1.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. ------ 158960/17459394. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((^y.y)(a a))(^z.b)) b) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.b)) b) 5. ==[ beta ]==> (((a a)(^y.b)) b) 6. ==[ alpha ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 158961/17459595. ------ 1. ==[ start ]==> (((^a.a)(a b))(^b.(b (^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. ------ 158962/17459781. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (^y.(((^z.(a a))(^x1.b))((^z.(a a))(^x1.b)))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(^z.b))((^x1.(a a))(^y1.b)))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))(^y1.b)))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(^z.b)))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 158963/17460663. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.a))(^b.b))) 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)) REDUCED to normal form. ------ 158964/17460702. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 158965/17461062. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 158966/17461419. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b)(^z.z))) 3. ==[ eta ]==> (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. ------ 158967/17461728. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.((^a.a) b))) 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)(^x1.x1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158968/17462859. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 158969/17463537. ------ 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)) REDUCED to normal form. ------ 158970/17463816. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(b z))) 3. ==[ eta ]==> ((((^x.x) b)(^y.y)) b) 4. ==[ beta ]==> ((b (^y.y)) b) 5. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 158971/17464173. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> (((((a a) a)(^y.(y y)))(((a a) a)(^y.(y y))))((((a a) a)(^y.(y y)))(((a a) a)(^y.(y y))))) 4. ==[ alpha ]==> (((((a a) a)(^x.(x x)))(((a a) a)(^y.(y y))))((((a a) a)(^z.(z z)))(((a a) a)(^x1.(x1 x1))))) REDUCED to normal form. ------ 158972/17464563. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 158973/17464572. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 158974/17465253. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 158975/17465643. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(a z))) 3. ==[ eta ]==> (((^x.x)(b (^y.y))) a) 4. ==[ beta ]==> ((b (^y.y)) a) 5. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 158976/17465841. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(z b))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(z b))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(y b))) REDUCED to normal form. ------ 158977/17466507. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.z))) 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. ------ 158978/17466912. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 158979/17467002. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 158980/17467137. ------ 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. ------ 158981/17467233. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 158982/17467236. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 158983/17467389. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.c)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 158984/17467470. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.c)) REDUCED to normal form. ------ 158985/17467632. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 158986/17467656. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(^z.z))) 3. ==[ beta ]==> (((a a)(^z.z))(((a a)(^z.z))(^y.y))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 158987/17467668. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.(a a))(^y.y)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 158988/17467788. ------ 1. ==[ start ]==> (((a a) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) a)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a) a)(b (^y.y))) 4. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 158989/17467806. ------ 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)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 158990/17467815. ------ 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. ------ 158991/17467842. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.(^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))) 5. ==[ beta ]==> (b ((^y.y)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 158992/17467869. ------ 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))) REDUCED to normal form. ------ 158993/17467896. ------ 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. ------ 158994/17467923. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(b (a (a a)))) REDUCED to normal form. ------ 158995/17467950. ------ 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)(^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. ------ 158996/17467977. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)((a a) a))) REDUCED to normal form. ------ 158997/17468031. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 158998/17468112. ------ 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.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(^z.z)))) REDUCED to normal form. ------ 158999/17468139. ------ 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))) 5. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 159000/17468166. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 159001/17468193. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 159002/17468220. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^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. ------ 159003/17468238. ------ 1. ==[ start ]==> ((a (^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 159004/17468256. ------ 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) 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. ------ 159005/17468283. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 159006/17468310. ------ 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. ------ 159007/17468337. ------ 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. ------ 159008/17468346. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a (a a)))((^y.y)(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)))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 159009/17468373. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 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. ------ 159010/17468454. ------ 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. ------ 159011/17468481. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((a a)(^y1.y1)))) 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. ------ 159012/17468535. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^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)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 159013/17468562. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b ((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 159014/17468661. ------ 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. ------ 159015/17468688. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z)) b)) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z)) b)) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 159016/17468778. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 159017/17468859. ------ 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. ------ 159018/17469246. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (b (((^y.y)(a a))(a b))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 7. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 159019/17469273. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a b)(a a))) REDUCED to normal form. ------ 159020/17469327. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(b a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b a)) REDUCED to normal form. ------ 159021/17469354. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 159022/17469381. ------ 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. ------ 159023/17469408. ------ 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 (^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159024/17469435. ------ 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. ------ 159025/17469471. ------ 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. ------ 159026/17469498. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 159027/17469525. ------ 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. ------ 159028/17469552. ------ 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. ------ 159029/17469579. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 159030/17469633. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))(^y.b))) 3. ==[ beta ]==> ((a (a b))((a a)(^y.b))) 4. ==[ alpha ]==> ((a (a b))((a a)(^x.b))) REDUCED to normal form. ------ 159031/17469642. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(a b))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(a b))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(a b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159032/17469723. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(b a))) IRREDUCIBLE: cycle. ------ 159033/17469804. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 159034/17469831. ------ 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)))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 159035/17469912. ------ 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. ------ 159036/17469993. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 159037/17470020. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 159038/17470191. ------ 1. ==[ start ]==> (((^a.b) b)(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 159039/17470407. ------ 1. ==[ start ]==> (((a b) b)((a b)(a b))) REDUCED to normal form. ------ 159040/17470434. ------ 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.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. ------ 159041/17470461. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 159042/17470488. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (a a))(b a))) REDUCED to normal form. ------ 159043/17470542. ------ 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. ------ 159044/17470569. ------ 1. ==[ start ]==> ((((^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 a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((a a)((a a)(a a)))) 7. ==[ beta ]==> (((a a)((a a)(a a)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 159045/17470614. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(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 a)) REDUCED to normal form. ------ 159046/17470686. ------ 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)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 159047/17470713. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 159048/17470767. ------ 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. ------ 159049/17470794. ------ 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. ------ 159050/17470875. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^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. ------ 159051/17470902. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 159052/17470938. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 159053/17471073. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 159054/17471181. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 159055/17471235. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 159056/17471271. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^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. ------ 159057/17471298. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 159058/17471325. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a b)(^x.a))(b (a a))) REDUCED to normal form. ------ 159059/17471352. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 159060/17471379. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((b a) a)) REDUCED to normal form. ------ 159061/17471658. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> ((a (b a))(b (^y.y))) 4. ==[ alpha ]==> ((a (b a))(b (^x.x))) REDUCED to normal form. ------ 159062/17471748. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(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. ------ 159063/17471829. ------ 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) REDUCED to normal form. ------ 159064/17471937. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 159065/17471964. ------ 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)((^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 ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 159066/17472018. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 159067/17472099. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 159068/17472306. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b) a)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x) a)) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 159069/17472333. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 159070/17472387. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y)) d)) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 159071/17472486. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^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. ------ 159072/17472585. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 159073/17472801. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(^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. ------ 159074/17472828. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1)(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. ------ 159075/17472882. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(b a))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(b a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(b a))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 159076/17473098. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 159077/17473224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1))) a)) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) a)) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 159078/17473278. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 159079/17473377. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^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. ------ 159080/17473584. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 159081/17473692. ------ 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 z1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159082/17473746. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159083/17473773. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(b a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(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. ------ 159084/17473908. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)(^b.(^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. ------ 159085/17474025. ------ 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. ------ 159086/17474052. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(a (b a))) 3. ==[ beta ]==> ((b (^y.y))(a (b a))) 4. ==[ alpha ]==> ((b (^x.x))(a (b a))) REDUCED to normal form. ------ 159087/17474088. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) b)) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 159088/17474115. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 159089/17474358. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 159090/17474385. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)(^b.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. ------ 159091/17474412. ------ 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. ------ 159092/17474448. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^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. ------ 159093/17474583. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 159094/17474691. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))(^b.(^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. ------ 159095/17474772. ------ 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.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 159096/17474799. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.a)(^c.(^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))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159097/17474808. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 159098/17474835. ------ 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)(a a))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 159099/17474916. ------ 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. ------ 159100/17474943. ------ 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. ------ 159101/17474997. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(a b))) REDUCED to normal form. ------ 159102/17475141. ------ 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)(^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. ------ 159103/17475168. ------ 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. ------ 159104/17475222. ------ 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. ------ 159105/17475249. ------ 1. ==[ start ]==> ((((^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)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a a)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 159106/17475276. ------ 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)) 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. ------ 159107/17475303. ------ 1. ==[ start ]==> (((a b)(a b))((a b) b)) REDUCED to normal form. ------ 159108/17475492. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a)) a)) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 159109/17475663. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b (^z.b))) 3. ==[ beta ]==> (b (b (^z.b))) 4. ==[ alpha ]==> (b (b (^x.b))) REDUCED to normal form. ------ 159110/17475771. ------ 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.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159111/17475807. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d e)) 2. ==[ alpha ]==> ((((^x.x) b) c)(d e)) 3. ==[ beta ]==> ((b c)(d e)) REDUCED to normal form. ------ 159112/17475879. ------ 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 (^x.x))(a b)) REDUCED to normal form. ------ 159113/17475906. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^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)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159114/17475960. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.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. ------ 159115/17476041. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 159116/17476050. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b ((a a) a))) REDUCED to normal form. ------ 159117/17476077. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a (a b))) 3. ==[ beta ]==> (((a a)(^y.b))(a (a b))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (a b))) REDUCED to normal form. ------ 159118/17476158. ------ 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. ------ 159119/17476185. ------ 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. ------ 159120/17476212. ------ 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 (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 159121/17476275. ------ 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. ------ 159122/17476302. ------ 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.(^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)))) 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. ------ 159123/17476329. ------ 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. ------ 159124/17476356. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.(z z)))) REDUCED to normal form. ------ 159125/17476383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 159126/17476437. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((a a) a) a)) 3. ==[ beta ]==> (((a b)(a a))(((a a) a) a)) REDUCED to normal form. ------ 159127/17476464. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 159128/17476743. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.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. ------ 159129/17476824. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.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. ------ 159130/17476932. ------ 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.(^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. ------ 159131/17477049. ------ 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. ------ 159132/17477094. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (^b.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. ------ 159133/17477148. ------ 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 ]==> ((((^y.y) b)((^y.y) b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (^y.(^z.z)))) 7. ==[ beta ]==> ((b b)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 159134/17477229. ------ 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))((^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. ------ 159135/17477238. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b d)) REDUCED to normal form. ------ 159136/17477337. ------ 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.(^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. ------ 159137/17477346. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b ((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b a)) REDUCED to normal form. ------ 159138/17477373. ------ 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. ------ 159139/17477400. ------ 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. ------ 159140/17477454. ------ 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)(^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. ------ 159141/17477472. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.(z z)))) REDUCED to normal form. ------ 159142/17477490. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 159143/17477517. ------ 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))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 159144/17477544. ------ 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. ------ 159145/17477571. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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)) 5. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 159146/17477598. ------ 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 (^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1)) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1)) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 159147/17477625. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a) c)) REDUCED to normal form. ------ 159148/17477652. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.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. ------ 159149/17477679. ------ 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.(^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. ------ 159150/17477706. ------ 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)(^x.x))(a b)) c) REDUCED to normal form. ------ 159151/17477760. ------ 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)(^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. ------ 159152/17477787. ------ 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 ]==> ((b (a (a a)))((a (^y.y)) a)) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 159153/17477814. ------ 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. ------ 159154/17477868. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 159155/17477886. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b a)) 3. ==[ beta ]==> ((a (^y.y))(b a)) 4. ==[ alpha ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 159156/17477895. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.y))) REDUCED to normal form. ------ 159157/17477904. ------ 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 ]==> (((^z.z)(a a))(^y.y)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 159158/17480463. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(b (^x1.x1)))(^z.(b (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(b (^z.z)))(^x1.(b (^y1.y1))))) 5. ==[ beta ]==> ((^y.(b (^z.z)))(^x1.(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(b (^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159159/17485728. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159160/17488275. ------ 1. ==[ start ]==> ((^a.b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.b)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 159161/17488296. ------ 1. ==[ start ]==> (((a a)(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 159162/17488311. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159163/17488356. ------ 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 (^z.z))(a (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((b (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 159164/17488545. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a b)((a a)(^z.z)))) 3. ==[ eta ]==> ((^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. ------ 159165/17489040. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a a))(^b.b))) 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. ------ 159166/17489133. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) 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)(^x.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 159167/17489547. ------ 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. ------ 159168/17489598. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((((a a)(a a))(a (^y.y)))(((a a)(a a))(a (^y.y))))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (((((a a)(a a))(a (^x.x)))(((a a)(a a))(a (^y.y))))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 159169/17490312. ------ 1. ==[ start ]==> (((^a.a)(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 159170/17490321. ------ 1. ==[ start ]==> (((a a)(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 159171/17490705. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(a (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a (b (^z.z)))(a (b (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a (b (^y.y)))(a (b (^z.z))))) 5. ==[ beta ]==> ((a (b (^y.y)))(a (b (^z.z)))) 6. ==[ alpha ]==> ((a (b (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 159172/17490708. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 159173/17491419. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 159174/17491779. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 159175/17492787. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a b))(^x.b)) REDUCED to normal form. ------ 159176/17492973. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((((^x1.x1)(^y1.y1))(a b))(^y.(^z.z))) 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. ------ 159177/17493399. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159178/17493705. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(y (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(^y.(y (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 159179/17493891. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (a a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159180/17494263. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(y1 a))) REDUCED to normal form. ------ 159181/17495289. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 159182/17495532. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 159183/17495970. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159184/17495973. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 159185/17496360. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 159186/17496558. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.y))) REDUCED to normal form. ------ 159187/17497080. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.((y y) y))) REDUCED to normal form. ------ 159188/17497131. ------ 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. ------ 159189/17497638. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 159190/17497746. ------ 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. ------ 159191/17497854. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 159192/17498133. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 159193/17498187. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(a (^z.z)))) REDUCED to normal form. ------ 159194/17498268. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.c)) 3. ==[ beta ]==> ((b (a (a a)))(^y.c)) 4. ==[ alpha ]==> ((b (a (a a)))(^x.c)) REDUCED to normal form. ------ 159195/17498367. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^a.(^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. ------ 159196/17498373. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b a)) 3. ==[ beta ]==> ((b a)((b a)(^y.y))) 4. ==[ alpha ]==> ((b a)((b a)(^x.x))) REDUCED to normal form. ------ 159197/17498523. ------ 1. ==[ start ]==> ((a b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a b)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a b)(b (^y.y))) 4. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 159198/17498541. ------ 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))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 159199/17498559. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 159200/17498577. ------ 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. ------ 159201/17498604. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 159202/17498739. ------ 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. ------ 159203/17498766. ------ 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))((^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. ------ 159204/17498793. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a b)((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. ------ 159205/17499072. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((((^y.y) b)(^z.(z z)))(((^y.y) b)(^z.(z z)))) 6. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) b)(^z.(z z)))) 9. ==[ beta ]==> ((b (^x.(x x)))(b (^z.(z z)))) 10. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 159206/17499099. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 159207/17499153. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 159208/17499180. ------ 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. ------ 159209/17499189. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 159210/17499207. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((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. ------ 159211/17499216. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 159212/17499261. ------ 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))(^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. ------ 159213/17499270. ------ 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. ------ 159214/17499288. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 159215/17499378. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((b b)((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((b b)((^x.x)((^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. ------ 159216/17499423. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 159217/17499513. ------ 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. ------ 159218/17499567. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 159219/17499594. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 159220/17499621. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 159221/17499675. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 159222/17499765. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b (b (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) a))(b (b (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 159223/17499792. ------ 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. ------ 159224/17499819. ------ 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. ------ 159225/17499846. ------ 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. ------ 159226/17500350. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.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. ------ 159227/17500368. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159228/17500512. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)((^y.y) b))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 159229/17500530. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 159230/17500539. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 159231/17500566. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.y))) REDUCED to normal form. ------ 159232/17500584. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((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) REDUCED to normal form. ------ 159233/17500620. ------ 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.(^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. ------ 159234/17500638. ------ 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. ------ 159235/17500647. ------ 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. ------ 159236/17500674. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 159237/17500728. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(^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. ------ 159238/17500917. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 159239/17500926. ------ 1. ==[ start ]==> (((a b)(a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 159240/17500953. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(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. ------ 159241/17500989. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(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. ------ 159242/17501268. ------ 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. ------ 159243/17501295. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))(b (^z.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))(b (^y.(a a)))) 7. ==[ beta ]==> ((b (^y.(a a)))(b (^y.(a a)))) 8. ==[ alpha ]==> ((b (^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 159244/17501340. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 159245/17501349. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 159246/17501376. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.b)(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. ------ 159247/17501565. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 159248/17501664. ------ 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)(^x1.(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. ------ 159249/17501808. ------ 1. ==[ start ]==> (((a b) c)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 159250/17501835. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 159251/17501862. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 159252/17501916. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 159253/17501997. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^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. ------ 159254/17502042. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 159255/17502141. ------ 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. ------ 159256/17502168. ------ 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)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(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 (^x.x))(a a))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((a a)((^y.y)(^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. ------ 159257/17502195. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a b)((a a) a))) 3. ==[ beta ]==> ((a (a b))((a b)((a a) a))) REDUCED to normal form. ------ 159258/17502222. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a) a)(a b))) REDUCED to normal form. ------ 159259/17502249. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1)(a a)))) 9. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a a))) 10. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a a))) 11. ==[ beta ]==> ((^y.y)((^z.z)(a a))) 12. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 13. ==[ beta ]==> ((^y.y)(a a)) 14. ==[ alpha ]==> ((^x.x)(a a)) 15. ==[ beta ]==> (a a) REDUCED to normal form. ------ 159260/17502276. ------ 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. ------ 159261/17502303. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a b) a)(((^y.y) a)(b a))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) a)(b a))) 5. ==[ beta ]==> (((a b) a)(a (b a))) REDUCED to normal form. ------ 159262/17502330. ------ 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. ------ 159263/17502357. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a) b)) REDUCED to normal form. ------ 159264/17502474. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (((a a)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 159265/17502555. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((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. ------ 159266/17502618. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 159267/17502663. ------ 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))))) REDUCED to normal form. ------ 159268/17502690. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 159269/17502726. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(^x1.x1))) 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. ------ 159270/17502744. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.(^z.z))) b)) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 159271/17502753. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 159272/17502807. ------ 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))(^y1.(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. ------ 159273/17502834. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 159274/17502861. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 159275/17503005. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 159276/17503032. ------ 1. ==[ start ]==> (((a (a a))(a b))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))(a ((^x.x) b))) 3. ==[ beta ]==> (((a (a a))(a b))(a b)) REDUCED to normal form. ------ 159277/17503059. ------ 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.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) 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))) REDUCED to normal form. ------ 159278/17503086. ------ 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)(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. ------ 159279/17503113. ------ 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))((^y.y) a))) 3. ==[ beta ]==> (((a b)(a (a a)))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 159280/17503140. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)(((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> (((a a) a)((a a)(a (a a)))) REDUCED to normal form. ------ 159281/17503167. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 159282/17503221. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 159283/17503392. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((b a)(^a.(^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. ------ 159284/17503527. ------ 1. ==[ start ]==> (((^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.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^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. ------ 159285/17503536. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 159286/17503554. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 159287/17503617. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(b 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. ------ 159288/17503644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159289/17503689. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a) b)) 3. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 159290/17503752. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 159291/17503923. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(b (b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(b (b a))) 3. ==[ beta ]==> (((a (a a))(a a))(b (b a))) REDUCED to normal form. ------ 159292/17503950. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a b))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(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. ------ 159293/17503977. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((b a)(a a))) REDUCED to normal form. ------ 159294/17504004. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 159295/17504031. ------ 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.z) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(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)))((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. ------ 159296/17504058. ------ 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 (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(a (a a)))) REDUCED to normal form. ------ 159297/17504112. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a) a)) REDUCED to normal form. ------ 159298/17504139. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (a a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))(a b))) 3. ==[ beta ]==> ((a b)((a (a a))(a b))) REDUCED to normal form. ------ 159299/17504310. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 159300/17504418. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159301/17504427. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a b)(a b))) REDUCED to normal form. ------ 159302/17504454. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.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. ------ 159303/17504472. ------ 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)))) REDUCED to normal form. ------ 159304/17504481. ------ 1. ==[ start ]==> (((a a)(^b.b))((^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)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 159305/17504508. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(b a)) REDUCED to normal form. ------ 159306/17504553. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 159307/17504589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 159308/17504616. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 159309/17504643. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 159310/17504670. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 159311/17504697. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 159312/17504814. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((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))) REDUCED to normal form. ------ 159313/17504841. ------ 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. ------ 159314/17504868. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a 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. ------ 159315/17504895. ------ 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. ------ 159316/17504922. ------ 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)(a a)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^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)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 13. ==[ beta ]==> ((a a)(^y.y)) 14. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 159317/17504949. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))((a a) a))) REDUCED to normal form. ------ 159318/17504976. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)(a b))) 3. ==[ beta ]==> (((a b)((a a) a))(a (a b))) REDUCED to normal form. ------ 159319/17505003. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 159320/17505030. ------ 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. ------ 159321/17505174. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 159322/17505309. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((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. ------ 159323/17505453. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((b b)((^y.a)(^y.a))) 6. ==[ alpha ]==> ((b b)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 159324/17505480. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 159325/17505534. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 159326/17505579. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a)) b)) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a)) b)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a)) b)) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 159327/17505723. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (^x1.b))) REDUCED to normal form. ------ 159328/17505777. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 159329/17505804. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 159330/17505831. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 159331/17506164. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c ((a a) a))) 3. ==[ beta ]==> ((b (a (^y.y)))(c ((a a) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c ((a a) a))) REDUCED to normal form. ------ 159332/17506191. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b (a b))) REDUCED to normal form. ------ 159333/17506218. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (a a))) REDUCED to normal form. ------ 159334/17506497. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^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. ------ 159335/17506533. ------ 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. ------ 159336/17506560. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 159337/17506605. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a a)(^z.b))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.b))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 159338/17506632. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((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. ------ 159339/17506668. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 159340/17506695. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^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. ------ 159341/17506776. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 159342/17506803. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.b)) REDUCED to normal form. ------ 159343/17506875. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159344/17507298. ------ 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 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. ------ 159345/17507325. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 159346/17507379. ------ 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. ------ 159347/17507550. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(^b.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. ------ 159348/17507658. ------ 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. ------ 159349/17507793. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 159350/17507820. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.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. ------ 159351/17507883. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 159352/17507910. ------ 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 z1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159353/17507955. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a))(^b.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. ------ 159354/17507964. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 159355/17507991. ------ 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. ------ 159356/17508018. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 159357/17508072. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^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. ------ 159358/17508099. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.(z z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 159359/17508180. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^b.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. ------ 159360/17508243. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c b)) REDUCED to normal form. ------ 159361/17508270. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b c)) 3. ==[ beta ]==> ((a ((a a)(a a)))(b c)) REDUCED to normal form. ------ 159362/17508351. ------ 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. ------ 159363/17508378. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a ((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 159364/17508405. ------ 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)(a a))((a (^y.y))(a a))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a a))) REDUCED to normal form. ------ 159365/17508432. ------ 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. ------ 159366/17508486. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b b)) REDUCED to normal form. ------ 159367/17508513. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a c)) 3. ==[ beta ]==> ((b (a (a a)))(a c)) REDUCED to normal form. ------ 159368/17508540. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (a a))) REDUCED to normal form. ------ 159369/17508594. ------ 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. ------ 159370/17508612. ------ 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 (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 159371/17508621. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b a)) REDUCED to normal form. ------ 159372/17508630. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> (((a a)(^z.z))(^y.y)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 159373/17508804. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159374/17510424. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 159375/17512629. ------ 1. ==[ start ]==> ((^a.(b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(y y)))) 3. ==[ eta ]==> (b (^y.(^z.(y y)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 159376/17516463. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159377/17518866. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^a.(^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. ------ 159378/17519055. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159379/17519058. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 159380/17519217. ------ 1. ==[ start ]==> ((^a.(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((b a)((a a) a))) 3. ==[ beta ]==> (^y.((b a)((a a) a))) 4. ==[ alpha ]==> (^x.((b a)((a a) a))) REDUCED to normal form. ------ 159381/17519460. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 159382/17519481. ------ 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) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 159383/17519886. ------ 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. ------ 159384/17520675. ------ 1. ==[ start ]==> ((^a.(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a a)(b (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 159385/17520678. ------ 1. ==[ start ]==> ((a (^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 159386/17520855. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))((a a) a)) b) 4. ==[ alpha ]==> (((^x.(^y.y))((a a) a)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159387/17521065. ------ 1. ==[ start ]==> (((a a)(^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 159388/17521461. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^a.(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. ------ 159389/17522124. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^z.a)(a (^x1.(^y1.y1))))((^z.a)(a (^x1.(^y1.y1)))))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)(a (^y.(^z.z))))((^x1.a)(a (^y1.(^z1.z1)))))(^x2.x2)) 5. ==[ beta ]==> ((a ((^x1.a)(a (^y1.(^z1.z1)))))(^x2.x2)) 6. ==[ alpha ]==> ((a ((^x.a)(a (^y.(^z.z)))))(^x1.x1)) 7. ==[ beta ]==> ((a a)(^x1.x1)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 159390/17522541. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (b (^z.((z z)(z z)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 159391/17522880. ------ 1. ==[ start ]==> ((^a.(b a))(a (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(a (^y.(a a)))) 3. ==[ eta ]==> (b (a (^y.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 159392/17522883. ------ 1. ==[ start ]==> ((a (b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 159393/17523531. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 159394/17524143. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159395/17524449. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 159396/17525634. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((((^y.b)((^z.z) a))((^y.b)((^z.z) a)))(((^y.b)((^z.z) a))((^y.b)((^z.z) a)))) 4. ==[ alpha ]==> ((((^x.b)((^y.y) a))((^z.b)((^x1.x1) a)))(((^y1.b)((^z1.z1) a))((^x2.b)((^y2.y2) a)))) 5. ==[ beta ]==> ((b ((^z.b)((^x1.x1) a)))(((^y1.b)((^z1.z1) a))((^x2.b)((^y2.y2) a)))) 6. ==[ alpha ]==> ((b ((^x.b)((^y.y) a)))(((^z.b)((^x1.x1) a))((^y1.b)((^z1.z1) a)))) 7. ==[ beta ]==> ((b b)(((^z.b)((^x1.x1) a))((^y1.b)((^z1.z1) a)))) 8. ==[ alpha ]==> ((b b)(((^x.b)((^y.y) a))((^z.b)((^x1.x1) a)))) 9. ==[ beta ]==> ((b b)(b ((^z.b)((^x1.x1) a)))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)((^y.y) a)))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 159397/17526501. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(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))(^x.(a a))) REDUCED to normal form. ------ 159398/17526714. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159399/17526717. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 159400/17527500. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 159401/17527662. ------ 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))) REDUCED to normal form. ------ 159402/17527824. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 159403/17527968. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.((^a.a)(^a.a)))) 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 ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159404/17528373. ------ 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. ------ 159405/17528490. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 159406/17528598. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.d)) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.d)) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.d)) REDUCED to normal form. ------ 159407/17528694. ------ 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))) REDUCED to normal form. ------ 159408/17528715. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 159409/17528796. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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)(^x.a)) REDUCED to normal form. ------ 159410/17528877. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 159411/17529012. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(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)))) REDUCED to normal form. ------ 159412/17529111. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.z)) 3. ==[ beta ]==> ((a (^y.y))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 159413/17529117. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^a.(^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. ------ 159414/17529120. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 159415/17529285. ------ 1. ==[ start ]==> (((^a.a)(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a a))(b ((^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. ------ 159416/17529312. ------ 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. ------ 159417/17529321. ------ 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 (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 159418/17529366. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 159419/17529393. ------ 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)(((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. ------ 159420/17529420. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^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. ------ 159421/17529447. ------ 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 (^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. ------ 159422/17529474. ------ 1. ==[ start ]==> ((a (^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.a))((b a)((a a) a))) REDUCED to normal form. ------ 159423/17529555. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.a)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.a)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 159424/17529582. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 159425/17529636. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.x) a)((a (a 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. ------ 159426/17529663. ------ 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) 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. ------ 159427/17529717. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a a)((^y.(^z.z)) 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. ------ 159428/17529735. ------ 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) a)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 159429/17529807. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a)(a a))(^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. ------ 159430/17529888. ------ 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. ------ 159431/17529915. ------ 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. ------ 159432/17529942. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 159433/17529969. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 159434/17530023. ------ 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. ------ 159435/17530059. ------ 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. ------ 159436/17530086. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 159437/17530113. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 159438/17530140. ------ 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. ------ 159439/17530464. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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))) 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. ------ 159440/17530491. ------ 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. ------ 159441/17530635. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)((^z1.z1) 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. ------ 159442/17530689. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((b a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (a ((b a)(^y.y))) 8. ==[ alpha ]==> (a ((b a)(^x.x))) REDUCED to normal form. ------ 159443/17530770. ------ 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. ------ 159444/17530797. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^y1.y1)))) 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. ------ 159445/17530851. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(a (^y.(^z.z))))) 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. ------ 159446/17530932. ------ 1. ==[ start ]==> ((a (^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a a)(b (^y.y)))) REDUCED to normal form. ------ 159447/17531031. ------ 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. ------ 159448/17531058. ------ 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.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 159449/17531103. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 159450/17531112. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 159451/17531265. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a)(^y.y))) 3. ==[ beta ]==> ((((a a) a) b)(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)(a (^x.x))) REDUCED to normal form. ------ 159452/17531292. ------ 1. ==[ start ]==> (((a b) a)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 159453/17531373. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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. ------ 159454/17531400. ------ 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. ------ 159455/17531517. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 159456/17531544. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) b) REDUCED to normal form. ------ 159457/17531625. ------ 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.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a ((^y.(y y))(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (a ((^x.(x x))(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 10. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 11. ==[ beta ]==> (a (^y.(^z.z))) 12. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 159458/17531652. ------ 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. ------ 159459/17531679. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 159460/17531715. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (b (^z.z)))) 3. ==[ beta ]==> ((^y.(a a))(a (b (^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))(a (b (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 159461/17531742. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((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. ------ 159462/17531796. ------ 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) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 159463/17531877. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> (b (((^x1.x1)(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. ------ 159464/17531931. ------ 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)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a 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. ------ 159465/17531958. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 159466/17532012. ------ 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) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.(^x1.x1))))) 11. ==[ beta ]==> (((^y.y) a)(a (^z.(^x1.x1)))) 12. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.z)))) 13. ==[ beta ]==> (a (a (^y.(^z.z)))) 14. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 159467/17532102. ------ 1. ==[ start ]==> (((a b)(^a.(^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. ------ 159468/17532129. ------ 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.(^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. ------ 159469/17532165. ------ 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)(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 159470/17532246. ------ 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. ------ 159471/17532273. ------ 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. ------ 159472/17532318. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 159473/17532327. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 159474/17532354. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(b a))) 5. ==[ beta ]==> (((a a)(a a))((b a)(b a))) REDUCED to normal form. ------ 159475/17532381. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 159476/17532795. ------ 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 (a ((a a)(a a)))) REDUCED to normal form. ------ 159477/17532804. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 159478/17532831. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b) 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)(^x.(^y.y))) b) REDUCED to normal form. ------ 159479/17533110. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 159480/17533137. ------ 1. ==[ start ]==> ((a (b a))(a (^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(a (^x.(a a)))) REDUCED to normal form. ------ 159481/17533371. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 159482/17533479. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b) a)) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b) a)) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b) a)) 5. ==[ beta ]==> ((a (^x.(a a)))(b a)) REDUCED to normal form. ------ 159483/17533506. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 159484/17533704. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(b a))(^y.y)) 6. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 159485/17533758. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 159486/17533785. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 159487/17533983. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159488/17534064. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.z))(b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.z))(b a))) 5. ==[ beta ]==> ((a a)((a (^z.z))(b a))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(b a))) REDUCED to normal form. ------ 159489/17534289. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.b)) 6. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 159490/17534397. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)((a a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159491/17534451. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a) b)) REDUCED to normal form. ------ 159492/17534595. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(^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. ------ 159493/17534622. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 159494/17534649. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 159495/17534703. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((^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. ------ 159496/17534901. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 159497/17534928. ------ 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)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1) a)((^x2.x2)(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. ------ 159498/17535180. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (a a))(^z.b))) REDUCED to normal form. ------ 159499/17535207. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> ((b a)(a (^y.(a a)))) 6. ==[ alpha ]==> ((b a)(a (^x.(a a)))) REDUCED to normal form. ------ 159500/17535234. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 159501/17535342. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(a a)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a)) c)) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a)) c)) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a)) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 159502/17535783. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 159503/17535864. ------ 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 a)) REDUCED to normal form. ------ 159504/17535891. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)((^y.y) a))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 159505/17536278. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 159506/17536332. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(a a))) 5. ==[ beta ]==> (((b a)(b a))((a a)(a a))) REDUCED to normal form. ------ 159507/17536395. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a) d)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a) d)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 159508/17536413. ------ 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. ------ 159509/17536521. ------ 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. ------ 159510/17536557. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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. ------ 159511/17536584. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 159512/17536647. ------ 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. ------ 159513/17536674. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.y1))) 10. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.x1))) 11. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 12. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 159514/17536701. ------ 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. ------ 159515/17536728. ------ 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.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 159516/17536755. ------ 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)(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. ------ 159517/17536782. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 159518/17536809. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 159519/17536890. ------ 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 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 159520/17536917. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 159521/17536944. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 159522/17536971. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 159523/17537061. ------ 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)(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))((^z2.z2) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))((^z2.z2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159524/17537142. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((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. ------ 159525/17537286. ------ 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. ------ 159526/17537313. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)(^b.(^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. ------ 159527/17537421. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((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. ------ 159528/17537520. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(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. ------ 159529/17537628. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159530/17537637. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1)) c)) 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. ------ 159531/17537754. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 159532/17537808. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 159533/17537835. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((^z.z) a))) 7. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 159534/17537862. ------ 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. ------ 159535/17537889. ------ 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.(^z.z))((^x1.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. ------ 159536/17537916. ------ 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. ------ 159537/17537943. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 159538/17537970. ------ 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.(^y1.y1)))) 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. ------ 159539/17538024. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 159540/17538051. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x) 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. ------ 159541/17538222. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((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))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 159542/17538303. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d c)) 3. ==[ beta ]==> (b (d c)) REDUCED to normal form. ------ 159543/17538528. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 159544/17538546. ------ 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. ------ 159545/17538573. ------ 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 (^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. ------ 159546/17538627. ------ 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. ------ 159547/17538663. ------ 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. ------ 159548/17538708. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c c)) 3. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 159549/17538717. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 159550/17538744. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 159551/17538771. ------ 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. ------ 159552/17538825. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1)) c)) REDUCED to normal form. ------ 159553/17538879. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 159554/17538951. ------ 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 (^x.(x (^y.y))))((a a) a)) REDUCED to normal form. ------ 159555/17538969. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 159556/17538996. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.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. ------ 159557/17539023. ------ 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 (^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. ------ 159558/17539050. ------ 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)) b)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)((^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. ------ 159559/17539077. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 159560/17539104. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 159561/17539131. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^b.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. ------ 159562/17539185. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 159563/17539239. ------ 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))(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. ------ 159564/17539266. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(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. ------ 159565/17539293. ------ 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)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 159566/17539347. ------ 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. ------ 159567/17539365. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 159568/17539374. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 159569/17539383. ------ 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 ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 159570/17539566. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159571/17549628. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.z)) 3. ==[ beta ]==> ((^z.z)((^z.z)(^y.y))) 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. ------ 159572/17549826. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159573/17549829. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 159574/17549838. ------ 1. ==[ start ]==> (((^a.a) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (b (^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (b (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 159575/17550330. ------ 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. ------ 159576/17550555. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(^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. ------ 159577/17550681. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^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. ------ 159578/17551626. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(^y.y))(^z.a)) b) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 159579/17551854. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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))) REDUCED to normal form. ------ 159580/17552013. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.a))((^z.(^x1.x1))(^y1.a)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a)))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(^x2.a)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.a)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.a))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.a))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159581/17552592. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 159582/17552895. ------ 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.(^z1.z1))))) 3. ==[ beta ]==> (((((^z.z) a)(^x1.(^y1.(^z1.z1))))(((^z.z) a)(^x1.(^y1.(^z1.z1)))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 5. ==[ beta ]==> (((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 6. ==[ alpha ]==> (((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.(^x2.x2)))))(^y2.y2)) 7. ==[ beta ]==> (((a (^x.(^y.(^z.z))))(a (^y1.(^z1.(^x2.x2)))))(^y2.y2)) 8. ==[ alpha ]==> (((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1)))))(^x2.x2)) REDUCED to normal form. ------ 159583/17553312. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 159584/17553321. ------ 1. ==[ start ]==> (((a b)(^b.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((y y)(y y)))) REDUCED to normal form. ------ 159585/17554200. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 159586/17555091. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159587/17556405. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)(^y.a))) 3. ==[ beta ]==> ((((a b)(^y.a))((a b)(^y.a)))(((a b)(^y.a))((a b)(^y.a)))) 4. ==[ alpha ]==> ((((a b)(^x.a))((a b)(^y.a)))(((a b)(^z.a))((a b)(^x1.a)))) REDUCED to normal form. ------ 159588/17556579. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^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. ------ 159589/17556831. ------ 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 y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 159590/17557047. ------ 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))(^x1.(a a))) REDUCED to normal form. ------ 159591/17557902. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(a z))) 3. ==[ eta ]==> (((^x.(^y.y))((a a)(a a))) a) 4. ==[ beta ]==> ((^y.y) a) 5. ==[ alpha ]==> ((^x.x) a) 6. ==[ beta ]==> a REDUCED to normal form. ------ 159592/17558433. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.a))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.a))) REDUCED to normal form. ------ 159593/17558646. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1)) b)) 3. ==[ eta ]==> ((^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. ------ 159594/17559045. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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 (^x.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 159595/17559153. ------ 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. ------ 159596/17559396. ------ 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. ------ 159597/17559465. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^b.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. ------ 159598/17559567. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^b.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. ------ 159599/17559648. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 159600/17559783. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^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. ------ 159601/17559888. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z) b)) 3. ==[ beta ]==> (((^z.z) b)(((^z.z) b)(^y.y))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (b (((^y.y) b)(^z.z))) 6. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 159602/17559891. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 159603/17559900. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(^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 ]==> ((^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. ------ 159604/17560074. ------ 1. ==[ start ]==> (((a a)(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 159605/17560092. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 159606/17560101. ------ 1. ==[ start ]==> (((^a.a) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) 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. ------ 159607/17560110. ------ 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. ------ 159608/17560128. ------ 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)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 159609/17560155. ------ 1. ==[ start ]==> (((a a) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a) b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 159610/17560182. ------ 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))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 159611/17560209. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 159612/17560236. ------ 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 (^x.x))(^y.y))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 159613/17560290. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((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. ------ 159614/17560371. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(b a))) REDUCED to normal form. ------ 159615/17560398. ------ 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)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 159616/17560425. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.a))((a (a a)) b)) REDUCED to normal form. ------ 159617/17560452. ------ 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) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a ((a a)(a a)))) REDUCED to normal form. ------ 159618/17560479. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 159619/17560542. ------ 1. ==[ start ]==> (((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.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. ------ 159620/17560569. ------ 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. ------ 159621/17560596. ------ 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. ------ 159622/17560632. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 159623/17560740. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(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. ------ 159624/17560821. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(^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)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 159625/17560839. ------ 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. ------ 159626/17560947. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^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) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 159627/17561037. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 159628/17561172. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 159629/17561505. ------ 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. ------ 159630/17561532. ------ 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. ------ 159631/17561586. ------ 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 a)(^x1.x1)))) REDUCED to normal form. ------ 159632/17561613. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(b a))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(b a))) 7. ==[ beta ]==> ((a (^x.(x x)))(b a)) REDUCED to normal form. ------ 159633/17561640. ------ 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. ------ 159634/17561667. ------ 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) a)((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159635/17561694. ------ 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. ------ 159636/17561757. ------ 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))(^z.z))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 159637/17561784. ------ 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. ------ 159638/17561811. ------ 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. ------ 159639/17561838. ------ 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 (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 159640/17561865. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 159641/17561892. ------ 1. ==[ start ]==> ((a (a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 159642/17561901. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159643/17562063. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 159644/17562090. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 159645/17562117. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 159646/17562279. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 159647/17562450. ------ 1. ==[ start ]==> (((^a.b) b)(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)(c ((^y.y) b))) 3. ==[ beta ]==> (b (c ((^y.y) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 159648/17562666. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(a a))((a a) a))) 3. ==[ beta ]==> (((a b) b)((a a)((a a) a))) REDUCED to normal form. ------ 159649/17562693. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a b)(a b))) 3. ==[ beta ]==> (((a a) a)((a b)(a b))) REDUCED to normal form. ------ 159650/17562720. ------ 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.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 159651/17562747. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(^z.z))) REDUCED to normal form. ------ 159652/17562801. ------ 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. ------ 159653/17562828. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.y))((^z.z) b))) 7. ==[ beta ]==> (((a (^y.y))((^z.z) b))((a (^y.y))((^z.z) b))) 8. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))((^x1.x1) b))) 9. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))((^x1.x1) b))) 10. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))((^z.z) b))) 11. ==[ beta ]==> (((a (^x.x)) b)((a (^y.y)) b)) REDUCED to normal form. ------ 159654/17562855. ------ 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. ------ 159655/17562945. ------ 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))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 159656/17562972. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b a)(^y.(y y)))) REDUCED to normal form. ------ 159657/17562999. ------ 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. ------ 159658/17563053. ------ 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. ------ 159659/17563080. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a 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. ------ 159660/17563107. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 159661/17563161. ------ 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.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 159662/17563197. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 159663/17563413. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 159664/17563530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(c (a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(c (a (^z.(^x1.x1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159665/17563557. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b ((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b b)) REDUCED to normal form. ------ 159666/17563575. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 159667/17563584. ------ 1. ==[ start ]==> (((a b)(^b.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 159668/17563611. ------ 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)(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(a a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 159669/17563638. ------ 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)))(a (^y1.y1)))) REDUCED to normal form. ------ 159670/17564088. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 159671/17564196. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(b a))) 3. ==[ beta ]==> ((b a)((^y.a)(b a))) 4. ==[ alpha ]==> ((b a)((^x.a)(b a))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 159672/17564223. ------ 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.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. ------ 159673/17564277. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 159674/17564358. ------ 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 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. ------ 159675/17564466. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 159676/17564592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.b) 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)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 159677/17564619. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 159678/17564745. ------ 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 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. ------ 159679/17564844. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(c (^d.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(c (^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(c (^z.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(c (^z.a))) 5. ==[ beta ]==> ((a a)(c (^z.a))) 6. ==[ alpha ]==> ((a a)(c (^x.a))) REDUCED to normal form. ------ 159680/17564925. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(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. ------ 159681/17565033. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 159682/17565087. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 159683/17565141. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.a)((a a)(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.a)((a a)(^y.y)))) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 159684/17565222. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.x2))) 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. ------ 159685/17565330. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 159686/17565357. ------ 1. ==[ start ]==> ((a (^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 159687/17565510. ------ 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))) 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. ------ 159688/17565636. ------ 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)(^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. ------ 159689/17565843. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 159690/17565951. ------ 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.(^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. ------ 159691/17566005. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.a)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 159692/17566032. ------ 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))((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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159693/17566167. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 159694/17566275. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^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. ------ 159695/17566311. ------ 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. ------ 159696/17566401. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(a a)) c)) 3. ==[ beta ]==> ((a (b a))((^y.(a a)) c)) 4. ==[ alpha ]==> ((a (b a))((^x.(a a)) c)) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 159697/17566617. ------ 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))) REDUCED to normal form. ------ 159698/17566644. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(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. ------ 159699/17566671. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a b)(^x.a))) REDUCED to normal form. ------ 159700/17566707. ------ 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. ------ 159701/17566842. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 159702/17566950. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159703/17567031. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 159704/17567058. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 159705/17567067. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b (a a))) REDUCED to normal form. ------ 159706/17567094. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 159707/17567175. ------ 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. ------ 159708/17567202. ------ 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. ------ 159709/17567256. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^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. ------ 159710/17567301. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(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. ------ 159711/17567310. ------ 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)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(a a))) REDUCED to normal form. ------ 159712/17567400. ------ 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. ------ 159713/17567427. ------ 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)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^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. ------ 159714/17567454. ------ 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. ------ 159715/17567481. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)(^c.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. ------ 159716/17567508. ------ 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 (^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 159717/17567535. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((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. ------ 159718/17567562. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a)) a)) 3. ==[ beta ]==> (((a b)(a b))((a a) a)) REDUCED to normal form. ------ 159719/17567589. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b) b)) 3. ==[ beta ]==> (((a a)((a a) a))((a b) b)) REDUCED to normal form. ------ 159720/17567922. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 159721/17568138. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^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. ------ 159722/17568165. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.z)(a b))) 3. ==[ beta ]==> ((^y.y)((^z.z)(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. ------ 159723/17568300. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 159724/17568309. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(c (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 159725/17568336. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))(b ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(b ((a a) a))) REDUCED to normal form. ------ 159726/17568417. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.x1))) REDUCED to normal form. ------ 159727/17568444. ------ 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. ------ 159728/17568471. ------ 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. ------ 159729/17568561. ------ 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. ------ 159730/17568588. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a b)(^y.(^z.z))) 10. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 159731/17568615. ------ 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. ------ 159732/17568642. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((b a)(a (^y.(y y)))) 8. ==[ alpha ]==> ((b a)(a (^x.(x x)))) REDUCED to normal form. ------ 159733/17568669. ------ 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 (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 159734/17568696. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 159735/17568723. ------ 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. ------ 159736/17568750. ------ 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))((^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. ------ 159737/17568912. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((a ((^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. ------ 159738/17569002. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.(^x1.x1)))) 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. ------ 159739/17569083. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(a (^y1.y1)))) 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. ------ 159740/17569191. ------ 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))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159741/17569308. ------ 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)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 159742/17569407. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b (^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b (^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b (^z.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(b (^z.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b (^y.(y y)))) 7. ==[ beta ]==> ((b b)(b (^y.(y y)))) 8. ==[ alpha ]==> ((b b)(b (^x.(x x)))) REDUCED to normal form. ------ 159743/17569416. ------ 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. ------ 159744/17569488. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.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. ------ 159745/17569497. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c c)) REDUCED to normal form. ------ 159746/17569596. ------ 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.(^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. ------ 159747/17569605. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (a (^y1.y1)))) REDUCED to normal form. ------ 159748/17569632. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(b ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(b a)) REDUCED to normal form. ------ 159749/17569659. ------ 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. ------ 159750/17569713. ------ 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 (^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. ------ 159751/17569731. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.a))) REDUCED to normal form. ------ 159752/17569776. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 159753/17569803. ------ 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. ------ 159754/17569830. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^b.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. ------ 159755/17569857. ------ 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) a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a) a)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 159756/17569884. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x)) b)) REDUCED to normal form. ------ 159757/17569911. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a) c)) REDUCED to normal form. ------ 159758/17569938. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a) a)) 5. ==[ beta ]==> (((a a)(a a))((^y.a) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.a) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 159759/17569965. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^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. ------ 159760/17570019. ------ 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))) REDUCED to normal form. ------ 159761/17570046. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)(^a.(^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. ------ 159762/17570073. ------ 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)) a)((a (^y.y)) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x)) a)) REDUCED to normal form. ------ 159763/17570127. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^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. ------ 159764/17570145. ------ 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. ------ 159765/17570154. ------ 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 (^x.x)))) b) REDUCED to normal form. ------ 159766/17570163. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (^a.(^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. ------ 159767/17574180. ------ 1. ==[ start ]==> ((^a.(b a))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((^z.z) b))) 3. ==[ eta ]==> (b (^y.((^z.z) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 159768/17580588. ------ 1. ==[ start ]==> ((^a.b)(c (b (^a.a)))) 2. ==[ alpha ]==> ((^x.b)(c (b (^y.y)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 159769/17580636. ------ 1. ==[ start ]==> (((^a.a) b)(^b.(^a.(a (^a.a))))) 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. ------ 159770/17580645. ------ 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. ------ 159771/17580669. ------ 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)) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(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. ------ 159772/17580858. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^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. ------ 159773/17581353. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159774/17581887. ------ 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. ------ 159775/17581911. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y))(a a))) 3. ==[ beta ]==> ((((b (^y.y))(a a))((b (^y.y))(a a)))((b (^y.y))(a a))) 4. ==[ alpha ]==> ((((b (^x.x))(a a))((b (^y.y))(a a)))((b (^z.z))(a a))) REDUCED to normal form. ------ 159776/17583018. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((b ((a a)(a a)))(b ((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)((b ((a a)(a a)))(b ((a a)(a a))))) 5. ==[ beta ]==> ((b ((a a)(a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 159777/17584119. ------ 1. ==[ start ]==> (((a b)(^b.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 159778/17584449. ------ 1. ==[ start ]==> ((^a.(b a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))((a a)((^y.y) b))) 3. ==[ eta ]==> (b ((a a)((^y.y) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 159779/17584452. ------ 1. ==[ start ]==> ((a (b a))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))(^x.((^y.y) b))) 3. ==[ beta ]==> ((a (b a))(^x.b)) REDUCED to normal form. ------ 159780/17584794. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(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. ------ 159781/17585127. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a a) a)(^y.((^z.z) b))) 6. ==[ alpha ]==> (((a a) a)(^x.((^y.y) b))) 7. ==[ beta ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 159782/17585286. ------ 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 ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 159783/17586045. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 159784/17586204. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159785/17586882. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^a.(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(b y))) 3. ==[ eta ]==> (((a a)((^x.x) b)) b) 4. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 159786/17587377. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 159787/17587629. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 159788/17587872. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^a.(^c.(^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. ------ 159789/17588283. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b (a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b (a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159790/17589069. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 159791/17589444. ------ 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. ------ 159792/17589843. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(^b.(^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. ------ 159793/17589978. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159794/17590086. ------ 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. ------ 159795/17590194. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 159796/17590473. ------ 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.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))((^y.y)(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. ------ 159797/17590662. ------ 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. ------ 159798/17590686. ------ 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. ------ 159799/17590698. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^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 ]==> ((^z.z)(^y.y)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159800/17590863. ------ 1. ==[ start ]==> ((a b)(c (b (^a.a)))) 2. ==[ alpha ]==> ((a b)(c (b (^x.x)))) REDUCED to normal form. ------ 159801/17590908. ------ 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. ------ 159802/17590917. ------ 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. ------ 159803/17590944. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((a (a (^x.x)))((^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. ------ 159804/17591079. ------ 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. ------ 159805/17591106. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 159806/17591133. ------ 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)(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(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. ------ 159807/17591322. ------ 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. ------ 159808/17591412. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.a))) 5. ==[ beta ]==> ((((a a)(a a))(^y.a))(((a a)(a a))(^y.a))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 159809/17591439. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(y1 y1)))) 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. ------ 159810/17591475. ------ 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. ------ 159811/17591493. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b a)(^z.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. ------ 159812/17591520. ------ 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. ------ 159813/17591547. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(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. ------ 159814/17591556. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 159815/17591583. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 159816/17591628. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^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))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 159817/17591718. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 159818/17591763. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^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. ------ 159819/17591790. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((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. ------ 159820/17591853. ------ 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. ------ 159821/17591880. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 159822/17591961. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 159823/17591988. ------ 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. ------ 159824/17592132. ------ 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. ------ 159825/17592159. ------ 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. ------ 159826/17592186. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(a a))) REDUCED to normal form. ------ 159827/17592222. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a)) c)) 3. ==[ beta ]==> ((^y.y)((^y1.(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. ------ 159828/17592537. ------ 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. ------ 159829/17592708. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 159830/17592852. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a) b)((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a) b)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 159831/17592870. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 159832/17592879. ------ 1. ==[ start ]==> (((a b) a)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) a)((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 159833/17592897. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a b)((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 159834/17592906. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 159835/17592978. ------ 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. ------ 159836/17593014. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(^y1.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. ------ 159837/17593041. ------ 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.(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. ------ 159838/17593257. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 159839/17593266. ------ 1. ==[ start ]==> (((a b)(a a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))(c ((^x.x) b))) 3. ==[ beta ]==> (((a b)(a a))(c b)) REDUCED to normal form. ------ 159840/17593293. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 159841/17593383. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1) c)) 5. ==[ beta ]==> ((^y.y)((^y1.y1) 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. ------ 159842/17593662. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.(a a)))) REDUCED to normal form. ------ 159843/17593905. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 159844/17594004. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((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. ------ 159845/17594148. ------ 1. ==[ start ]==> (((a b) c)((^d.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(y y)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 159846/17594175. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 159847/17594202. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 159848/17594256. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 159849/17594283. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 159850/17594337. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159851/17594364. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(^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. ------ 159852/17594391. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(a a))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 159853/17594481. ------ 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) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((b a) a)) REDUCED to normal form. ------ 159854/17594508. ------ 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)(^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)))) REDUCED to normal form. ------ 159855/17594535. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a b))((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (a b))((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (a b))((a a)(^y.y))) 8. ==[ alpha ]==> ((a (a b))((a a)(^x.x))) REDUCED to normal form. ------ 159856/17594562. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a b)((a a) a))) REDUCED to normal form. ------ 159857/17594589. ------ 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. ------ 159858/17594616. ------ 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. ------ 159859/17594643. ------ 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. ------ 159860/17594670. ------ 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. ------ 159861/17594697. ------ 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))))) REDUCED to normal form. ------ 159862/17594724. ------ 1. ==[ start ]==> ((a (b a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))((a a)((^x.x) b))) 3. ==[ beta ]==> ((a (b a))((a a) b)) REDUCED to normal form. ------ 159863/17594814. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(^z.a))) 5. ==[ beta ]==> (b ((b a)(^z.a))) 6. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 159864/17594895. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a b)(^z.a))) 3. ==[ beta ]==> (b ((a b)(^z.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 159865/17594958. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))((^x1.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. ------ 159866/17595030. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 159867/17595066. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 159868/17595084. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b) a)) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b) a)) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b) a)) 5. ==[ beta ]==> (((a b)(a b))(b a)) REDUCED to normal form. ------ 159869/17595093. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b)(^a.a))) 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. ------ 159870/17595174. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 159871/17595201. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 159872/17595228. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 159873/17595372. ------ 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. ------ 159874/17595399. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(a ((^z.z) b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(a ((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(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. ------ 159875/17595426. ------ 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 (^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. ------ 159876/17595453. ------ 1. ==[ start ]==> (((a b)(a (a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((b a)(a (^x.x)))) REDUCED to normal form. ------ 159877/17595480. ------ 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) a))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)(((a a)(^y.y))((^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. ------ 159878/17595507. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 159879/17595561. ------ 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))) REDUCED to normal form. ------ 159880/17595732. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 159881/17595840. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 159882/17595849. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 159883/17595894. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 159884/17595957. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 159885/17595984. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 159886/17596029. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 159887/17596038. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^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. ------ 159888/17596092. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.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. ------ 159889/17596146. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 159890/17596290. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(b (b a))) 3. ==[ beta ]==> (((^y.y)(a b))(b (b a))) 4. ==[ alpha ]==> (((^x.x)(a b))(b (b a))) 5. ==[ beta ]==> ((a b)(b (b a))) REDUCED to normal form. ------ 159891/17596317. ------ 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. ------ 159892/17596344. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((b a)(a a))) 3. ==[ beta ]==> (((a b)(^y.y))((b a)(a a))) 4. ==[ alpha ]==> (((a b)(^x.x))((b a)(a a))) REDUCED to normal form. ------ 159893/17596371. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 159894/17596398. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))((^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. ------ 159895/17596452. ------ 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)(^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. ------ 159896/17596479. ------ 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 b)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^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. ------ 159897/17596650. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 159898/17596767. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 159899/17596794. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))(a b))) 3. ==[ beta ]==> ((b a)((^y.(y y))(a b))) 4. ==[ alpha ]==> ((b a)((^x.(x x))(a b))) 5. ==[ beta ]==> ((b a)((a b)(a b))) REDUCED to normal form. ------ 159900/17596812. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 7. ==[ beta ]==> (b (a (^y.(a a)))) 8. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 159901/17596821. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 159902/17596848. ------ 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))((a a)(^x2.x2)))) 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. ------ 159903/17596893. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a) a)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a) a)) REDUCED to normal form. ------ 159904/17596929. ------ 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.(^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 a) REDUCED to normal form. ------ 159905/17596956. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(a a))(^b.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. ------ 159906/17596983. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 159907/17597010. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.a)(^b.(^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. ------ 159908/17597037. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.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. ------ 159909/17597091. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 159910/17597118. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.a))(^c.(^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. ------ 159911/17597154. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(a (b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(a (b a))) 3. ==[ beta ]==> (((a a) b)(a (b a))) REDUCED to normal form. ------ 159912/17597181. ------ 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.x1))(a a))) REDUCED to normal form. ------ 159913/17597208. ------ 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. ------ 159914/17597235. ------ 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.y) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a b) a)) REDUCED to normal form. ------ 159915/17597262. ------ 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. ------ 159916/17597289. ------ 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. ------ 159917/17597316. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))((a a) a))) REDUCED to normal form. ------ 159918/17597343. ------ 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)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 159919/17597370. ------ 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)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a (^y.y))(a a))) REDUCED to normal form. ------ 159920/17597514. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 159921/17597649. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a a)(^c.(^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. ------ 159922/17597793. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))(^b.(^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. ------ 159923/17597874. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.a))(^b.(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. ------ 159924/17597919. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 159925/17598000. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a) d)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a) d)) 3. ==[ beta ]==> (b ((^y.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 159926/17598117. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b (^x1.(a a)))) REDUCED to normal form. ------ 159927/17598144. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(a (^c.(^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. ------ 159928/17598171. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 159929/17598558. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b (a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b (a b))) REDUCED to normal form. ------ 159930/17598837. ------ 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.(^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. ------ 159931/17598873. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 159932/17598900. ------ 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. ------ 159933/17598945. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 159934/17598972. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 159935/17599008. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 159936/17599026. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a) a) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a) a) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a) b)) REDUCED to normal form. ------ 159937/17599116. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 159938/17599143. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 159939/17599341. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 159940/17599638. ------ 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. ------ 159941/17599665. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 159942/17599719. ------ 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. ------ 159943/17599890. ------ 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. ------ 159944/17599998. ------ 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)(^x2.x2)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159945/17600115. ------ 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)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 159946/17600133. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 159947/17600160. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1)) 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. ------ 159948/17600223. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 159949/17600250. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159950/17600295. ------ 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.(^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. ------ 159951/17600304. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.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. ------ 159952/17600331. ------ 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))((^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. ------ 159953/17600358. ------ 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. ------ 159954/17600403. ------ 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. ------ 159955/17600412. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 159956/17600439. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^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. ------ 159957/17600466. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.(z z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(y y))) REDUCED to normal form. ------ 159958/17600556. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 159959/17600637. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b c)) 3. ==[ beta ]==> (((a (a a)) b)(b c)) REDUCED to normal form. ------ 159960/17600691. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (a a))) REDUCED to normal form. ------ 159961/17600718. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 159962/17600745. ------ 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.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)(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. ------ 159963/17600772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(a a))) REDUCED to normal form. ------ 159964/17600853. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b b)) 3. ==[ beta ]==> ((b (a (a a)))(b b)) REDUCED to normal form. ------ 159965/17600934. ------ 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. ------ 159966/17600952. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (^z.z))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 159967/17600961. ------ 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. ------ 159968/17600970. ------ 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 ]==> (((^z.z) b)(^y.y)) 6. ==[ alpha ]==> (((^x.x) b)(^y.y)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159969/17601077. ------ 1. ==[ start ]==> (^a.((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 159970/17601078. ------ 1. ==[ start ]==> (a ((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 159971/17602026. ------ 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)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159972/17611359. ------ 1. ==[ start ]==> ((^a.a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^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. ------ 159973/17611449. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 159974/17611470. ------ 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. ------ 159975/17611611. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((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 ]==> (^x.((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> (^x.((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 159976/17611854. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 159977/17611902. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 159978/17612304. ------ 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)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 159979/17612307. ------ 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 (^y.y))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 159980/17613069. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 159981/17613882. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^a.(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. ------ 159982/17614233. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 159983/17614518. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((^z.(z z))(b a))((^z.(z z))(b a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))(b a))((^y.(y y))(b a)))(^z.z)) 5. ==[ beta ]==> ((((b a)(b a))((^y.(y y))(b a)))(^z.z)) 6. ==[ alpha ]==> ((((b a)(b a))((^x.(x x))(b a)))(^y.y)) 7. ==[ beta ]==> ((((b a)(b a))((b a)(b a)))(^y.y)) 8. ==[ alpha ]==> ((((b a)(b a))((b a)(b a)))(^x.x)) REDUCED to normal form. ------ 159984/17615274. ------ 1. ==[ start ]==> ((^a.(b a))(b (^b.b))) 2. ==[ alpha ]==> ((^x.(b x))(b (^y.y))) 3. ==[ eta ]==> (b (b (^y.y))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 159985/17615619. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 159986/17615952. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(^b.b))) 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. ------ 159987/17616870. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 159988/17618028. ------ 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 a)((^z.(a a))(a (^x1.x1))))(((^y1.(a a))(a (^z1.z1)))((^x2.(a a))(a (^y2.y2))))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(a (^y.y))))(((^z.(a a))(a (^x1.x1)))((^y1.(a a))(a (^z1.z1))))) 7. ==[ beta ]==> (((a a)(a a))(((^z.(a a))(a (^x1.x1)))((^y1.(a a))(a (^z1.z1))))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(a (^y.y)))((^z.(a a))(a (^x1.x1))))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^z.(a a))(a (^x1.x1))))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(a (^y.y))))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 159989/17618472. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.((y y)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 159990/17618922. ------ 1. ==[ start ]==> (((a b)(a b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^x.(a a))) REDUCED to normal form. ------ 159991/17619108. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 159992/17619921. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 159993/17620083. ------ 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))) REDUCED to normal form. ------ 159994/17620686. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)(^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. ------ 159995/17620911. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 159996/17621019. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.d)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.d)) REDUCED to normal form. ------ 159997/17621088. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 159998/17621136. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 159999/17621217. ------ 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.((^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 (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 160000/17621298. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.(^b.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. ------ 160001/17621379. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(^b.a))) 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. ------ 160002/17621433. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(a (^y.y)))) REDUCED to normal form. ------ 160003/17621487. ------ 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 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. ------ 160004/17621511. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (^z.z))) 3. ==[ beta ]==> ((b (^z.z))((b (^z.z))(^y.y))) 4. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 160005/17621643. ------ 1. ==[ start ]==> ((a a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 160006/17621733. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 160007/17621751. ------ 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. ------ 160008/17621769. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 160009/17621787. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160010/17621814. ------ 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)((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. ------ 160011/17621841. ------ 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) 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. ------ 160012/17621868. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 160013/17621895. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.a))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 160014/17621976. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 160015/17622003. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 160016/17622057. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 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. ------ 160017/17622084. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) 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. ------ 160018/17622138. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 160019/17622183. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 160020/17622228. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((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. ------ 160021/17622309. ------ 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. ------ 160022/17622336. ------ 1. ==[ start ]==> (((a (a a)) a)((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a)) a)((b a)(^x.a))) REDUCED to normal form. ------ 160023/17622363. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 160024/17622390. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(^z.(a a)))) REDUCED to normal form. ------ 160025/17622417. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 160026/17622480. ------ 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. ------ 160027/17622507. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> (((a (^x.x)) a)(b ((^z.z) b))) 8. ==[ alpha ]==> (((a (^x.x)) a)(b ((^y.y) b))) 9. ==[ beta ]==> (((a (^x.x)) a)(b b)) REDUCED to normal form. ------ 160028/17622534. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 160029/17622561. ------ 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. ------ 160030/17622588. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.x))((^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. ------ 160031/17622885. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 160032/17622912. ------ 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. ------ 160033/17622939. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 160034/17623056. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^y1.y1)))) 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. ------ 160035/17623110. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.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)))) REDUCED to normal form. ------ 160036/17623191. ------ 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. ------ 160037/17623218. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^y1.y1)(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. ------ 160038/17623272. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(b a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(b a))) 9. ==[ beta ]==> ((a a)((^y.y)(b a))) 10. ==[ alpha ]==> ((a a)((^x.x)(b a))) 11. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 160039/17623353. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 160040/17623479. ------ 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) 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. ------ 160041/17623506. ------ 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. ------ 160042/17623524. ------ 1. ==[ start ]==> (((^a.b) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 160043/17623686. ------ 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. ------ 160044/17623713. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a)(^b.b))) 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. ------ 160045/17623740. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 160046/17623794. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 160047/17623821. ------ 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. ------ 160048/17623848. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b) c)) 5. ==[ beta ]==> ((^y.a)(((^z.z) b) c)) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 160049/17623938. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 160050/17623965. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 160051/17623992. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 160052/17624073. ------ 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. ------ 160053/17624100. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 160054/17624136. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(b ((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160055/17624163. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(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. ------ 160056/17624217. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 8. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 9. ==[ beta ]==> (b (a (^y.y))) 10. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 160057/17624298. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 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. ------ 160058/17624352. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)(a b))) 5. ==[ beta ]==> ((a a)((a b)(a b))) REDUCED to normal form. ------ 160059/17624379. ------ 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.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. ------ 160060/17624433. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (a a))(b a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (a a))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (a a))(b a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))(b a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(b a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(b a))) 9. ==[ beta ]==> ((^y.y)((a (a a))(b a))) 10. ==[ alpha ]==> ((^x.x)((a (a a))(b a))) 11. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 160061/17624514. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 160062/17624550. ------ 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. ------ 160063/17624586. ------ 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)(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. ------ 160064/17624613. ------ 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) 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. ------ 160065/17624694. ------ 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. ------ 160066/17624721. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.b)(a b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.b)(a b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.b)(a b))) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 160067/17624739. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 160068/17624748. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 160069/17624775. ------ 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 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. ------ 160070/17624802. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(b a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((b a)(b a))) REDUCED to normal form. ------ 160071/17624982. ------ 1. ==[ start ]==> (((a b) c)((b a) d)) REDUCED to normal form. ------ 160072/17625216. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b ((^z.z) b))) 3. ==[ beta ]==> (b (b ((^z.z) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 160073/17625279. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b) 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. ------ 160074/17625558. ------ 1. ==[ start ]==> ((a (b a))(b (^b.b))) 2. ==[ alpha ]==> ((a (b a))(b (^x.x))) REDUCED to normal form. ------ 160075/17625792. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(a a))) REDUCED to normal form. ------ 160076/17625900. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)(^b.b))) 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. ------ 160077/17625927. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) b) a)) 3. ==[ beta ]==> (((a (a a))(^x.b))(b a)) REDUCED to normal form. ------ 160078/17625981. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((b a) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a) c)) REDUCED to normal form. ------ 160079/17626125. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 160080/17626206. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 160081/17626233. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(^b.b))) 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))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 160082/17626404. ------ 1. ==[ start ]==> (((^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) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)((a a) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160083/17626485. ------ 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)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x) 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. ------ 160084/17626683. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 160085/17626791. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 160086/17626872. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 160087/17626899. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((b a) b)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a) b)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a) b)) REDUCED to normal form. ------ 160088/17626926. ------ 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. ------ 160089/17627043. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 160090/17627070. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 160091/17627097. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(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. ------ 160092/17627151. ------ 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.(^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. ------ 160093/17627322. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^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 ]==> (((^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. ------ 160094/17627349. ------ 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))(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. ------ 160095/17627601. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.a)) REDUCED to normal form. ------ 160096/17627628. ------ 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. ------ 160097/17627655. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 160098/17627763. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z)) b)) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z)) b)) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y)) b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160099/17627790. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a a) c)) REDUCED to normal form. ------ 160100/17627817. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b) d)) 2. ==[ alpha ]==> (((a b)(^x.a))((a b) d)) REDUCED to normal form. ------ 160101/17628285. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^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))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 160102/17628312. ------ 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 a)) REDUCED to normal form. ------ 160103/17628699. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c (a b))) 3. ==[ beta ]==> ((^y.y)(c (a b))) 4. ==[ alpha ]==> ((^x.x)(c (a b))) 5. ==[ beta ]==> (c (a b)) REDUCED to normal form. ------ 160104/17628753. ------ 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 a)(b a))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 160105/17628816. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 160106/17628834. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (b (((a a) a)((^y.y) a))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x) a))) 5. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 160107/17628843. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a) d)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a) d)) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 160108/17628942. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((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. ------ 160109/17629005. ------ 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. ------ 160110/17629041. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 160111/17629068. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 160112/17629095. ------ 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. ------ 160113/17629122. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(b a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a))(b a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 10. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 160114/17629149. ------ 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)))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 160115/17629176. ------ 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.z))(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 160116/17629203. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(a a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(a a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 160117/17629230. ------ 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))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 160118/17629257. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 160119/17629311. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 160120/17629338. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 160121/17629365. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 160122/17629392. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^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. ------ 160123/17629482. ------ 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. ------ 160124/17629563. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^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. ------ 160125/17629707. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((b c)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b c)((^x.x)(^y.a))) 7. ==[ beta ]==> ((b c)(^y.a)) 8. ==[ alpha ]==> ((b c)(^x.a)) REDUCED to normal form. ------ 160126/17629734. ------ 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. ------ 160127/17629842. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b) a)) 3. ==[ beta ]==> ((a (^y.y))((a b) a)) 4. ==[ alpha ]==> ((a (^x.x))((a b) a)) REDUCED to normal form. ------ 160128/17629869. ------ 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. ------ 160129/17630049. ------ 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. ------ 160130/17630085. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 160131/17630175. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 160132/17630202. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.b))) REDUCED to normal form. ------ 160133/17630229. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.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) REDUCED to normal form. ------ 160134/17630256. ------ 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 (^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. ------ 160135/17630283. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((b a)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((b a)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((b a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((b a)(a ((^x.x) a))) 11. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 160136/17630310. ------ 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. ------ 160137/17630337. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 160138/17630364. ------ 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. ------ 160139/17630445. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 160140/17630472. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x) 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. ------ 160141/17630499. ------ 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.(^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. ------ 160142/17630643. ------ 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. ------ 160143/17630967. ------ 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)(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. ------ 160144/17630994. ------ 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. ------ 160145/17631048. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b b)((a (^y.y))((^z.z) a))) 8. ==[ alpha ]==> ((b b)((a (^x.x))((^y.y) a))) 9. ==[ beta ]==> ((b b)((a (^x.x)) a)) REDUCED to normal form. ------ 160146/17631138. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(^a.(^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. ------ 160147/17631165. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a))(^b.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. ------ 160148/17631192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.(z z)))) REDUCED to normal form. ------ 160149/17631246. ------ 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. ------ 160150/17631273. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y)) c)) REDUCED to normal form. ------ 160151/17631354. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 160152/17631372. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 160153/17631390. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^b.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. ------ 160154/17631417. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 160155/17631444. ------ 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))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 160156/17631471. ------ 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 (^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. ------ 160157/17631498. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 160158/17631525. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.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. ------ 160159/17631552. ------ 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))(^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. ------ 160160/17631579. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 160161/17631606. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.y))) REDUCED to normal form. ------ 160162/17631660. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a (^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.a))) REDUCED to normal form. ------ 160163/17631687. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^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. ------ 160164/17631714. ------ 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)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(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. ------ 160165/17631768. ------ 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 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. ------ 160166/17631786. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^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. ------ 160167/17631795. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.y))) REDUCED to normal form. ------ 160168/17631804. ------ 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. ------ 160169/17642220. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160170/17642340. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 160171/17642346. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((^z.(z (^x1.x1))) a)(^y.y)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.z)) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 160172/17642805. ------ 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. ------ 160173/17643030. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160174/17643168. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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. ------ 160175/17643921. ------ 1. ==[ start ]==> ((^a.(^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(c (^z.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 160176/17644101. ------ 1. ==[ start ]==> ((^a.(a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(^y.(^z.z))) b) 4. ==[ alpha ]==> (((b a)(^x.(^y.y))) b) REDUCED to normal form. ------ 160177/17645094. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 160178/17645823. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 160179/17646489. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.(x x))(a b))(^z.z)) 4. ==[ alpha ]==> (((^x.(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. ------ 160180/17647137. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (b (^x1.(^y1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 160181/17647434. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 160182/17647566. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160183/17648298. ------ 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))) REDUCED to normal form. ------ 160184/17648880. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((((^y.y)(a a))(^z.(^x1.x1)))(((^y.y)(a a))(^z.(^x1.x1))))((((^y.y)(a a))(^z.(^x1.x1)))(((^y.y)(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1))))((((^x2.x2)(a a))(^y2.(^z2.z2)))(((^x3.x3)(a a))(^y3.(^z3.z3))))) 5. ==[ beta ]==> ((((a a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1))))((((^x2.x2)(a a))(^y2.(^z2.z2)))(((^x3.x3)(a a))(^y3.(^z3.z3))))) 6. ==[ alpha ]==> ((((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1))))((((^z1.z1)(a a))(^x2.(^y2.y2)))(((^z2.z2)(a a))(^x3.(^y3.y3))))) 7. ==[ beta ]==> ((((a a)(^x.(^y.y)))((a a)(^x1.(^y1.y1))))((((^z1.z1)(a a))(^x2.(^y2.y2)))(((^z2.z2)(a a))(^x3.(^y3.y3))))) 8. ==[ alpha ]==> ((((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))((((^y1.y1)(a a))(^z1.(^x2.x2)))(((^y2.y2)(a a))(^z2.(^x3.x3))))) 9. ==[ beta ]==> ((((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))(((a a)(^z1.(^x2.x2)))(((^y2.y2)(a a))(^z2.(^x3.x3))))) 10. ==[ alpha ]==> ((((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))(((a a)(^y1.(^z1.z1)))(((^x2.x2)(a a))(^y2.(^z2.z2))))) 11. ==[ beta ]==> ((((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))(((a a)(^y1.(^z1.z1)))((a a)(^y2.(^z2.z2))))) 12. ==[ 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. ------ 160185/17649324. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 160186/17649549. ------ 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)))(^z.(a a))) REDUCED to normal form. ------ 160187/17649774. ------ 1. ==[ start ]==> (((a b)(a b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 160188/17650935. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 160189/17651403. ------ 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)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160190/17651538. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(^b.(^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)(^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. ------ 160191/17652231. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.c)) REDUCED to normal form. ------ 160192/17652357. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^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. ------ 160193/17652363. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^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. ------ 160194/17652513. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 160195/17652603. ------ 1. ==[ start ]==> (((^a.a) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) b)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (b (b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (b (b ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 160196/17652630. ------ 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)(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. ------ 160197/17652639. ------ 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)))(a (^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 160198/17652657. ------ 1. ==[ start ]==> (((a a) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a) b)(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a a) b)((^y.y)(a a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(a a))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 160199/17652684. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 160200/17652711. ------ 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)(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 160201/17652738. ------ 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 (^x.x))(^y.y))(b (a (a a)))) REDUCED to normal form. ------ 160202/17652792. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 160203/17652873. ------ 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. ------ 160204/17652900. ------ 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. ------ 160205/17652927. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.a))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 160206/17652954. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 160207/17652981. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 160208/17653071. ------ 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. ------ 160209/17653098. ------ 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. ------ 160210/17653134. ------ 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) 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. ------ 160211/17653188. ------ 1. ==[ start ]==> (((^a.(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)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160212/17653296. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 160213/17653323. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 160214/17653341. ------ 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. ------ 160215/17653368. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a (a a))(^b.b))) 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. ------ 160216/17653458. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160217/17653593. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 160218/17653674. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 160219/17654007. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((b a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((b a)(^y.y))) 8. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 160220/17654034. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 160221/17654088. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a b)(a a))) REDUCED to normal form. ------ 160222/17654115. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 160223/17654142. ------ 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. ------ 160224/17654169. ------ 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.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160225/17654196. ------ 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. ------ 160226/17654214. ------ 1. ==[ start ]==> ((a (^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(c (^y.(a a)))) REDUCED to normal form. ------ 160227/17654286. ------ 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. ------ 160228/17654313. ------ 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. ------ 160229/17654340. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.a))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 160230/17654367. ------ 1. ==[ start ]==> ((((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 z)))) REDUCED to normal form. ------ 160231/17654394. ------ 1. ==[ start ]==> ((a (a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 160232/17654484. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)((^x1.x1)(a a)))) IRREDUCIBLE: cycle. ------ 160233/17654565. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 160234/17654592. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a b)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a b)((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 160235/17654619. ------ 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))((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. ------ 160236/17654754. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 160237/17654997. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160238/17655168. ------ 1. ==[ start ]==> (((a b) b)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) b)(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 160239/17655195. ------ 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. ------ 160240/17655222. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)(a b))) REDUCED to normal form. ------ 160241/17655249. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(((a a) a)(a a))) REDUCED to normal form. ------ 160242/17655303. ------ 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. ------ 160243/17655330. ------ 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) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((((^y.y) a)(a (^z.(^x1.x1))))(((^y.y) a)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 9. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(a (^x1.(^y1.y1))))) 11. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (a (^x1.(^y1.y1))))) 12. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 160244/17655357. ------ 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 (^y.y)) b)) REDUCED to normal form. ------ 160245/17655375. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 160246/17655384. ------ 1. ==[ start ]==> (((a b)(^a.(^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. ------ 160247/17655447. ------ 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)(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. ------ 160248/17655474. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 160249/17655501. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a) a))((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((a ((a a) a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 160250/17655528. ------ 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. ------ 160251/17655582. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a b)(^y.b))) 3. ==[ beta ]==> ((((a a) a) a)((a b)(^y.b))) 4. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.b))) REDUCED to normal form. ------ 160252/17655609. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 160253/17655699. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.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 REDUCED to normal form. ------ 160254/17655834. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 160255/17655915. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 160256/17655942. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 160257/17655996. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(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)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 160258/17656077. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 160259/17656086. ------ 1. ==[ start ]==> (((a b)(^b.a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.a))(b b)) REDUCED to normal form. ------ 160260/17656113. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 160261/17656140. ------ 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))(^y.y))(b (a a))) REDUCED to normal form. ------ 160262/17656509. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 160263/17656590. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 160264/17656698. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> ((b a)((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b a)((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> ((b a)(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> ((b a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 160265/17656725. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 160266/17656779. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)((^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. ------ 160267/17657121. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 160268/17657148. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.(^z.z))) b)) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 160269/17657247. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((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. ------ 160270/17657427. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> (b (a (^x1.x1))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 160271/17657535. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 160272/17657562. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 160273/17657589. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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 REDUCED to normal form. ------ 160274/17657643. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(y y))((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((^y.y)(a a)))) 9. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))((^y.y)(a a)))) 10. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((^y.y)(a a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(a a)))) 12. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(a a)))) 13. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 160275/17657724. ------ 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 ((^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. ------ 160276/17657832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 160277/17657859. ------ 1. ==[ start ]==> ((a (^b.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 160278/17658039. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 160279/17658138. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 160280/17658345. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 160281/17658507. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(a b))) 5. ==[ beta ]==> (b ((^y.(y y))(a b))) 6. ==[ alpha ]==> (b ((^x.(x x))(a b))) 7. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 160282/17658534. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)((^z1.z1)(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. ------ 160283/17658588. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.z)(b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z)(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(b a)) REDUCED to normal form. ------ 160284/17658669. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(a a))(^b.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. ------ 160285/17658777. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^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. ------ 160286/17658813. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(c ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.y))(c ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(c ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(c (a a))) REDUCED to normal form. ------ 160287/17658903. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y)) b)) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 160288/17658930. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(a a)) c)) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 160289/17659146. ------ 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))) REDUCED to normal form. ------ 160290/17659173. ------ 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)))) 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. ------ 160291/17659209. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1) 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. ------ 160292/17659344. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 160293/17659452. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 160294/17659560. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.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. ------ 160295/17659569. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c (a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c (a b))) REDUCED to normal form. ------ 160296/17659596. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b ((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 160297/17659614. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.a)(^c.(^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)))) 5. ==[ beta ]==> (((b a)(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((b a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 160298/17659677. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 160299/17659704. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.b))(((a a) a) a)) REDUCED to normal form. ------ 160300/17659758. ------ 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. ------ 160301/17659812. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(a b))) REDUCED to normal form. ------ 160302/17659839. ------ 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)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 160303/17659902. ------ 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. ------ 160304/17659929. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.a))) REDUCED to normal form. ------ 160305/17659956. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 160306/17659983. ------ 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. ------ 160307/17660037. ------ 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. ------ 160308/17660064. ------ 1. ==[ start ]==> (((a b)(a b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 160309/17660091. ------ 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. ------ 160310/17660118. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b) b)) REDUCED to normal form. ------ 160311/17660532. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160312/17660640. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 160313/17660667. ------ 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.(^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. ------ 160314/17660721. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 160315/17660802. ------ 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))(^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. ------ 160316/17660838. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.b))(c (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.b))(c (^y.y))) REDUCED to normal form. ------ 160317/17660919. ------ 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)(a a))) REDUCED to normal form. ------ 160318/17660946. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((b (^x.a))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.a))(a (^y.y))) REDUCED to normal form. ------ 160319/17660973. ------ 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. ------ 160320/17661090. ------ 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. ------ 160321/17661117. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 160322/17661144. ------ 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. ------ 160323/17661171. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 160324/17661198. ------ 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. ------ 160325/17661225. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 160326/17661252. ------ 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. ------ 160327/17661504. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c (^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(c (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(c (^y.(y y)))) 7. ==[ beta ]==> (c (^y.(y y))) 8. ==[ alpha ]==> (c (^x.(x x))) REDUCED to normal form. ------ 160328/17661585. ------ 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 160329/17661693. ------ 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)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160330/17661810. ------ 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. ------ 160331/17661828. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(^b.(^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)((^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. ------ 160332/17661909. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (^b.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. ------ 160333/17661918. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((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. ------ 160334/17661945. ------ 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. ------ 160335/17661990. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))(a a))) 3. ==[ beta ]==> (b ((^z.(z z))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 160336/17661999. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d b)) REDUCED to normal form. ------ 160337/17662026. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c c)) REDUCED to normal form. ------ 160338/17662098. ------ 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 z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160339/17662134. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (a (^y.y)))) REDUCED to normal form. ------ 160340/17662161. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(b a)) REDUCED to normal form. ------ 160341/17662215. ------ 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. ------ 160342/17662305. ------ 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)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) 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. ------ 160343/17662332. ------ 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.(^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. ------ 160344/17662359. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 160345/17662386. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a) a)) 3. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 160346/17662413. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 160347/17662467. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.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. ------ 160348/17662548. ------ 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))) REDUCED to normal form. ------ 160349/17662575. ------ 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)(^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. ------ 160350/17662629. ------ 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. ------ 160351/17662647. ------ 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 (^y.y))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 160352/17662656. ------ 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. ------ 160353/17662665. ------ 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 ]==> ((b (^z.z))(^y.y)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 160354/17662929. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((^z.(z (z (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.z)) 5. ==[ beta ]==> ((^z.z)((^z.z)(^y.y))) 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. ------ 160355/17664171. ------ 1. ==[ start ]==> ((^a.((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((^x.((x x) x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.((x x) x))(^y.(^z.z))) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^y.(^z.z))) 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. ------ 160356/17671704. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.((x1 x1) x1))) 3. ==[ eta ]==> ((^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. ------ 160357/17672946. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(a (^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)))(^y1.y1))(^y.y)) 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. ------ 160358/17673219. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^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)))) REDUCED to normal form. ------ 160359/17673225. ------ 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 (a (^z.z))))(^y.y)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 160360/17673228. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 160361/17673414. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(^z.z))(a b))) 3. ==[ eta ]==> ((^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. ------ 160362/17674467. ------ 1. ==[ start ]==> ((^a.((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^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))) 4. ==[ alpha ]==> (((a ((^x.(^y.y)) a))(a ((^z.(^x1.x1)) a)))(a ((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (((a (^y.y))(a ((^z.(^x1.x1)) a)))(a ((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> (((a (^x.x))(a ((^y.(^z.z)) a)))(a ((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (((a (^x.x))(a (^z.z)))(a ((^x1.(^y1.y1)) a))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a ((^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. ------ 160363/17674470. ------ 1. ==[ start ]==> ((a ((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 160364/17675244. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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)))) REDUCED to normal form. ------ 160365/17676702. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 160366/17677005. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))(a (^z.(^x1.x1))))) 3. ==[ eta ]==> (b ((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 160367/17677368. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 160368/17677377. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 160369/17677710. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 160370/17677842. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)((^x1.x1)(^y1.y1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 160371/17678313. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 160372/17678322. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 160373/17678628. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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))))) REDUCED to normal form. ------ 160374/17678760. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 160375/17679465. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(b x1))) 3. ==[ eta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 160376/17680839. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c ((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 160377/17681292. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) a)(^y.y)) a) 4. ==[ beta ]==> ((a (^y.y)) a) 5. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 160378/17682000. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a ((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a ((a a) a))) 3. ==[ eta ]==> ((^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. ------ 160379/17682003. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.((a a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 160380/17682282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160381/17682819. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 160382/17682867. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^z.a)) REDUCED to normal form. ------ 160383/17683056. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z) y))) 3. ==[ eta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 160384/17683236. ------ 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 (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 160385/17683242. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (a (^z.z)))) 3. ==[ beta ]==> ((a (a (^z.z)))((a (a (^z.z)))(^y.y))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 160386/17683245. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(y (^z.z)))) REDUCED to normal form. ------ 160387/17683410. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (a ((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 160388/17683500. ------ 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. ------ 160389/17683518. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^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))) REDUCED to normal form. ------ 160390/17683527. ------ 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. ------ 160391/17683536. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160392/17683662. ------ 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. ------ 160393/17683689. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)((a a) a))) REDUCED to normal form. ------ 160394/17683716. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 160395/17683905. ------ 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)))) REDUCED to normal form. ------ 160396/17683932. ------ 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.(^x1.x1)) 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. ------ 160397/17683995. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b (^y.y))(^z.(^x1.x1)))((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((b (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 160398/17684022. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.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. ------ 160399/17684058. ------ 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. ------ 160400/17684076. ------ 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)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 160401/17684085. ------ 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. ------ 160402/17684103. ------ 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. ------ 160403/17684130. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.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. ------ 160404/17684139. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^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)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 160405/17684166. ------ 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)(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. ------ 160406/17684184. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 160407/17684193. ------ 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. ------ 160408/17684301. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.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) REDUCED to normal form. ------ 160409/17684373. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^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. ------ 160410/17684436. ------ 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. ------ 160411/17684463. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 160412/17684490. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 160413/17684544. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 160414/17684571. ------ 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. ------ 160415/17684598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(^z1.z1)))) 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. ------ 160416/17684742. ------ 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. ------ 160417/17684769. ------ 1. ==[ start ]==> ((a ((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((a a) a))(a ((^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. ------ 160418/17685120. ------ 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)(a a)))) REDUCED to normal form. ------ 160419/17685147. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(b (^z.z)))) REDUCED to normal form. ------ 160420/17685273. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 160421/17685291. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 160422/17685372. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)(^z.(a a)))) IRREDUCIBLE: cycle. ------ 160423/17685435. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(b a))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 160424/17685453. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 160425/17685462. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 160426/17685480. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) a)(^b.b))) 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))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 160427/17685489. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 160428/17685543. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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. ------ 160429/17685561. ------ 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. ------ 160430/17685597. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 160431/17685624. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 160432/17685651. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 160433/17685840. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (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. ------ 160434/17685966. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a)) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a)) b)) 5. ==[ beta ]==> ((^y.y)((^y1.(a a)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(a a)) b)) 7. ==[ beta ]==> ((^y.(a a)) b) 8. ==[ alpha ]==> ((^x.(a a)) b) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160435/17686245. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 160436/17686272. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 160437/17686488. ------ 1. ==[ start ]==> (((^a.b) c)((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 160438/17686587. ------ 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) 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. ------ 160439/17686722. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 160440/17686731. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 160441/17686839. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 160442/17686866. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 160443/17686947. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 160444/17686974. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 160445/17687064. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 160446/17687091. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))((b a) a)) REDUCED to normal form. ------ 160447/17687118. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y))(a (a a)))) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 160448/17687145. ------ 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)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((a a) a))((a a)((^x.x)(^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. ------ 160449/17687172. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a b)((a a) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((a a) a))) 7. ==[ beta ]==> ((^y.y)((a b)((a a) a))) 8. ==[ alpha ]==> ((^x.x)((a b)((a a) a))) 9. ==[ beta ]==> ((a b)((a a) a)) REDUCED to normal form. ------ 160450/17687199. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a) a)(a b))) REDUCED to normal form. ------ 160451/17687226. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b) a)((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b) a)((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b) a)((^y.y)(a a))) 8. ==[ alpha ]==> (((a b) a)((^x.x)(a a))) 9. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 160452/17687253. ------ 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. ------ 160453/17687280. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (b a))) REDUCED to normal form. ------ 160454/17687307. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 160455/17687397. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 160456/17687478. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(a a))(^b.(^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. ------ 160457/17687541. ------ 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) REDUCED to normal form. ------ 160458/17687586. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (a a))(^c.(^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. ------ 160459/17687649. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 160460/17687667. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((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. ------ 160461/17687676. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z) b)) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y) b)) 5. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 160462/17687730. ------ 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.(^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. ------ 160463/17687748. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a) c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 160464/17687784. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 160465/17687811. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 160466/17687955. ------ 1. ==[ start ]==> (((a (a a))(a b))(c (b a))) REDUCED to normal form. ------ 160467/17687982. ------ 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.(^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. ------ 160468/17688009. ------ 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)(^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. ------ 160469/17688036. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 160470/17688063. ------ 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)(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)))) 5. ==[ beta ]==> (((a a) a)((b a)(a (^y.y)))) 6. ==[ alpha ]==> (((a a) a)((b a)(a (^x.x)))) REDUCED to normal form. ------ 160471/17688090. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 160472/17688144. ------ 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 (^x.(^y.y))))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.z))) REDUCED to normal form. ------ 160473/17688423. ------ 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))(^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. ------ 160474/17688432. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 160475/17688450. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a b)(^b.(^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. ------ 160476/17688459. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 160477/17688477. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 160478/17688531. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(^y.(a a)))) 7. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 160479/17688540. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 160480/17688567. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 160481/17688612. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 160482/17688621. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.a)(a (^a.(^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. ------ 160483/17688648. ------ 1. ==[ start ]==> ((((^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.z1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^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. ------ 160484/17688729. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 160485/17688873. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a b))(c ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a b))(c ((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)(c ((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)(c ((a a)(^x.x)))) REDUCED to normal form. ------ 160486/17688900. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(b (b a))) REDUCED to normal form. ------ 160487/17688927. ------ 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)(^y.y))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 160488/17688954. ------ 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. ------ 160489/17688981. ------ 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. ------ 160490/17689035. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)(a (a a)))) REDUCED to normal form. ------ 160491/17689062. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a b)(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a b)(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((a b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 160492/17689233. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(^z.z))) 3. ==[ beta ]==> (b ((b a)(^z.z))) 4. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 160493/17689341. ------ 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.(^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. ------ 160494/17689350. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 160495/17689377. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^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))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 160496/17689395. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a))(^z.b))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.b))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.b))) 5. ==[ beta ]==> (b ((a (a a))(^y.b))) 6. ==[ alpha ]==> (b ((a (a a))(^x.b))) REDUCED to normal form. ------ 160497/17689404. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a)(^x.x))((a b)(a b))) REDUCED to normal form. ------ 160498/17689422. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(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. ------ 160499/17689431. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 160500/17689539. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a))(^a.(^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. ------ 160501/17689557. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^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. ------ 160502/17689566. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 160503/17689593. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 160504/17689674. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.b)(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(^z1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 160505/17689701. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 160506/17689737. ------ 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. ------ 160507/17689764. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (b a))) REDUCED to normal form. ------ 160508/17689791. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(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))) REDUCED to normal form. ------ 160509/17689818. ------ 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. ------ 160510/17689845. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)((^z.z) a))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)((^z.z) a))) 6. ==[ alpha ]==> (((^x.x)(a a))((a 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. ------ 160511/17689872. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 160512/17689899. ------ 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)(^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))((^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. ------ 160513/17689926. ------ 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))((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (a a))((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 160514/17689953. ------ 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) a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a (a b))) REDUCED to normal form. ------ 160515/17690007. ------ 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)((a a)(^x1.x1)))) REDUCED to normal form. ------ 160516/17690097. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.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. ------ 160517/17690232. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 160518/17690340. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.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. ------ 160519/17690376. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 160520/17690403. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^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. ------ 160521/17690457. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 160522/17690484. ------ 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.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 160523/17690583. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b) c)) 3. ==[ beta ]==> (b ((^y.b) c)) 4. ==[ alpha ]==> (b ((^x.b) c)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 160524/17690700. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (^x1.b))) REDUCED to normal form. ------ 160525/17690727. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 160526/17691141. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c ((a a) a))) REDUCED to normal form. ------ 160527/17691231. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160528/17691420. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a b)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160529/17691456. ------ 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)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 160530/17691483. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^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. ------ 160531/17691528. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)(^b.(^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. ------ 160532/17691591. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 160533/17691609. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b) a)) REDUCED to normal form. ------ 160534/17691618. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 160535/17691699. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 160536/17691726. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 160537/17691798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160538/17691924. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 160539/17691951. ------ 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. ------ 160540/17692302. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a ((a a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 160541/17692473. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.z1))) 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. ------ 160542/17692581. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160543/17692698. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^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. ------ 160544/17692743. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 160545/17692797. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.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. ------ 160546/17692806. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.a))) REDUCED to normal form. ------ 160547/17692833. ------ 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 (^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b (^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160548/17692878. ------ 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. ------ 160549/17692887. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 160550/17692914. ------ 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 (^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. ------ 160551/17692941. ------ 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))((^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. ------ 160552/17692986. ------ 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. ------ 160553/17692995. ------ 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 y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 160554/17693022. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.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. ------ 160555/17693049. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^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. ------ 160556/17693121. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a) b)) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 160557/17693139. ------ 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 (^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. ------ 160558/17693166. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a a) a)) REDUCED to normal form. ------ 160559/17693220. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c b)) 3. ==[ beta ]==> (((a (a a)) b)(c b)) REDUCED to normal form. ------ 160560/17693247. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b c)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b c)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b c)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b c)) REDUCED to normal form. ------ 160561/17693301. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (a a))) REDUCED to normal form. ------ 160562/17693328. ------ 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 (^z.z)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (a (^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. ------ 160563/17693355. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 160564/17693409. ------ 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. ------ 160565/17693436. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c a)) 3. ==[ beta ]==> ((b (a (a a)))(c a)) REDUCED to normal form. ------ 160566/17693463. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b b)) 3. ==[ beta ]==> ((((a a)(a a)) a)(b b)) REDUCED to normal form. ------ 160567/17693517. ------ 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. ------ 160568/17693535. ------ 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 (^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. ------ 160569/17693544. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a (^y.y)))) REDUCED to normal form. ------ 160570/17693553. ------ 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 ]==> (((^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. ------ 160571/17693826. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^z.(^x1.(x1 (^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.x1)) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 160572/17702601. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.a))) 3. ==[ eta ]==> ((^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. ------ 160573/17703843. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^a.(^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. ------ 160574/17704023. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 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. ------ 160575/17704050. ------ 1. ==[ start ]==> ((^a.b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 160576/17704131. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160577/17704134. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 160578/17704143. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160579/17704248. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (^y.(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (^x.(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (^x.(b (a (a a)))) REDUCED to normal form. ------ 160580/17704491. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 160581/17704566. ------ 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. ------ 160582/17704941. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))(b (^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. ------ 160583/17705706. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 160584/17705886. ------ 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 ]==> (((^y.(^z.(^x1.x1)))(a (a a))) b) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a))) 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. ------ 160585/17706150. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 160586/17706480. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.a)(^x1.x1))((^z.a)(^x1.x1)))) 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 ((^z.a)(^x1.x1))) 8. ==[ alpha ]==> (a ((^x.a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160587/17707155. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1))((a a)(^y1.y1)))((^z.(^x1.x1))((a a)(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1))))(^x2.x2)) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1))))(^x2.x2)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a)(^x1.x1))))(^y1.y1)) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))((a 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. ------ 160588/17707911. ------ 1. ==[ start ]==> ((^a.(b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(c (^y.(^z.(^x1.x1))))) 3. ==[ eta ]==> (b (c (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 160589/17708283. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 160590/17708616. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(^b.b))) 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))) REDUCED to normal form. ------ 160591/17708922. ------ 1. ==[ start ]==> (((^a.b)(^b.(^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))))) REDUCED to normal form. ------ 160592/17709228. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 160593/17709534. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 160594/17711586. ------ 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))(^x.(a a))) REDUCED to normal form. ------ 160595/17711745. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 160596/17712198. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 160597/17712405. ------ 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. ------ 160598/17712585. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.b))) 5. ==[ beta ]==> ((a b)(^y.(^z.b))) 6. ==[ alpha ]==> ((a b)(^x.(^y.b))) REDUCED to normal form. ------ 160599/17712747. ------ 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))) REDUCED to normal form. ------ 160600/17712909. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(^c.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 160601/17713350. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160602/17713725. ------ 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. ------ 160603/17713800. ------ 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 z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 160604/17713881. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^x.a)) REDUCED to normal form. ------ 160605/17713962. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.a))) REDUCED to normal form. ------ 160606/17714043. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^b.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. ------ 160607/17714148. ------ 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 ]==> (((^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. ------ 160608/17714151. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 160609/17714160. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> ((^z.(z (^x1.x1)))(^y.y)) 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. ------ 160610/17714334. ------ 1. ==[ start ]==> ((a (a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a a))(^y.y)) 4. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 160611/17714361. ------ 1. ==[ start ]==> ((a b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 160612/17714442. ------ 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)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 160613/17714451. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160614/17714460. ------ 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)(a (^y.y))) 4. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 160615/17714478. ------ 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)(((^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. ------ 160616/17714505. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^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. ------ 160617/17714532. ------ 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))((^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. ------ 160618/17714559. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.a))(b (a (a a)))) REDUCED to normal form. ------ 160619/17714640. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 160620/17714667. ------ 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))((^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. ------ 160621/17714721. ------ 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. ------ 160622/17714748. ------ 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)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 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. ------ 160623/17714802. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 160624/17714874. ------ 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. ------ 160625/17714892. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) 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))) 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. ------ 160626/17714973. ------ 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. ------ 160627/17715000. ------ 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. ------ 160628/17715027. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 160629/17715054. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 160630/17715081. ------ 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.(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. ------ 160631/17715108. ------ 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. ------ 160632/17715171. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^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)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 160633/17715198. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (a (^x.x)))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (a (^x.x)))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (a (^x.x)))(b b)) REDUCED to normal form. ------ 160634/17715216. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 160635/17715225. ------ 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. ------ 160636/17715252. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 160637/17715351. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(a a)) c)) REDUCED to normal form. ------ 160638/17715576. ------ 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. ------ 160639/17715603. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a a))(^b.b))) 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))) 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. ------ 160640/17715630. ------ 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. ------ 160641/17715720. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(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. ------ 160642/17715774. ------ 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) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> (a (((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> (a (((^x.x) b)((^y.y) a))) 7. ==[ beta ]==> (a (b ((^y.y) a))) 8. ==[ alpha ]==> (a (b ((^x.x) a))) 9. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 160643/17715855. ------ 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. ------ 160644/17715882. ------ 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)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(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. ------ 160645/17715936. ------ 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 a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)(((a a) a)((a a)(^y.y)))) 8. ==[ alpha ]==> ((a a)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 160646/17716017. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.b))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.b))(a ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.b))(a b)) REDUCED to normal form. ------ 160647/17716170. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^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. ------ 160648/17716188. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 160649/17716197. ------ 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. ------ 160650/17716377. ------ 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. ------ 160651/17716404. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 160652/17716485. ------ 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. ------ 160653/17716512. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a)) b)) 5. ==[ beta ]==> ((^y.a)(((a a)(a a)) b)) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a)) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 160654/17716539. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 160655/17716656. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.b))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 160656/17716683. ------ 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. ------ 160657/17716764. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 160658/17716791. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a (a a))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(^y.y))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 160659/17716800. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c ((^z.z) b))) 3. ==[ beta ]==> ((^y.(a a))(c ((^z.z) b))) 4. ==[ alpha ]==> ((^x.(a a))(c ((^y.y) b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160660/17716827. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(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. ------ 160661/17716881. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 160662/17716962. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 160663/17717016. ------ 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. ------ 160664/17717043. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 160665/17717097. ------ 1. ==[ start ]==> (((^a.(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)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 11. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 13. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 14. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 15. ==[ beta ]==> ((a a)(^y.y)) 16. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 160666/17717178. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 160667/17717277. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b)(a (^a.a)))) 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. ------ 160668/17717304. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 160669/17717385. ------ 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 a)) REDUCED to normal form. ------ 160670/17717403. ------ 1. ==[ start ]==> (((^a.b) c)((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)((a b)(^y.b))) 3. ==[ beta ]==> (b ((a b)(^y.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 160671/17717412. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.b)(a b))) 3. ==[ beta ]==> (((a b)(a (^x.x))) b) REDUCED to normal form. ------ 160672/17717466. ------ 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 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. ------ 160673/17717646. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 160674/17717880. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 160675/17718222. ------ 1. ==[ start ]==> ((a (b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 160676/17718456. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)(^y.b))) REDUCED to normal form. ------ 160677/17718564. ------ 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.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 160678/17718591. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 160679/17718645. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 160680/17718672. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a) c)) REDUCED to normal form. ------ 160681/17718789. ------ 1. ==[ start ]==> (((a a)(b a))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(^y.b))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 160682/17718816. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a 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. ------ 160683/17718897. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 160684/17718924. ------ 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)(^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. ------ 160685/17719068. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160686/17719149. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)((a (a a))((^z.z)(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. ------ 160687/17719230. ------ 1. ==[ start ]==> (((^a.b)(^b.(^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. ------ 160688/17719347. ------ 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.(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. ------ 160689/17719374. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 160690/17719455. ------ 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.(a a)))) REDUCED to normal form. ------ 160691/17719482. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 160692/17719536. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 160693/17719563. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 160694/17719590. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a) b)) REDUCED to normal form. ------ 160695/17719680. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.b)(^b.(^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. ------ 160696/17719707. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 160697/17719734. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 160698/17719761. ------ 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 y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 160699/17719788. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 160700/17719842. ------ 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)(^y.y))((^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. ------ 160701/17719986. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((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))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 160702/17720013. ------ 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)(^x2.x2))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(^x2.x2))((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. ------ 160703/17720265. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 160704/17720292. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.a))) 7. ==[ beta ]==> ((b a)(^y.a)) 8. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 160705/17720319. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.b))) REDUCED to normal form. ------ 160706/17720346. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (^y1.(a a)))) REDUCED to normal form. ------ 160707/17720427. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a) a)) 5. ==[ beta ]==> ((^y.(a a))((b a) a)) 6. ==[ alpha ]==> ((^x.(a a))((b a) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160708/17720454. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 160709/17720481. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.a))((a a) c)) REDUCED to normal form. ------ 160710/17720652. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 160711/17720922. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 160712/17721417. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((b a)(b a))(b ((^y.y)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(b ((^x.x)(a a)))) 5. ==[ beta ]==> (((b a)(b a))(b (a a))) REDUCED to normal form. ------ 160713/17721480. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 160714/17721498. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)(a (^y.y)))) 3. ==[ beta ]==> (b ((a b)(a (^y.y)))) 4. ==[ alpha ]==> (b ((a b)(a (^x.x)))) REDUCED to normal form. ------ 160715/17721507. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b) c)) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 160716/17721606. ------ 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)((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. ------ 160717/17721705. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a))(a a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 160718/17721732. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 160719/17721786. ------ 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. ------ 160720/17721813. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 12. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 13. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 14. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 160721/17721840. ------ 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 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. ------ 160722/17721867. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 160723/17721894. ------ 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. ------ 160724/17721921. ------ 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))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 160725/17722002. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 160726/17722029. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^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. ------ 160727/17722056. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 160728/17722146. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160729/17722227. ------ 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. ------ 160730/17722371. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 160731/17722398. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^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))) 5. ==[ beta ]==> ((((a a)(a a)) b)(^y.a)) 6. ==[ alpha ]==> ((((a a)(a a)) b)(^x.a)) REDUCED to normal form. ------ 160732/17722506. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 160733/17722533. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b) a)) REDUCED to normal form. ------ 160734/17722713. ------ 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. ------ 160735/17722722. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 160736/17722749. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a) b)) 3. ==[ beta ]==> ((b (^y.a))((^z.a) b)) 4. ==[ alpha ]==> ((b (^x.a))((^y.a) b)) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 160737/17722776. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1)) c)) 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. ------ 160738/17722839. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 160739/17722866. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (^y.a))) REDUCED to normal form. ------ 160740/17722893. ------ 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))) 5. ==[ beta ]==> ((a b)(a (^y.b))) 6. ==[ alpha ]==> ((a b)(a (^x.b))) REDUCED to normal form. ------ 160741/17722947. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 160742/17722974. ------ 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))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 160743/17723001. ------ 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. ------ 160744/17723028. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 160745/17723055. ------ 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. ------ 160746/17723109. ------ 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.(^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. ------ 160747/17723136. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) 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. ------ 160748/17723163. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 160749/17723307. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)((^x1.x1) 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. ------ 160750/17723631. ------ 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. ------ 160751/17723658. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 160752/17723712. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(a (^z.z)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(a (^z.z)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(a (^y.y)))) 9. ==[ beta ]==> ((b b)(a (a (^y.y)))) 10. ==[ alpha ]==> ((b b)(a (a (^x.x)))) REDUCED to normal form. ------ 160753/17723721. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 160754/17723802. ------ 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. ------ 160755/17723829. ------ 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.(^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. ------ 160756/17723856. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 160757/17723910. ------ 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. ------ 160758/17723937. ------ 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. ------ 160759/17723964. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y)) c)) REDUCED to normal form. ------ 160760/17724018. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 160761/17724036. ------ 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. ------ 160762/17724081. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.a))) REDUCED to normal form. ------ 160763/17724108. ------ 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. ------ 160764/17724135. ------ 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))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 160765/17724162. ------ 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 (^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. ------ 160766/17724189. ------ 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. ------ 160767/17724216. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.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. ------ 160768/17724243. ------ 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)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 160769/17724270. ------ 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)(^x.x))(a b))(^z.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 160770/17724324. ------ 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 (^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. ------ 160771/17724351. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a (^b.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. ------ 160772/17724378. ------ 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))(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. ------ 160773/17724432. ------ 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)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 160774/17724450. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a) b)) 3. ==[ beta ]==> ((a (^y.y))((a a) b)) 4. ==[ alpha ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 160775/17724459. ------ 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 (^x.x))))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 160776/17724468. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> ((a (a (^z.z)))(^y.y)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 160777/17735076. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160778/17735085. ------ 1. ==[ start ]==> (((a a) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 160779/17735523. ------ 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. ------ 160780/17735748. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160781/17735913. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160782/17736819. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(x1 x1))) b) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 160783/17737101. ------ 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. ------ 160784/17737206. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))((^z1.(^x2.(^y2.y2)))(^z2.(z2 z2))))) 5. ==[ beta ]==> (^x.((^z.(^x1.x1))((^z1.(^x2.(^y2.y2)))(^z2.(z2 z2))))) 6. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2))))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160785/17738568. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((z z)(z z)))) REDUCED to normal form. ------ 160786/17739393. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 160787/17740284. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160788/17740773. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^a.(^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. ------ 160789/17741598. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((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))(((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))(((a a)(^x2.x2))(^y2.y2)))) REDUCED to normal form. ------ 160790/17742960. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(^z1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160791/17743149. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.(x x))(a (^y.(^z.z)))) a) 4. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z)))) a) 5. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 160792/17743338. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.(^a.b))) 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. ------ 160793/17743347. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(x1 b))) REDUCED to normal form. ------ 160794/17744013. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(^c.a))) 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. ------ 160795/17744283. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^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. ------ 160796/17744418. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 160797/17744526. ------ 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. ------ 160798/17744643. ------ 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. ------ 160799/17744814. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 160800/17744895. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 160801/17744976. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.c)) 3. ==[ beta ]==> ((b (a (a a)))(^y.c)) 4. ==[ alpha ]==> ((b (a (a a)))(^x.c)) REDUCED to normal form. ------ 160802/17745081. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a) b)) 3. ==[ beta ]==> (((a a) b)(((a a) b)(^y.y))) 4. ==[ alpha ]==> (((a a) b)(((a a) b)(^x.x))) REDUCED to normal form. ------ 160803/17745093. ------ 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 ]==> ((^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. ------ 160804/17745285. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(^a.a))(^b.b))) 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. ------ 160805/17745348. ------ 1. ==[ start ]==> (((^a.a) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(c (b (^y.y)))) 3. ==[ beta ]==> (b (c (b (^y.y)))) 4. ==[ alpha ]==> (b (c (b (^x.x)))) REDUCED to normal form. ------ 160806/17745375. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(b ((^a.(^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. ------ 160807/17745393. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 160808/17745402. ------ 1. ==[ start ]==> (((a a) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(a (a (a (^x.x))))) REDUCED to normal form. ------ 160809/17745429. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x)) 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. ------ 160810/17745456. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 160811/17745483. ------ 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 (^x.x))(^y.y))(((a a)(a a)) a)) REDUCED to normal form. ------ 160812/17745537. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 160813/17745618. ------ 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)(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)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(a a))) REDUCED to normal form. ------ 160814/17745645. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a b)((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. ------ 160815/17745672. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(b a))) REDUCED to normal form. ------ 160816/17745699. ------ 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)(^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. ------ 160817/17745726. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.y))((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. ------ 160818/17745843. ------ 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. ------ 160819/17745933. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.b)(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. ------ 160820/17745960. ------ 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. ------ 160821/17746041. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 160822/17746068. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 160823/17746113. ------ 1. ==[ start ]==> (((a (^a.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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 160824/17746140. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a (a a))(^b.b))) 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. ------ 160825/17746203. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160826/17746230. ------ 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.(^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. ------ 160827/17746338. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.b)(^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. ------ 160828/17746365. ------ 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. ------ 160829/17746752. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.(^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)))) REDUCED to normal form. ------ 160830/17746779. ------ 1. ==[ start ]==> ((((a a) a) a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((b a)((^x.x)(^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. ------ 160831/17746833. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a b))) REDUCED to normal form. ------ 160832/17746860. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a b)(a a))) REDUCED to normal form. ------ 160833/17746887. ------ 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. ------ 160834/17746914. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160835/17746941. ------ 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. ------ 160836/17747058. ------ 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. ------ 160837/17747085. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 160838/17747112. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) 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. ------ 160839/17747139. ------ 1. ==[ start ]==> ((a (a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 160840/17747148. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 160841/17747229. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(a b))) IRREDUCIBLE: cycle. ------ 160842/17747310. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 160843/17747337. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 160844/17747364. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) 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. ------ 160845/17747418. ------ 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. ------ 160846/17747499. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 160847/17747526. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 160848/17747742. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 160849/17747769. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 160850/17747913. ------ 1. ==[ start ]==> (((a b) b)((b a)(a (a a)))) REDUCED to normal form. ------ 160851/17747940. ------ 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)(^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 160852/17747967. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 160853/17747994. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b)(a b))) REDUCED to normal form. ------ 160854/17748048. ------ 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. ------ 160855/17748075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(b a))) 5. ==[ beta ]==> ((^y.(y y))((a (a a))(b a))) 6. ==[ alpha ]==> ((^x.(x x))((a (a a))(b a))) 7. ==[ beta ]==> (((a (a a))(b a))((a (a a))(b a))) REDUCED to normal form. ------ 160856/17748102. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 160857/17748120. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(c (^z.z))) 3. ==[ beta ]==> (b (c (^z.z))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 160858/17748129. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 160859/17748156. ------ 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. ------ 160860/17748192. ------ 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))) 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. ------ 160861/17748219. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 160862/17748246. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (^a.(^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))) REDUCED to normal form. ------ 160863/17748273. ------ 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. ------ 160864/17748300. ------ 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. ------ 160865/17748354. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a b)(^y.b))) REDUCED to normal form. ------ 160866/17748381. ------ 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.(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. ------ 160867/17748444. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 160868/17748579. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 160869/17748687. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 160870/17748822. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 160871/17748831. ------ 1. ==[ start ]==> (((a b)(^b.a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 160872/17748858. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b ((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b ((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 160873/17748885. ------ 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. ------ 160874/17748921. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b) 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. ------ 160875/17749254. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(a a))) 5. ==[ beta ]==> (b ((^z.z)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 160876/17749335. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 160877/17749443. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 160878/17749470. ------ 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 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((a a)(^y1.y1)))) 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. ------ 160879/17749524. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 160880/17749605. ------ 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.(^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. ------ 160881/17749713. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 160882/17749893. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x) a)) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 160883/17749920. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 160884/17749992. ------ 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))(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. ------ 160885/17750172. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 160886/17750307. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^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 a)) REDUCED to normal form. ------ 160887/17750334. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 160888/17750388. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a b))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a b))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a b))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 160889/17750469. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 160890/17750604. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 160891/17750811. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 160892/17750883. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1) 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. ------ 160893/17751090. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(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. ------ 160894/17751198. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.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. ------ 160895/17751252. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(^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)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 160896/17751279. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(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. ------ 160897/17751333. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 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. ------ 160898/17751414. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a))(^a.(^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. ------ 160899/17751522. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^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. ------ 160900/17751702. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a)) c)) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(a a)) c)) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a)) c)) 7. ==[ beta ]==> ((a a)((^y.(a a)) c)) 8. ==[ alpha ]==> ((a a)((^x.(a a)) c)) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 160901/17751918. ------ 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. ------ 160902/17751954. ------ 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 a) REDUCED to normal form. ------ 160903/17752089. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 160904/17752197. ------ 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.(^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. ------ 160905/17752278. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^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)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 160906/17752305. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((^y.(y y))(^z.a)) 6. ==[ alpha ]==> ((^x.(x x))(^y.a)) 7. ==[ beta ]==> ((^y.a)(^y.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 160907/17752359. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 160908/17752422. ------ 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))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 160909/17752449. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)(a (^y.y)))) REDUCED to normal form. ------ 160910/17752503. ------ 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. ------ 160911/17752557. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a ((a a) a))) REDUCED to normal form. ------ 160912/17752584. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(a b))) REDUCED to normal form. ------ 160913/17752611. ------ 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))(^x.x))((a a)(a a))) REDUCED to normal form. ------ 160914/17752647. ------ 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. ------ 160915/17752674. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 160916/17752701. ------ 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)(^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. ------ 160917/17752728. ------ 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.(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)))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.(y y))) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.(x x))) REDUCED to normal form. ------ 160918/17752755. ------ 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. ------ 160919/17752809. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.b))) REDUCED to normal form. ------ 160920/17752836. ------ 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.(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. ------ 160921/17752863. ------ 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)))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 160922/17753277. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(a (^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160923/17753385. ------ 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. ------ 160924/17753412. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(^y1.y1)))) 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. ------ 160925/17753466. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.x1)(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a b)) REDUCED to normal form. ------ 160926/17753547. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 160927/17753655. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 160928/17753664. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (a b))) REDUCED to normal form. ------ 160929/17753691. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a)(a a))) 3. ==[ beta ]==> ((b (^y.a))(((a a) a)(a a))) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 160930/17753718. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(a (^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. ------ 160931/17753862. ------ 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. ------ 160932/17753889. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((b a)(^y.(^z.z))) 10. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 160933/17753916. ------ 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. ------ 160934/17753943. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) 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. ------ 160935/17753970. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 160936/17754051. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^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)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 160937/17754078. ------ 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. ------ 160938/17754330. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.a))) 3. ==[ beta ]==> (b (a (^x1.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 160939/17754438. ------ 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. ------ 160940/17754573. ------ 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.(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. ------ 160941/17754600. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 160942/17754663. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 160943/17754690. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160944/17754735. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 160945/17754798. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c c)) REDUCED to normal form. ------ 160946/17754843. ------ 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. ------ 160947/17754906. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (a (^y.y)))) REDUCED to normal form. ------ 160948/17754960. ------ 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. ------ 160949/17754996. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a) b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 160950/17755023. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^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. ------ 160951/17755077. ------ 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))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 160952/17755104. ------ 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.(^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. ------ 160953/17755131. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 160954/17755158. ------ 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. ------ 160955/17755185. ------ 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)) REDUCED to normal form. ------ 160956/17755212. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a) c)) REDUCED to normal form. ------ 160957/17755266. ------ 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.(^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. ------ 160958/17755293. ------ 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)) 5. ==[ beta ]==> ((b (a (a a))) c) REDUCED to normal form. ------ 160959/17755320. ------ 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))) REDUCED to normal form. ------ 160960/17755374. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) REDUCED to normal form. ------ 160961/17755392. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (a a))) 3. ==[ beta ]==> ((a (^y.y))(b (a a))) 4. ==[ alpha ]==> ((a (^x.x))(b (a a))) REDUCED to normal form. ------ 160962/17755401. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a) b)) REDUCED to normal form. ------ 160963/17755410. ------ 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 ]==> (((^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. ------ 160964/17766024. ------ 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 ((^z.(^x1.x1)) a))(^y.y)) 4. ==[ alpha ]==> ((b ((^x.(^y.y)) a))(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 160965/17766045. ------ 1. ==[ start ]==> (((a a) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 160966/17766141. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a)) d)) 3. ==[ beta ]==> (^y.((^z.(a a)) d)) 4. ==[ alpha ]==> (^x.((^y.(a a)) d)) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 160967/17766213. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)((a a) a))) 3. ==[ eta ]==> ((^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. ------ 160968/17766477. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 160969/17766708. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 160970/17767266. ------ 1. ==[ start ]==> ((^a.((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(b (b (^y.y)))) 3. ==[ beta ]==> (((b (b (^y.y)))(b (b (^y.y))))(b (b (^y.y)))) 4. ==[ alpha ]==> (((b (b (^x.x)))(b (b (^y.y))))(b (b (^z.z)))) REDUCED to normal form. ------ 160971/17768070. ------ 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. ------ 160972/17769528. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 160973/17769804. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(b a))) 3. ==[ eta ]==> (b (((^y.y) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 160974/17770536. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.((^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. ------ 160975/17770641. ------ 1. ==[ start ]==> ((^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 a)))) 3. ==[ beta ]==> ((((^x1.x1)(a a))(a (a a)))(^y.(^z.z))) 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. ------ 160976/17771148. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 160977/17771454. ------ 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 (^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))))) REDUCED to normal form. ------ 160978/17771559. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 160979/17772012. ------ 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. ------ 160980/17772291. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(b y))) 3. ==[ eta ]==> ((((^x.x) a)(b a)) b) 4. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 160981/17772534. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 160982/17774118. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(a x1))) 3. ==[ eta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 160983/17774307. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.x1))) REDUCED to normal form. ------ 160984/17774478. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.((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))) REDUCED to normal form. ------ 160985/17774799. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b ((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 160986/17775387. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 160987/17775495. ------ 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. ------ 160988/17775603. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 160989/17775618. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 160990/17775936. ------ 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)))) REDUCED to normal form. ------ 160991/17776041. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (a a))) 3. ==[ beta ]==> ((b (a a))((b (a a))(^y.y))) 4. ==[ alpha ]==> ((b (a a))((b (a a))(^x.x))) REDUCED to normal form. ------ 160992/17776263. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 160993/17776353. ------ 1. ==[ start ]==> ((a (a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 160994/17776371. ------ 1. ==[ start ]==> (((a a) b)((^a.a)(^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)))) REDUCED to normal form. ------ 160995/17776389. ------ 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)((^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. ------ 160996/17776470. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a)) d)) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 160997/17776488. ------ 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. ------ 160998/17776515. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 160999/17776542. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)((a a) a))) 3. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 161000/17776731. ------ 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) 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. ------ 161001/17776758. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 161002/17776785. ------ 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. ------ 161003/17776803. ------ 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)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 161004/17776821. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(y y))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.x1))(((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.y1))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 11. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 12. ==[ alpha ]==> (((^x.(^y.y)) a)(^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. ------ 161005/17776848. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.(^z1.z1)))) 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. ------ 161006/17776884. ------ 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. ------ 161007/17776902. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 9. ==[ beta ]==> (b (^y.(y y))) 10. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 161008/17776911. ------ 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. ------ 161009/17776929. ------ 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. ------ 161010/17776938. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 161011/17776956. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.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. ------ 161012/17777010. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 161013/17777019. ------ 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. ------ 161014/17777037. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 161015/17777127. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((b b)((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> ((b b)((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> ((b b)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> ((b b)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> ((b b)(b ((^y.y) b))) 8. ==[ alpha ]==> ((b b)(b ((^x.x) b))) 9. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 161016/17777253. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 161017/17777316. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 161018/17777343. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 161019/17777424. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(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. ------ 161020/17777595. ------ 1. ==[ start ]==> ((a ((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))(b (b (^x.x)))) REDUCED to normal form. ------ 161021/17777685. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a)) c)) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a)) c)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a)) c)) 5. ==[ beta ]==> (a ((^z.(a a)) c)) 6. ==[ alpha ]==> (a ((^x.(a a)) c)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 161022/17777946. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) 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. ------ 161023/17777973. ------ 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 (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 161024/17778000. ------ 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. ------ 161025/17778099. ------ 1. ==[ start ]==> (((^a.b) a)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.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. ------ 161026/17778117. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 161027/17778198. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(^x1.b))) IRREDUCIBLE: cycle. ------ 161028/17778261. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 161029/17778288. ------ 1. ==[ start ]==> (((a b) a)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 161030/17778306. ------ 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. ------ 161031/17778315. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.b))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 161032/17778333. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 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. ------ 161033/17778369. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 161034/17778396. ------ 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. ------ 161035/17778468. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)(a a))(((^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. ------ 161036/17778477. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.a)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.a)) REDUCED to normal form. ------ 161037/17779098. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 161038/17779125. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 161039/17779314. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 161040/17779548. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 161041/17779557. ------ 1. ==[ start ]==> (((a b) c)((^b.b)(^a.(^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. ------ 161042/17779584. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 161043/17779665. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 161044/17779692. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((a (^y.b))((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.b)(^z.b))) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 161045/17779746. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 161046/17779800. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 161047/17779827. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 161048/17779890. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b (a a))) REDUCED to normal form. ------ 161049/17779917. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 161050/17779944. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a)((^y.y) a))) 3. ==[ beta ]==> ((a (a b))((b a)((^y.y) a))) 4. ==[ alpha ]==> ((a (a b))((b a)((^x.x) a))) 5. ==[ beta ]==> ((a (a b))((b a) a)) REDUCED to normal form. ------ 161051/17779971. ------ 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. ------ 161052/17779998. ------ 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)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.z))) 11. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 13. ==[ beta ]==> ((a a)(^y.y)) 14. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 161053/17780025. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a b)((a a) a))) REDUCED to normal form. ------ 161054/17780052. ------ 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. ------ 161055/17780079. ------ 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. ------ 161056/17780106. ------ 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. ------ 161057/17780133. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) a)(b a))) 3. ==[ beta ]==> ((a (b a))(a (b a))) REDUCED to normal form. ------ 161058/17780223. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (b (((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 161059/17780304. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 161060/17780367. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.b)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 161061/17780412. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^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. ------ 161062/17780475. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(b a))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 161063/17780493. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 161064/17780502. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(a (^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. ------ 161065/17780556. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 161066/17780574. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.(^z.z))) b)) 3. ==[ beta ]==> (b ((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 161067/17780583. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 161068/17780835. ------ 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.(^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. ------ 161069/17780862. ------ 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. ------ 161070/17780889. ------ 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.(^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))) REDUCED to normal form. ------ 161071/17780916. ------ 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)(a (^z.z)))) REDUCED to normal form. ------ 161072/17780970. ------ 1. ==[ start ]==> ((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 a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a (a a)))) REDUCED to normal form. ------ 161073/17781249. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 161074/17781276. ------ 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)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 161075/17781285. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 161076/17781303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 161077/17781357. ------ 1. ==[ start ]==> (((^a.(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))(^y1.b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.b))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.b))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.b))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.b))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.b))) 11. ==[ beta ]==> (((a a)(a a))(^y.b)) 12. ==[ alpha ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 161078/17781366. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(a 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. ------ 161079/17781393. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(y y))((^z.z)(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 161080/17781447. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^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. ------ 161081/17781474. ------ 1. ==[ start ]==> ((((^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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 161082/17781501. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(^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. ------ 161083/17781753. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(b (b a))) 3. ==[ beta ]==> (((a b)(^y.y))(b (b a))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (b a))) REDUCED to normal form. ------ 161084/17781780. ------ 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. ------ 161085/17781807. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((b a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a)(a a))) REDUCED to normal form. ------ 161086/17781861. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a) a)) REDUCED to normal form. ------ 161087/17781888. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a b)(a (a a)))) 3. ==[ beta ]==> ((a b)((a b)(a (a a)))) REDUCED to normal form. ------ 161088/17782167. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161089/17782176. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 161090/17782203. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 161091/17782221. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^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 ((^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. ------ 161092/17782230. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 161093/17782248. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^y1.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. ------ 161094/17782257. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(a b))) REDUCED to normal form. ------ 161095/17782338. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.x1)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(b a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(b a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161096/17782383. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((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. ------ 161097/17782392. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 161098/17782419. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 161099/17782446. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 161100/17782500. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(^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. ------ 161101/17782527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.b))) 5. ==[ beta ]==> ((b (^x.x))((^z.b)(^z.b))) 6. ==[ alpha ]==> ((b (^x.x))((^y.b)(^z.b))) 7. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 161102/17782563. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)(c ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a) b)(c ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a) b)(c (a a))) REDUCED to normal form. ------ 161103/17782590. ------ 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 a)(^x1.x1)))) REDUCED to normal form. ------ 161104/17782617. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(a (b a))) 3. ==[ beta ]==> ((a (b a))(a (b a))) REDUCED to normal form. ------ 161105/17782644. ------ 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))) REDUCED to normal form. ------ 161106/17782671. ------ 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. ------ 161107/17782698. ------ 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. ------ 161108/17782725. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 161109/17782752. ------ 1. ==[ start ]==> ((((^a.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))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 161110/17782779. ------ 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. ------ 161111/17782833. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 161112/17782860. ------ 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. ------ 161113/17782923. ------ 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.(^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. ------ 161114/17783058. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 161115/17783166. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 161116/17783202. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)(^z.a))) 3. ==[ beta ]==> ((b b)((^y.b)(^z.a))) 4. ==[ alpha ]==> ((b b)((^x.b)(^y.a))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 161117/17783283. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))(^c.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. ------ 161118/17783310. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 161119/17783409. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(a a)) b)) 3. ==[ beta ]==> (b ((^y.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 161120/17783553. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.b))) REDUCED to normal form. ------ 161121/17783580. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 161122/17784057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a)) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a)) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161123/17784282. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(a a))) 3. ==[ beta ]==> ((b c)((^y.b)(a a))) 4. ==[ alpha ]==> ((b c)((^x.b)(a a))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 161124/17784309. ------ 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) REDUCED to normal form. ------ 161125/17784354. ------ 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. ------ 161126/17784381. ------ 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.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. ------ 161127/17784417. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^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. ------ 161128/17784435. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)(^x1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.b))) REDUCED to normal form. ------ 161129/17784444. ------ 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. ------ 161130/17784516. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^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. ------ 161131/17784525. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 161132/17784552. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 161133/17784633. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.b)) REDUCED to normal form. ------ 161134/17784750. ------ 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. ------ 161135/17784777. ------ 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 (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 161136/17784804. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)((a a) a))) 5. ==[ beta ]==> ((a b)((a a)((a a) a))) REDUCED to normal form. ------ 161137/17785128. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 161138/17785218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z)) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(z z)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(y y)) c)) 7. ==[ beta ]==> ((^y.(y y)) c) 8. ==[ alpha ]==> ((^x.(x x)) c) 9. ==[ beta ]==> (c c) REDUCED to normal form. ------ 161139/17785407. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161140/17785524. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(^b.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. ------ 161141/17785623. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z)) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z)) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z)) b)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z)) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y)) b)) 7. ==[ beta ]==> ((b b)((^y.(y y)) b)) 8. ==[ alpha ]==> ((b b)((^x.(x x)) b)) 9. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 161142/17785713. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 161143/17785740. ------ 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 z))(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(a a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 161144/17785767. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 161145/17785812. ------ 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)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161146/17785821. ------ 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. ------ 161147/17785848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 161148/17785875. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 161149/17785929. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 161150/17785947. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z)) a)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 161151/17785965. ------ 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. ------ 161152/17785992. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 161153/17786019. ------ 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. ------ 161154/17786100. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b c)) REDUCED to normal form. ------ 161155/17786181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (a (^y.y)))) REDUCED to normal form. ------ 161156/17786235. ------ 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))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 161157/17786262. ------ 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. ------ 161158/17786361. ------ 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))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 161159/17786370. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (a a))) REDUCED to normal form. ------ 161160/17786379. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^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 ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 161161/17787138. ------ 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))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 161162/17796273. ------ 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. ------ 161163/17796930. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 161164/17797050. ------ 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)(^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. ------ 161165/17797128. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (^y.(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (^x.(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (^x.(((a a)(a a)) a)) REDUCED to normal form. ------ 161166/17797371. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 161167/17797470. ------ 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. ------ 161168/17797473. ------ 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. ------ 161169/17797821. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)((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. ------ 161170/17798292. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) y1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^z1.(^x2.x2))) 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. ------ 161171/17798586. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 161172/17798766. ------ 1. ==[ start ]==> ((^a.(a b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) 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. ------ 161173/17799360. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^z.(z z))(^x1.(^y1.(^z1.z1))))((^z.(z z))(^x1.(^y1.(^z1.z1)))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(^y2.(^z2.z2)))))) 5. ==[ beta ]==> (((^y.(y y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(^y2.(^z2.z2))))) 6. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3))))) 9. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3))))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161174/17799453. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^a.(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. ------ 161175/17801523. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 161176/17802441. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 161177/17802720. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(b a))) 3. ==[ beta ]==> (b (^z.(b a))) 4. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 161178/17802999. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161179/17804493. ------ 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.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 161180/17804625. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 161181/17804718. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((^y2.y2)(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((^y2.y2)(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161182/17805492. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.b))) REDUCED to normal form. ------ 161183/17805786. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ eta ]==> ((^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. ------ 161184/17805960. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 161185/17806365. ------ 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. ------ 161186/17806482. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) REDUCED to normal form. ------ 161187/17806605. ------ 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. ------ 161188/17806608. ------ 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. ------ 161189/17806707. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 161190/17806788. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 161191/17806950. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(^b.a))) 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. ------ 161192/17807004. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(a (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(a (^y.y)))) REDUCED to normal form. ------ 161193/17807028. ------ 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)(((^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. ------ 161194/17807268. ------ 1. ==[ start ]==> ((a b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 161195/17807358. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 161196/17807385. ------ 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)(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. ------ 161197/17807394. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (^x.x)) a)(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 161198/17807412. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.(^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)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 161199/17807439. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 161200/17807466. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((a (^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 161201/17807547. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.a)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.a)((b a)((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 161202/17807574. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 161203/17807628. ------ 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. ------ 161204/17807655. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 161205/17807709. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (^x.(x x)))((a (a a)) b)) REDUCED to normal form. ------ 161206/17807808. ------ 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. ------ 161207/17807880. ------ 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. ------ 161208/17807907. ------ 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. ------ 161209/17807934. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 161210/17807961. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b a)(^z.a))) REDUCED to normal form. ------ 161211/17807988. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 161212/17808015. ------ 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. ------ 161213/17808051. ------ 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. ------ 161214/17808105. ------ 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))(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)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 161215/17808123. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a a))(^b.b))) 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. ------ 161216/17808132. ------ 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. ------ 161217/17808159. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 161218/17808258. ------ 1. ==[ start ]==> (((a (a a)) b)((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a)) b)((b (^x.x)) b)) REDUCED to normal form. ------ 161219/17808456. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 161220/17808510. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 161221/17808537. ------ 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. ------ 161222/17808564. ------ 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. ------ 161223/17808627. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 161224/17808681. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> (a (((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> (a (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 161225/17808762. ------ 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. ------ 161226/17808789. ------ 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)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((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. ------ 161227/17808843. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)((a b)((^y.y)(a a)))) 8. ==[ alpha ]==> ((a a)((a b)((^x.x)(a a)))) 9. ==[ beta ]==> ((a a)((a b)(a a))) REDUCED to normal form. ------ 161228/17808924. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 161229/17809095. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 161230/17809104. ------ 1. ==[ start ]==> ((a (a b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.x)((^y.y) 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. ------ 161231/17809257. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 161232/17809311. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 161233/17809365. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 161234/17809419. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.a))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z)) a)) 5. ==[ beta ]==> ((^y.a)((b (^z.z)) a)) 6. ==[ alpha ]==> ((^x.a)((b (^y.y)) a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 161235/17809446. ------ 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. ------ 161236/17809473. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b) c)) 3. ==[ beta ]==> (((a b)(^x.x))(b c)) REDUCED to normal form. ------ 161237/17809509. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 161238/17809590. ------ 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. ------ 161239/17809617. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.b)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.(a a)))) 7. ==[ beta ]==> (a ((^y.b)(^z.(a a)))) 8. ==[ alpha ]==> (a ((^x.b)(^y.(a a)))) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 161240/17809698. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 161241/17809734. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(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. ------ 161242/17809788. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (b (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(a (b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 161243/17809869. ------ 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) a))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 161244/17809923. ------ 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))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((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)(^x.x))(^z.z))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 161245/17809950. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 161246/17810004. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((^z.z)(a a)))) 9. ==[ beta ]==> ((^y.y)(((a a) a)((^z.z)(a a)))) 10. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 11. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 12. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 13. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 161247/17810085. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 161248/17810184. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 161249/17810211. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b)(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)))) 5. ==[ beta ]==> ((a ((a a) a))(a (^y.y))) 6. ==[ alpha ]==> ((a ((a a) a))(a (^x.x))) REDUCED to normal form. ------ 161250/17810238. ------ 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. ------ 161251/17810310. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 161252/17810319. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 161253/17810346. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.b)(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(a b))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 161254/17810553. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b) b)) 3. ==[ beta ]==> (((a b) c)(b b)) REDUCED to normal form. ------ 161255/17810580. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.(^z.z))) c)) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 161256/17811363. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a b)(^y.a))) REDUCED to normal form. ------ 161257/17811498. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 161258/17811552. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 161259/17811579. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 161260/17811606. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a) c)) 3. ==[ beta ]==> (((a a)(^y.a))((b a) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((b a) c)) REDUCED to normal form. ------ 161261/17811696. ------ 1. ==[ start ]==> (((a a)(b a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 161262/17811750. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 161263/17811777. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 161264/17811831. ------ 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))(^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. ------ 161265/17811858. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 161266/17811975. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(a (a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161267/17812056. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> ((a a)(((^z.z)(^x1.x1))(a b))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> ((a a)((^y.y)(a b))) 8. ==[ alpha ]==> ((a a)((^x.x)(a b))) 9. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 161268/17812137. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (b ((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 161269/17812254. ------ 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))) REDUCED to normal form. ------ 161270/17812281. ------ 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)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 161271/17812362. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.b)) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.b)) REDUCED to normal form. ------ 161272/17812389. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> ((^y.b)((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> ((^x.b)((a (a a))(^y.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 161273/17812470. ------ 1. ==[ start ]==> ((((^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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 161274/17812497. ------ 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)) REDUCED to normal form. ------ 161275/17812587. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 161276/17812614. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 161277/17812668. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 161278/17812695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(a a)))) 7. ==[ beta ]==> ((a b)((^y.(a a))(^y.(a a)))) 8. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 161279/17812722. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 161280/17812776. ------ 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.(^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. ------ 161281/17812848. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161282/17812893. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 161283/17812920. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^z1.z1)(^x2.x2)))) 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. ------ 161284/17813055. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(b a))) 3. ==[ beta ]==> (b ((a a)(b a))) REDUCED to normal form. ------ 161285/17813172. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a b)(^z.(z z)))) REDUCED to normal form. ------ 161286/17813199. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a) a)(^b.(^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. ------ 161287/17813226. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 161288/17813253. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (a a))(^y1.b))) REDUCED to normal form. ------ 161289/17813361. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a) a)) REDUCED to normal form. ------ 161290/17813388. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 161291/17813415. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a)) c)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a)) c)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a) c)) REDUCED to normal form. ------ 161292/17813559. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 161293/17813856. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(b (^c.(^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. ------ 161294/17814198. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b) c)) 3. ==[ beta ]==> ((b b)((a b) c)) REDUCED to normal form. ------ 161295/17814324. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c (a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c (a b))) 3. ==[ beta ]==> (((b a)(b a))(c (a b))) REDUCED to normal form. ------ 161296/17814387. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^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. ------ 161297/17814405. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^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. ------ 161298/17814414. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 161299/17814468. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a) d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a) d)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 161300/17814513. ------ 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. ------ 161301/17814639. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(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 a)) REDUCED to normal form. ------ 161302/17814666. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 161303/17814693. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.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. ------ 161304/17814720. ------ 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. ------ 161305/17814747. ------ 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))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a) a)(a a))((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.z))) 10. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.y))) 11. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 12. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 161306/17814774. ------ 1. ==[ start ]==> (((a b)(a b))((^b.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. ------ 161307/17814801. ------ 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.z))(a b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 161308/17814828. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 161309/17814882. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 161310/17814909. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 161311/17814936. ------ 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))(^z.(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. ------ 161312/17814963. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 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. ------ 161313/17815053. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a ((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a ((^x2.x2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((^x2.x2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161314/17815134. ------ 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))((^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. ------ 161315/17815242. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((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. ------ 161316/17815278. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(^y.y))) 3. ==[ beta ]==> ((b c)((a b)(^y.y))) 4. ==[ alpha ]==> ((b c)((a b)(^x.x))) REDUCED to normal form. ------ 161317/17815305. ------ 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. ------ 161318/17815413. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 161319/17815440. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.b))) REDUCED to normal form. ------ 161320/17815521. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z) c)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y) c)) 5. ==[ beta ]==> (((a b)(^x.(a a))) c) REDUCED to normal form. ------ 161321/17815620. ------ 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. ------ 161322/17815656. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b) a)) 3. ==[ beta ]==> ((b (^y.a))((^z.b) a)) 4. ==[ alpha ]==> ((b (^x.a))((^y.b) a)) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 161323/17815800. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (^z.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.a))) 5. ==[ beta ]==> ((a b)(b (^y.a))) 6. ==[ alpha ]==> ((a b)(b (^x.a))) REDUCED to normal form. ------ 161324/17815827. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.b))) REDUCED to normal form. ------ 161325/17815854. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.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) REDUCED to normal form. ------ 161326/17815881. ------ 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 (^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. ------ 161327/17815908. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (((a b)(a a))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (((a b)(a a))(a ((^y.y) a))) 8. ==[ alpha ]==> (((a b)(a a))(a ((^x.x) a))) 9. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 161328/17815935. ------ 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. ------ 161329/17815962. ------ 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.(^z.z))((^x1.x1)(^y1.y1)))) 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. ------ 161330/17816043. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x) 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. ------ 161331/17816070. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 161332/17816124. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 161333/17816214. ------ 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. ------ 161334/17816295. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 161335/17816403. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c d)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c d)) 3. ==[ beta ]==> ((^y.(^z.z))(c d)) 4. ==[ alpha ]==> ((^x.(^y.y))(c d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161336/17816565. ------ 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. ------ 161337/17816619. ------ 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. ------ 161338/17816628. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 161339/17816655. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a) c)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a) c)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a) c)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161340/17816700. ------ 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. ------ 161341/17816736. ------ 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. ------ 161342/17816763. ------ 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.(^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. ------ 161343/17816817. ------ 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)(^y1.(y1 y1)))) REDUCED to normal form. ------ 161344/17816844. ------ 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. ------ 161345/17816871. ------ 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. ------ 161346/17816943. ------ 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. ------ 161347/17816988. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 161348/17817015. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (^b.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. ------ 161349/17817042. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.(y y)))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.(x x)))) REDUCED to normal form. ------ 161350/17817069. ------ 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))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 161351/17817096. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 161352/17817123. ------ 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. ------ 161353/17817150. ------ 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)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.y))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 161354/17817177. ------ 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.(^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. ------ 161355/17817258. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (^a.(^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. ------ 161356/17817285. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a (^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. ------ 161357/17817339. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (^x1.x1)))) 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)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 161358/17817357. ------ 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 (^y.y))((a (^z.z)) a)) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 161359/17817366. ------ 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))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 161360/17817375. ------ 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 ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 161361/17827278. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 161362/17828064. ------ 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)(^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. ------ 161363/17828073. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 161364/17828496. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.(^z.(z (^x1.x1))))(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 (^z1.z1))))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 161365/17828709. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161366/17829780. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) b)(^z.a))) 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) REDUCED to normal form. ------ 161367/17830167. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.a))((^z.z)(^x1.a)))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.a))((^x1.x1)(^y1.a)))) 5. ==[ beta ]==> (^x.((^z.a)((^x1.x1)(^y1.a)))) 6. ==[ alpha ]==> (^x.((^y.a)((^z.z)(^x1.a)))) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 161368/17831049. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((((a a) a)(^z.(a a)))(((a a) a)(^z.(a a))))(^y.y)) 4. ==[ alpha ]==> (((((a a) a)(^x.(a a)))(((a a) a)(^y.(a a))))(^z.z)) REDUCED to normal form. ------ 161369/17831898. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (b (^z.(^x1.(z z)))) 6. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 161370/17832354. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(a a))(^b.(^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. ------ 161371/17833245. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161372/17833734. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^d.(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 161373/17835066. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 161374/17835732. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.(^y2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.(^y2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161375/17836335. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(z b))) 3. ==[ beta ]==> ((b (^y.a))(^z.(z b))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(y b))) REDUCED to normal form. ------ 161376/17836974. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 161377/17837388. ------ 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. ------ 161378/17837619. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 161379/17837622. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 161380/17837802. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 161381/17837964. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.c)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.c)) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.c)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.c)) REDUCED to normal form. ------ 161382/17838042. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z)) a)) 3. ==[ beta ]==> (((a (^z.z)) a)(((a (^z.z)) a)(^y.y))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y)) a)(^z.z))) REDUCED to normal form. ------ 161383/17838300. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 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. ------ 161384/17838390. ------ 1. ==[ start ]==> (((a a) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) b)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a) b)(b (^y.y))) 4. ==[ alpha ]==> (((a a) b)(b (^x.x))) REDUCED to normal form. ------ 161385/17838408. ------ 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)((^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. ------ 161386/17838417. ------ 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. ------ 161387/17838444. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 161388/17838471. ------ 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)))) REDUCED to normal form. ------ 161389/17838525. ------ 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)(((^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. ------ 161390/17838606. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 161391/17838633. ------ 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)(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(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. ------ 161392/17838660. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 161393/17838687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(b a))) REDUCED to normal form. ------ 161394/17838714. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(((^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))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^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. ------ 161395/17838822. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(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. ------ 161396/17838840. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))(a (^y.(y (^z.z))))) 5. ==[ beta ]==> ((a (^y.(y (^z.z))))(a (^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 161397/17838948. ------ 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. ------ 161398/17838975. ------ 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.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 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. ------ 161399/17839056. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 161400/17839074. ------ 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. ------ 161401/17839128. ------ 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 (^x.x)))((^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. ------ 161402/17839155. ------ 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. ------ 161403/17839191. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.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. ------ 161404/17839218. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 161405/17839353. ------ 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. ------ 161406/17839740. ------ 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) a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(((^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 (b ((^y.y) a))) 8. ==[ alpha ]==> (b (b ((^x.x) a))) 9. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 161407/17839767. ------ 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. ------ 161408/17839821. ------ 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)(^x1.x1))((a a) a))) REDUCED to normal form. ------ 161409/17839848. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(a b))) REDUCED to normal form. ------ 161410/17839875. ------ 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. ------ 161411/17839902. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161412/17839929. ------ 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. ------ 161413/17840073. ------ 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))) REDUCED to normal form. ------ 161414/17840100. ------ 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. ------ 161415/17840127. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) b)(^y.a))) 3. ==[ beta ]==> ((a (a b))(b (^y.a))) 4. ==[ alpha ]==> ((a (a b))(b (^x.a))) REDUCED to normal form. ------ 161416/17840136. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.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 ]==> b REDUCED to normal form. ------ 161417/17840298. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 161418/17840325. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 161419/17840352. ------ 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 (^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. ------ 161420/17840406. ------ 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. ------ 161421/17840487. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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 a)) REDUCED to normal form. ------ 161422/17840514. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.a)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.a)) REDUCED to normal form. ------ 161423/17840730. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161424/17840757. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 161425/17840901. ------ 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 (^x.(^y.y))) a)) REDUCED to normal form. ------ 161426/17840928. ------ 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. ------ 161427/17840955. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 161428/17840982. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a a)((a a) a))) REDUCED to normal form. ------ 161429/17841036. ------ 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. ------ 161430/17841063. ------ 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 z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((((^y.y)(^z.z))((a a)(^x1.x1)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 9. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 10. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 11. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 12. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 13. ==[ beta ]==> (((a a)(^x.x))((^z.z)((a a)(^x1.x1)))) 14. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^z.z)))) 15. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 16. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 161431/17841090. ------ 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. ------ 161432/17841117. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) a)(a (^a.(^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. ------ 161433/17841144. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((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 (^y.y)) b)) REDUCED to normal form. ------ 161434/17841207. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 161435/17841234. ------ 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)))) 5. ==[ beta ]==> ((a ((a a) a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a ((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 161436/17841261. ------ 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. ------ 161437/17841288. ------ 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. ------ 161438/17841315. ------ 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.(^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. ------ 161439/17841342. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 161440/17841369. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a b)(^y.b))) 3. ==[ beta ]==> (((a a)(a a))((a b)(^y.b))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(^x.b))) REDUCED to normal form. ------ 161441/17841396. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 161442/17841432. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 161443/17841567. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(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 a)) REDUCED to normal form. ------ 161444/17841729. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.b)(^z.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. ------ 161445/17841873. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b b)) REDUCED to normal form. ------ 161446/17841936. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 161447/17841963. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 161448/17842242. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(a (^z.(a a)))) 5. ==[ beta ]==> (b (a (^z.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 161449/17842431. ------ 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) REDUCED to normal form. ------ 161450/17842458. ------ 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))((^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. ------ 161451/17842512. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(b a))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(b a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(b a))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 161452/17842593. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b)(^a.a))) 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. ------ 161453/17842701. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 161454/17842908. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) 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) a)((^y.y) a)) 6. ==[ alpha ]==> (((a a) a)((^x.x) a)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 161455/17842935. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1))) b)) 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. ------ 161456/17842980. ------ 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))(((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. ------ 161457/17843160. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(c (^d.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. ------ 161458/17843322. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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 a) REDUCED to normal form. ------ 161459/17843457. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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) REDUCED to normal form. ------ 161460/17843592. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 161461/17843826. ------ 1. ==[ start ]==> ((((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)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 161462/17843871. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161463/17844078. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(b (^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (^z.a))) 3. ==[ beta ]==> (b (b (^z.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 161464/17844186. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161465/17844240. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 161466/17844267. ------ 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.(^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. ------ 161467/17844321. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 161468/17844717. ------ 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. ------ 161469/17844942. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161470/17845077. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 161471/17845185. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 161472/17845293. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))(^b.(^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. ------ 161473/17845347. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(^z.b))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.b))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 161474/17845410. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 161475/17845437. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 161476/17845491. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a) a)) REDUCED to normal form. ------ 161477/17845545. ------ 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. ------ 161478/17845572. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 161479/17845599. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 161480/17845662. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 161481/17845689. ------ 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.(^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. ------ 161482/17845716. ------ 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. ------ 161483/17845743. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(x1 x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(z z)))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.(z z))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 161484/17845770. ------ 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. ------ 161485/17845797. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.a))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.a))) REDUCED to normal form. ------ 161486/17845824. ------ 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. ------ 161487/17845851. ------ 1. ==[ start ]==> ((((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)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.(a a)))) REDUCED to normal form. ------ 161488/17845905. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b) b)) REDUCED to normal form. ------ 161489/17845932. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a) a) c)) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a) a) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a) a) c)) REDUCED to normal form. ------ 161490/17846076. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.x2)(^y2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.x2)(^y2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161491/17846265. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b (^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161492/17846373. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^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. ------ 161493/17846400. ------ 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. ------ 161494/17846454. ------ 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.(^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. ------ 161495/17846535. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 161496/17846652. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b ((a a) a))) REDUCED to normal form. ------ 161497/17846679. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a (a b))) 3. ==[ beta ]==> ((b (^y.a))(a (a b))) 4. ==[ alpha ]==> ((b (^x.a))(a (a b))) REDUCED to normal form. ------ 161498/17846706. ------ 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)(a a))) REDUCED to normal form. ------ 161499/17846877. ------ 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. ------ 161500/17846904. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^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)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 161501/17846931. ------ 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. ------ 161502/17846958. ------ 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)(^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. ------ 161503/17846985. ------ 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. ------ 161504/17847039. ------ 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. ------ 161505/17847066. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z)) b)) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y)) b)) 7. ==[ beta ]==> ((b a)((^y.y) b)) 8. ==[ alpha ]==> ((b a)((^x.x) b)) 9. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 161506/17847318. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 161507/17847426. ------ 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)((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161508/17847561. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(^b.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. ------ 161509/17847588. ------ 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))(^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. ------ 161510/17847651. ------ 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. ------ 161511/17847678. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161512/17847723. ------ 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 (b (^z.(z z)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 161513/17847732. ------ 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. ------ 161514/17847831. ------ 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))((^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. ------ 161515/17847948. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 161516/17847966. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(z z))) REDUCED to normal form. ------ 161517/17847984. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 161518/17848011. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.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. ------ 161519/17848092. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 161520/17848119. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 161521/17848146. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 161522/17848173. ------ 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) a) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) 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. ------ 161523/17848200. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y)) b)) REDUCED to normal form. ------ 161524/17848254. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 161525/17848281. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^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. ------ 161526/17848362. ------ 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. ------ 161527/17848389. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y)) a)) REDUCED to normal form. ------ 161528/17848398. ------ 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)(^x1.x1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161529/17859114. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 161530/17859255. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 161531/17859525. ------ 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. ------ 161532/17859750. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161533/17861139. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(x1 (^y1.y1)))) 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. ------ 161534/17861208. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) b) c)) 3. ==[ beta ]==> (^y.((((^z.z) b) c)(((^z.z) b) c))) 4. ==[ alpha ]==> (^x.((((^y.y) b) c)(((^z.z) b) c))) 5. ==[ beta ]==> (^x.((b c)(((^z.z) b) c))) 6. ==[ alpha ]==> (^x.((b c)(((^y.y) b) c))) 7. ==[ beta ]==> (^x.((b c)(b c))) REDUCED to normal form. ------ 161535/17862606. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 161536/17862846. ------ 1. ==[ start ]==> ((^a.(b a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((a (a a))((a a)(^y.y)))) 3. ==[ eta ]==> (b ((a (a a))((a a)(^y.y)))) 4. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 161537/17863272. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 161538/17863605. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a a) a)(^y.((^z.z) b))) 6. ==[ alpha ]==> (((a a) a)(^x.((^y.y) b))) 7. ==[ beta ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 161539/17863683. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x1.x1))((^y1.y1) a))(^y.(^z.z))) 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. ------ 161540/17864217. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 161541/17864286. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161542/17864523. ------ 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))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 161543/17864601. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 161544/17865081. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^b.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(y a))) REDUCED to normal form. ------ 161545/17865360. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(b y))) 3. ==[ eta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 161546/17865600. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((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)))((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)))((a a)((a a)(^x1.x1))))) REDUCED to normal form. ------ 161547/17866107. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 161548/17866998. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(y y)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(x x)))) REDUCED to normal form. ------ 161549/17867376. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.z))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 161550/17868429. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 161551/17868456. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 161552/17868564. ------ 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. ------ 161553/17868681. ------ 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. ------ 161554/17868762. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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)(^x.a)) REDUCED to normal form. ------ 161555/17868951. ------ 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.((^z1.z1) y1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^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)) REDUCED to normal form. ------ 161556/17869077. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 161557/17869359. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 161558/17869386. ------ 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 ((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 161559/17869467. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^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)))) REDUCED to normal form. ------ 161560/17869485. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a (^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. ------ 161561/17869557. ------ 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. ------ 161562/17869584. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (a (a a)))) REDUCED to normal form. ------ 161563/17869611. ------ 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 a)((a (^y.(^z.z)))((^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. ------ 161564/17869800. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 161565/17869827. ------ 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) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 161566/17869854. ------ 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. ------ 161567/17869881. ------ 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. ------ 161568/17869917. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161569/17869971. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 161570/17869998. ------ 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. ------ 161571/17870007. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 161572/17870025. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 161573/17870034. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 161574/17870079. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 161575/17870106. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 161576/17870196. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(^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)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 161577/17870241. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(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. ------ 161578/17870322. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 161579/17870385. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(a a))(^b.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. ------ 161580/17870412. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(z z))) REDUCED to normal form. ------ 161581/17870439. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 161582/17871015. ------ 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. ------ 161583/17871042. ------ 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) a)((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(a b)) REDUCED to normal form. ------ 161584/17871069. ------ 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. ------ 161585/17871096. ------ 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. ------ 161586/17871168. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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 a)) REDUCED to normal form. ------ 161587/17871186. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((^y.b)(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 161588/17871330. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 161589/17871348. ------ 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 a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 161590/17871357. ------ 1. ==[ start ]==> (((a b) a)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 161591/17871384. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 161592/17871402. ------ 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. ------ 161593/17871438. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 161594/17871465. ------ 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. ------ 161595/17871492. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(b (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 161596/17871537. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 161597/17871546. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(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. ------ 161598/17871564. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b) c)) 3. ==[ beta ]==> ((a (^x.(a a)))(b c)) REDUCED to normal form. ------ 161599/17871735. ------ 1. ==[ start ]==> (((^a.b) b)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 161600/17871942. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (b ((^x1.x1) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 161601/17872230. ------ 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. ------ 161602/17872383. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 161603/17872482. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^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. ------ 161604/17872617. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(a a)) a)) 3. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 161605/17872626. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 161606/17872653. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) 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)))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 161607/17872680. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.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. ------ 161608/17872734. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 161609/17872761. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 161610/17872815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161611/17872842. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(^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. ------ 161612/17872896. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 161613/17872923. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.a))(^b.b))) 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. ------ 161614/17872959. ------ 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. ------ 161615/17872986. ------ 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)(a a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (a a))) REDUCED to normal form. ------ 161616/17873013. ------ 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)))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 161617/17873040. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))((b a) a)) REDUCED to normal form. ------ 161618/17873067. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(a (a a)))) 7. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a (a a)))) 8. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a (a a)))) 9. ==[ beta ]==> (((a a)(^y.y))(a (a a))) 10. ==[ alpha ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 161619/17873094. ------ 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)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))((a a)((^x.x)(^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. ------ 161620/17873121. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a b)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a b)((a a) a))) 3. ==[ beta ]==> (((a b) a)((a b)((a a) a))) REDUCED to normal form. ------ 161621/17873148. ------ 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. ------ 161622/17873175. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(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)(^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. ------ 161623/17873202. ------ 1. ==[ start ]==> ((a (b a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 161624/17873373. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> (b ((b a)(^z.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 161625/17873436. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 161626/17873481. ------ 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. ------ 161627/17873508. ------ 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)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(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. ------ 161628/17873544. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(a a)))(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 161629/17873571. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 161630/17873625. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 161631/17873643. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^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. ------ 161632/17873652. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 161633/17873679. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 161634/17873931. ------ 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. ------ 161635/17873958. ------ 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))) 7. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 161636/17873985. ------ 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 (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 161637/17874039. ------ 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) a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 161638/17874318. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 161639/17874345. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 161640/17874372. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^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. ------ 161641/17874435. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 161642/17874462. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 161643/17874507. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 161644/17874516. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.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. ------ 161645/17874543. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 161646/17874570. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(a (^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. ------ 161647/17874615. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a 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. ------ 161648/17874642. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 161649/17874822. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c ((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.y))(c ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.x))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 161650/17874849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b (b a))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (b a))) REDUCED to normal form. ------ 161651/17874876. ------ 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. ------ 161652/17874930. ------ 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. ------ 161653/17874957. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) 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)((a a)((^y.y) a))) 6. ==[ alpha ]==> ((a b)((a a)((^x.x) a))) 7. ==[ beta ]==> ((a b)((a a) a)) REDUCED to normal form. ------ 161654/17875236. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(a a))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(a a))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161655/17875245. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 161656/17875272. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.b)(a (a a)))) 3. ==[ beta ]==> ((b a)((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((b a)((^x.b)(a (a a)))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 161657/17875290. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a) a)(^b.(^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. ------ 161658/17875299. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 161659/17875326. ------ 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.(^z1.z1))((a 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. ------ 161660/17875371. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 161661/17875407. ------ 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))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161662/17875434. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(b a)) REDUCED to normal form. ------ 161663/17875452. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a) a)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a) a)) 3. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 161664/17875461. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 161665/17875488. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^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. ------ 161666/17875515. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 161667/17875596. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(^a.a))(^c.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. ------ 161668/17875686. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(b ((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. ------ 161669/17875713. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(a (b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (b a))) REDUCED to normal form. ------ 161670/17875740. ------ 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.x1))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((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))) REDUCED to normal form. ------ 161671/17875767. ------ 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. ------ 161672/17875794. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((a b)((^x.x) a))) 3. ==[ beta ]==> (((a b)((a a) a))((a b) a)) REDUCED to normal form. ------ 161673/17875821. ------ 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)(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 161674/17875848. ------ 1. ==[ start ]==> ((((a 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)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(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)(^x.x))(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. ------ 161675/17875902. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (a b))) REDUCED to normal form. ------ 161676/17875929. ------ 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 (^x.x))(a a))) REDUCED to normal form. ------ 161677/17875956. ------ 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. ------ 161678/17875992. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((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. ------ 161679/17876127. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 161680/17876235. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((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. ------ 161681/17876271. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 161682/17876298. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 161683/17876352. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^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. ------ 161684/17876460. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 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. ------ 161685/17876478. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 161686/17876685. ------ 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)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 161687/17877207. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 161688/17877351. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (^y.(a a)))) 3. ==[ beta ]==> ((b c)(a (^y.(a a)))) 4. ==[ alpha ]==> ((b c)(a (^x.(a a)))) REDUCED to normal form. ------ 161689/17877378. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 161690/17877423. ------ 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 (^x.x))((^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. ------ 161691/17877450. ------ 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. ------ 161692/17877486. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 161693/17877513. ------ 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. ------ 161694/17877585. ------ 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) b)) REDUCED to normal form. ------ 161695/17877594. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 161696/17877621. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 161697/17877729. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.b))) 5. ==[ beta ]==> ((b (^x.a))(^z.b)) 6. ==[ alpha ]==> ((b (^x.a))(^y.b)) REDUCED to normal form. ------ 161698/17877819. ------ 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. ------ 161699/17877846. ------ 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. ------ 161700/17877873. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b)((a (^x.x))(^z.z))) 8. ==[ alpha ]==> ((a b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 161701/17877900. ------ 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 a) a))) REDUCED to normal form. ------ 161702/17878287. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1)) 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. ------ 161703/17878476. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(^b.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. ------ 161704/17878593. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(^a.(^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. ------ 161705/17878692. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((b b)((^y.(^z.z)) a)) 8. ==[ alpha ]==> ((b b)((^x.(^y.y)) a)) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 161706/17878782. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 161707/17878809. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 161708/17878836. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a a)(a a))) REDUCED to normal form. ------ 161709/17878881. ------ 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 (^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. ------ 161710/17878890. ------ 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))((^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. ------ 161711/17878917. ------ 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. ------ 161712/17878944. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 161713/17878998. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^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. ------ 161714/17879034. ------ 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. ------ 161715/17879061. ------ 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. ------ 161716/17879088. ------ 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. ------ 161717/17879115. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a 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. ------ 161718/17879169. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c b)) REDUCED to normal form. ------ 161719/17879196. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b c)) REDUCED to normal form. ------ 161720/17879250. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (a a))) REDUCED to normal form. ------ 161721/17879304. ------ 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 ((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a ((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 161722/17879331. ------ 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))) REDUCED to normal form. ------ 161723/17879358. ------ 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. ------ 161724/17879412. ------ 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. ------ 161725/17879430. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^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. ------ 161726/17879448. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((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 ]==> (((a (^z.z)) a)(^y.y)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 161727/17879636. ------ 1. ==[ start ]==> (^a.((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.(x x))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 161728/17879637. ------ 1. ==[ start ]==> (a ((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (a ((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 161729/17889792. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(a (^a.a)))) 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 (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 161730/17889999. ------ 1. ==[ start ]==> ((^a.a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161731/17890053. ------ 1. ==[ start ]==> ((^a.b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 161732/17890200. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^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. ------ 161733/17890251. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (^x.((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 161734/17890494. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 161735/17890944. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1) 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. ------ 161736/17891376. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((^y.a)(^z.(a a)))((^y.a)(^z.(a a))))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((((^x.a)(^y.(a a)))((^z.a)(^x1.(a a))))((^y1.a)(^z1.(a a)))) 5. ==[ beta ]==> ((a ((^z.a)(^x1.(a a))))((^y1.a)(^z1.(a a)))) 6. ==[ alpha ]==> ((a ((^x.a)(^y.(a a))))((^z.a)(^x1.(a a)))) 7. ==[ beta ]==> ((a a)((^z.a)(^x1.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 161737/17891709. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 161738/17891889. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.(a a))(a (^z.z))) b) 4. ==[ alpha ]==> (((^x.(a a))(a (^y.y))) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 161739/17892207. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 161740/17893158. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> ((((^z.b)(a b))((^z.b)(a b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.b)(a b))((^y.b)(a b)))(^z.z)) 5. ==[ beta ]==> ((b ((^y.b)(a b)))(^z.z)) 6. ==[ alpha ]==> ((b ((^x.b)(a b)))(^y.y)) 7. ==[ beta ]==> ((b b)(^y.y)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 161741/17893674. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 161742/17894007. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (b (^z.((^x1.x1) b))) 6. ==[ alpha ]==> (b (^x.((^y.y) b))) 7. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 161743/17894340. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 161744/17894673. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.(^b.b))) 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))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 161745/17895285. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 161746/17895591. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 161747/17896149. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^c.(^d.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 161748/17896668. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(b (^y.(^z.z)))) 3. ==[ beta ]==> (((b (^y.(^z.z)))(b (^y.(^z.z))))((b (^y.(^z.z)))(b (^y.(^z.z))))) 4. ==[ alpha ]==> (((b (^x.(^y.y)))(b (^z.(^x1.x1))))((b (^y1.(^z1.z1)))(b (^x2.(^y2.y2))))) REDUCED to normal form. ------ 161749/17897193. ------ 1. ==[ start ]==> (((^a.b)(a b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.((y y)(^z.z)))) 3. ==[ beta ]==> (b (^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (b (^x.((x x)(^y.y)))) REDUCED to normal form. ------ 161750/17897427. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^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. ------ 161751/17897748. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 161752/17898642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.b))) 5. ==[ beta ]==> ((b a)(^y.(^z.b))) 6. ==[ alpha ]==> ((b a)(^x.(^y.b))) REDUCED to normal form. ------ 161753/17898804. ------ 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))) REDUCED to normal form. ------ 161754/17898909. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161755/17899407. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)(^x.(^z.z))) 10. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 161756/17899632. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 161757/17899728. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b ((^x1.x1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 161758/17899749. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 161759/17899857. ------ 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 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 161760/17899938. ------ 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.((^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)(a a))(^y.((^z.z) a))) 6. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 161761/17900019. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^b.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. ------ 161762/17900151. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(a (^a.a)))) 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. ------ 161763/17900154. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(a (^z.z)))) REDUCED to normal form. ------ 161764/17900364. ------ 1. ==[ start ]==> ((a a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 161765/17900418. ------ 1. ==[ start ]==> ((a b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 161766/17900535. ------ 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)(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. ------ 161767/17900562. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(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. ------ 161768/17900571. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 161769/17900589. ------ 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)(((^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. ------ 161770/17900616. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 161771/17900652. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a)) d)) 3. ==[ beta ]==> ((^y.y)((^z.(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. ------ 161772/17900697. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 161773/17900724. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 161774/17900778. ------ 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. ------ 161775/17900805. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^x1.x1)))) 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. ------ 161776/17900859. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 161777/17900967. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.(y y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.(x x))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)((^y.(^z.z)) a))((a a)((^y.(^z.z)) a))) 6. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a a)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.(^z.z)) 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. ------ 161778/17901030. ------ 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. ------ 161779/17901057. ------ 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. ------ 161780/17901084. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 161781/17901111. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 161782/17901138. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 161783/17901165. ------ 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. ------ 161784/17901201. ------ 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. ------ 161785/17901228. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 161786/17901273. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((b b)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 161787/17901282. ------ 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. ------ 161788/17901309. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 161789/17901408. ------ 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. ------ 161790/17901435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b (^z.z)) b)) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z)) b)) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y)) b)) 5. ==[ beta ]==> (a ((b (^y.y)) b)) 6. ==[ alpha ]==> (a ((b (^x.x)) b)) REDUCED to normal form. ------ 161791/17901462. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a)) c)) REDUCED to normal form. ------ 161792/17901606. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 161793/17901633. ------ 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. ------ 161794/17901687. ------ 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. ------ 161795/17901714. ------ 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. ------ 161796/17901741. ------ 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)) a) REDUCED to normal form. ------ 161797/17901777. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 161798/17901831. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b (^z.z))(a a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b (^z.z))(a a))) 5. ==[ beta ]==> (a ((b (^z.z))(a a))) 6. ==[ alpha ]==> (a ((b (^x.x))(a a))) REDUCED to normal form. ------ 161799/17901867. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a)) c)) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a)) c)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a)) c)) 5. ==[ beta ]==> (b ((^y.(a a)) c)) 6. ==[ alpha ]==> (b ((^x.(a a)) c)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 161800/17901912. ------ 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. ------ 161801/17901939. ------ 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 a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^y1.y1)(^z1.z1)))) 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. ------ 161802/17901993. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(a b))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(a b))) 9. ==[ beta ]==> ((a a)((a a)(a b))) REDUCED to normal form. ------ 161803/17902074. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(b a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(b a))) 5. ==[ beta ]==> ((a (^x.b))(b a)) REDUCED to normal form. ------ 161804/17902245. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(((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. ------ 161805/17902254. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 161806/17902407. ------ 1. ==[ start ]==> ((((a a) a) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a b)(^x.(a a)))) REDUCED to normal form. ------ 161807/17902434. ------ 1. ==[ start ]==> (((a b) a)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 161808/17902515. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 161809/17902596. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 161810/17902623. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 161811/17902659. ------ 1. ==[ start ]==> (((a a)(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a a)(a b))(^y.a)) 4. ==[ alpha ]==> (((a a)(a b))(^x.a)) REDUCED to normal form. ------ 161812/17902686. ------ 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.(^x1.x1)))(^y1.(y1 y1)))) 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. ------ 161813/17902767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> (((^y.y) a)((^z.(a a))(^x1.b))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(^z.b))) 7. ==[ beta ]==> (a ((^y.(a a))(^z.b))) 8. ==[ alpha ]==> (a ((^x.(a a))(^y.b))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 161814/17902794. ------ 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. ------ 161815/17902821. ------ 1. ==[ start ]==> (((a b)(a a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 161816/17902938. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^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. ------ 161817/17903019. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^x1.x1) b)(a (^y1.y1)))) 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. ------ 161818/17903028. ------ 1. ==[ start ]==> (((a b) b)((^b.b) c)) 2. ==[ alpha ]==> (((a b) b)((^x.x) c)) 3. ==[ beta ]==> (((a b) b) c) REDUCED to normal form. ------ 161819/17903073. ------ 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. ------ 161820/17903100. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((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. ------ 161821/17903154. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a b)(a b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a b)(a b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(a b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(a b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(a b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a b)(a b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(a b))) 9. ==[ beta ]==> ((^y.y)((a b)(a b))) 10. ==[ alpha ]==> ((^x.x)((a b)(a b))) 11. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 161822/17903235. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 161823/17903307. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 161824/17903388. ------ 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. ------ 161825/17903415. ------ 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. ------ 161826/17903460. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 161827/17903469. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 161828/17903496. ------ 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 a)) REDUCED to normal form. ------ 161829/17903523. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(a b))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 161830/17903703. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a)) a)) REDUCED to normal form. ------ 161831/17903730. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b) b)) 3. ==[ beta ]==> (((a a) b)(((^y.y) b) b)) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b) b)) 5. ==[ beta ]==> (((a a) b)(b b)) REDUCED to normal form. ------ 161832/17904369. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)((^z.z) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)((^z.z) b))) 5. ==[ beta ]==> (b ((a a)((^z.z) b))) 6. ==[ alpha ]==> (b ((a a)((^x.x) b))) 7. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 161833/17904513. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(a a))(^b.(^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. ------ 161834/17904621. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 161835/17904702. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 161836/17904729. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b) a)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b a)) REDUCED to normal form. ------ 161837/17904756. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 161838/17904783. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((b a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a) c)) REDUCED to normal form. ------ 161839/17904846. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 161840/17904873. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 161841/17904927. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(^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. ------ 161842/17905008. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 161843/17905035. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a)(^b.b))) 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) 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. ------ 161844/17905125. ------ 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) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161845/17905206. ------ 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)((a a) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a) a)((a a) a))) 5. ==[ beta ]==> ((a a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 161846/17905287. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)((a a)(^y1.y1)))) 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. ------ 161847/17905404. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 161848/17905431. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.a))) REDUCED to normal form. ------ 161849/17905512. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 161850/17905539. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 161851/17905593. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) a)(^c.(^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. ------ 161852/17905647. ------ 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.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 161853/17905701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a) b)) REDUCED to normal form. ------ 161854/17905764. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 161855/17905791. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 161856/17905845. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 161857/17905872. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(a a))(^y.(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. ------ 161858/17905899. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 161859/17905953. ------ 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.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 161860/17906043. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^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)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 161861/17906070. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((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. ------ 161862/17906205. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 161863/17906322. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.a))) REDUCED to normal form. ------ 161864/17906349. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a b)(^y.(y y)))) 3. ==[ beta ]==> ((b a)((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((b a)((a b)(^x.(x x)))) REDUCED to normal form. ------ 161865/17906376. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 161866/17906484. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 161867/17906538. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((b a) a)) REDUCED to normal form. ------ 161868/17906565. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 161869/17906709. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((a a) b)((^y.b)(^y.b))) 6. ==[ alpha ]==> (((a a) b)((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 161870/17906736. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 161871/17906763. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.a))(^c.(^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)))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 161872/17907006. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(c (^y.(a a)))) 3. ==[ beta ]==> ((b (a a))(c (^y.(a a)))) 4. ==[ alpha ]==> ((b (a a))(c (^x.(a a)))) REDUCED to normal form. ------ 161873/17907033. ------ 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. ------ 161874/17907348. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((b b)(((^y.y)(a a)) b)) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a)) b)) 5. ==[ beta ]==> ((b b)((a a) b)) REDUCED to normal form. ------ 161875/17907375. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b) c)) REDUCED to normal form. ------ 161876/17907555. ------ 1. ==[ start ]==> (((^a.b)(a b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 161877/17907564. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 161878/17907618. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 161879/17907663. ------ 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. ------ 161880/17907762. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(b (^x.(a a)))) REDUCED to normal form. ------ 161881/17907789. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a (^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. ------ 161882/17907816. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(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 a)) REDUCED to normal form. ------ 161883/17907843. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 161884/17907897. ------ 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. ------ 161885/17907924. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a b)(a b))(^y.y)) 10. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 161886/17907951. ------ 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. ------ 161887/17907978. ------ 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.(^y1.y1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 161888/17908032. ------ 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))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 161889/17908059. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 161890/17908113. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 161891/17908203. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b (a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b (a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b (a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b (a b))) 5. ==[ beta ]==> ((^y.(^z.z))(b (a b))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161892/17908284. ------ 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. ------ 161893/17908392. ------ 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 (^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((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. ------ 161894/17908455. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)(^x.x))) REDUCED to normal form. ------ 161895/17908563. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^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. ------ 161896/17908671. ------ 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. ------ 161897/17908698. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z) c)) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y) c)) 7. ==[ beta ]==> (((a a)(^x.b)) c) REDUCED to normal form. ------ 161898/17908833. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 161899/17908950. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c (^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(c (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 161900/17908977. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.a))) REDUCED to normal form. ------ 161901/17909004. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a (^z.b))) 3. ==[ beta ]==> (((^y.y)(b a))(a (^z.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(a (^y.b))) 5. ==[ beta ]==> ((b a)(a (^y.b))) 6. ==[ alpha ]==> ((b a)(a (^x.b))) REDUCED to normal form. ------ 161902/17909058. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 161903/17909085. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 161904/17909112. ------ 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. ------ 161905/17909166. ------ 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. ------ 161906/17909193. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.y))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 161907/17909220. ------ 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.(^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. ------ 161908/17909274. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 161909/17909364. ------ 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. ------ 161910/17909445. ------ 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. ------ 161911/17909670. ------ 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. ------ 161912/17909715. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c ((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y) a))) 5. ==[ beta ]==> (c ((^y.y) a)) 6. ==[ alpha ]==> (c ((^x.x) a)) 7. ==[ beta ]==> (c a) REDUCED to normal form. ------ 161913/17909769. ------ 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 ]==> ((((^y.y) b)((^y.y) b))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b b)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b b)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b b)(a (^y.y))) 10. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 161914/17909778. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 161915/17909805. ------ 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 z1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1)) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1)) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 161916/17909850. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 161917/17909859. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 161918/17909913. ------ 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. ------ 161919/17909967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) REDUCED to normal form. ------ 161920/17909994. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(^z.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 161921/17910021. ------ 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. ------ 161922/17910093. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b ((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(b a)) REDUCED to normal form. ------ 161923/17910111. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 161924/17910192. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^b.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. ------ 161925/17910219. ------ 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.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a (^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 161926/17910246. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.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. ------ 161927/17910273. ------ 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 (^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. ------ 161928/17910300. ------ 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. ------ 161929/17910327. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.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. ------ 161930/17910381. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.a)) REDUCED to normal form. ------ 161931/17910408. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (^y.y))) 3. ==[ beta ]==> ((b (a (a a)))(c (^y.y))) 4. ==[ alpha ]==> ((b (a (a a)))(c (^x.x))) REDUCED to normal form. ------ 161932/17910435. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (^a.(^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. ------ 161933/17910489. ------ 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)(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. ------ 161934/17910507. ------ 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 (^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 161935/17910516. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)(a (^a.a)))) 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. ------ 161936/17921103. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(a a))(^c.(^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. ------ 161937/17921184. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 161938/17921295. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^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))))) REDUCED to normal form. ------ 161939/17921304. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 161940/17921727. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(^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. ------ 161941/17921913. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^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. ------ 161942/17922039. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (a a))(^b.b))) 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. ------ 161943/17922132. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 161944/17922984. ------ 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 ]==> ((((a a)(a a))(^y.(^z.z))) b) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 161945/17923371. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.(a a))(^x1.(^y1.y1)))((^z.(a a))(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(^z.(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.((a a)((^y1.(a a))(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(^z.(^x1.x1))))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 161946/17924253. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> ((((a b)(^z.b))((a b)(^z.b)))(^y.y)) 4. ==[ alpha ]==> ((((a b)(^x.b))((a b)(^y.b)))(^z.z)) REDUCED to normal form. ------ 161947/17924427. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^b.((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)))) REDUCED to normal form. ------ 161948/17925453. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.b)(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.y)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 161949/17926764. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 161950/17927262. ------ 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))) REDUCED to normal form. ------ 161951/17928045. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 161952/17928288. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 161953/17928297. ------ 1. ==[ start ]==> (((a b)(^a.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 161954/17929161. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(a b))) 3. ==[ beta ]==> ((b c)(^y.(a b))) 4. ==[ alpha ]==> ((b c)(^x.(a b))) REDUCED to normal form. ------ 161955/17929566. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 161956/17930502. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 161957/17930511. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^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. ------ 161958/17930619. ------ 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. ------ 161959/17930823. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^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. ------ 161960/17931246. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(^a.(^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. ------ 161961/17931258. ------ 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 ]==> ((^y.(y (^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((^z.(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(a (^y.y)))(^z.z)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 161962/17931477. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 161963/17931558. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 161964/17931621. ------ 1. ==[ start ]==> (((a a) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((a a) b)(c (b (^x.x)))) REDUCED to normal form. ------ 161965/17931648. ------ 1. ==[ start ]==> (((a (^a.a)) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 161966/17931666. ------ 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))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 161967/17931675. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 161968/17931702. ------ 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)(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. ------ 161969/17931756. ------ 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) 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. ------ 161970/17931837. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)((a a) a))) REDUCED to normal form. ------ 161971/17931864. ------ 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. ------ 161972/17931891. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 161973/17931918. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 161974/17931945. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 161975/17932053. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 161976/17932098. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(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. ------ 161977/17932206. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 161978/17932287. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 161979/17932305. ------ 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. ------ 161980/17932332. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a 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. ------ 161981/17932386. ------ 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. ------ 161982/17932413. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (a a))(^b.b))) 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. ------ 161983/17932422. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161984/17932449. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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 REDUCED to normal form. ------ 161985/17932503. ------ 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.(^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. ------ 161986/17932638. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 161987/17932971. ------ 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. ------ 161988/17932998. ------ 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)(b ((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a) a)(b ((^x.x) a))) 5. ==[ beta ]==> ((((a a) a) a)(b a)) REDUCED to normal form. ------ 161989/17933052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^x1.x1))) REDUCED to normal form. ------ 161990/17933079. ------ 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)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 161991/17933106. ------ 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. ------ 161992/17933133. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 161993/17933160. ------ 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. ------ 161994/17933331. ------ 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. ------ 161995/17933358. ------ 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. ------ 161996/17933367. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 161997/17933529. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 161998/17933556. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 161999/17933583. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 162000/17933637. ------ 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. ------ 162001/17933745. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 162002/17933763. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) b) c)) 3. ==[ beta ]==> (((a a)(a b))(b c)) REDUCED to normal form. ------ 162003/17933988. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 162004/17934042. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(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. ------ 162005/17934132. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> (((a b) b)(b (a (^y.y)))) 4. ==[ alpha ]==> (((a b) b)(b (a (^x.x)))) REDUCED to normal form. ------ 162006/17934159. ------ 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) a))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))((^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. ------ 162007/17934186. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 162008/17934213. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 162009/17934267. ------ 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. ------ 162010/17934294. ------ 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.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(y y))(((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a) a)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a) a)((^y.y)(a a)))(((a a) a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a) a)((^y.y)(a a)))) 9. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)((^y.y)(a a)))) 10. ==[ alpha ]==> ((((a a) a)(a a))(((a a) a)((^x.x)(a a)))) 11. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 162011/17934321. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.a))((a a)(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 162012/17934348. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(b a))) REDUCED to normal form. ------ 162013/17934375. ------ 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)(^x.x))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 162014/17934465. ------ 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. ------ 162015/17934492. ------ 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. ------ 162016/17934519. ------ 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. ------ 162017/17934546. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) a)((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a) a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 162018/17934573. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 162019/17934627. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.b))) REDUCED to normal form. ------ 162020/17934663. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 162021/17934798. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 162022/17934879. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 162023/17934960. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 162024/17935041. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 162025/17935194. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y) b)) 3. ==[ beta ]==> ((a (a b))((^y.y) b)) 4. ==[ alpha ]==> ((a (a b))((^x.x) b)) 5. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 162026/17935473. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b (^z.z))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b (^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b (^z.z))) 5. ==[ beta ]==> (b (b (^z.z))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 162027/17935554. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 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. ------ 162028/17935662. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.b)((a a) a))) 3. ==[ beta ]==> ((b a)((^y.b)((a a) a))) 4. ==[ alpha ]==> ((b a)((^x.b)((a a) a))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 162029/17935743. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 162030/17935824. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^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)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 162031/17936166. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 162032/17936211. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 162033/17936499. ------ 1. ==[ start ]==> (((^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 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. ------ 162034/17936553. ------ 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) 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. ------ 162035/17936607. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 162036/17936688. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((^y1.y1)(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. ------ 162037/17936796. ------ 1. ==[ start ]==> (((^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.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162038/17937102. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 162039/17937138. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((a b)((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((a b)((^x.(^y.y)) c)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 162040/17937309. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 162041/17937471. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(a (a a)))) 5. ==[ beta ]==> (b ((^y.b)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.b)(a (a a)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 162042/17937552. ------ 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 z))(a b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(z z))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(z z))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 162043/17937633. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 162044/17937741. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^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. ------ 162045/17937948. ------ 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. ------ 162046/17937975. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(a a)) c)) 3. ==[ beta ]==> (((a b)((a a) a))(a a)) REDUCED to normal form. ------ 162047/17938308. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 162048/17938416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 162049/17938497. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 162050/17938524. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.a)(^z.(z z))) 6. ==[ alpha ]==> ((^x.a)(^y.(y y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 162051/17938578. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))(^y.a))) 5. ==[ beta ]==> (((b a)(b a))((^y.a)(^y.a))) 6. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.a))) 7. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 162052/17938641. ------ 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. ------ 162053/17938659. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)(^c.(^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)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 162054/17938668. ------ 1. ==[ start ]==> (((a b)(^a.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 162055/17938722. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 162056/17938776. ------ 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. ------ 162057/17938803. ------ 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. ------ 162058/17938830. ------ 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 a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a ((a a) a))) REDUCED to normal form. ------ 162059/17938920. ------ 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)(a a))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^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. ------ 162060/17938947. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 162061/17938974. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 162062/17939001. ------ 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)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^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))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^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. ------ 162063/17939028. ------ 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. ------ 162064/17939082. ------ 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 (^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 162065/17939136. ------ 1. ==[ start ]==> (((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)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a) a)) REDUCED to normal form. ------ 162066/17939163. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b) b)) 3. ==[ beta ]==> ((b (a (^y.y)))((a b) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b) b)) REDUCED to normal form. ------ 162067/17939307. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162068/17939532. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)(a b))) 3. ==[ beta ]==> ((b c)((a a)(a b))) REDUCED to normal form. ------ 162069/17939604. ------ 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)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 162070/17939631. ------ 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))((^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. ------ 162071/17939685. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 162072/17939766. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 162073/17939874. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(^b.(^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. ------ 162074/17939910. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b ((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(b ((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(b ((a a) a))) REDUCED to normal form. ------ 162075/17939937. ------ 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. ------ 162076/17940000. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 162077/17940135. ------ 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. ------ 162078/17940162. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(^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. ------ 162079/17940189. ------ 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. ------ 162080/17940216. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.(y y)))) REDUCED to normal form. ------ 162081/17940297. ------ 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 ]==> ((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. ------ 162082/17940324. ------ 1. ==[ start ]==> ((((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)) b)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z) b)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y) b)) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 162083/17940549. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.(x1 x1)))) 3. ==[ beta ]==> (b (c (^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (c (^x.(x x)))) REDUCED to normal form. ------ 162084/17940657. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162085/17940792. ------ 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.(^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. ------ 162086/17940819. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(^b.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. ------ 162087/17940873. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((b b)(^y.(^z.z))) 10. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 162088/17940882. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(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. ------ 162089/17940909. ------ 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. ------ 162090/17940954. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (^b.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. ------ 162091/17940963. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 162092/17940990. ------ 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. ------ 162093/17941062. ------ 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 (^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. ------ 162094/17941071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c c)) REDUCED to normal form. ------ 162095/17941197. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^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. ------ 162096/17941242. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a a)) REDUCED to normal form. ------ 162097/17941269. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a) b)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a) b)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a) b)) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 162098/17941296. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^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. ------ 162099/17941350. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) 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. ------ 162100/17941377. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 162101/17941404. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 162102/17941431. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 162103/17941512. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.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. ------ 162104/17941539. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^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. ------ 162105/17941593. ------ 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))) REDUCED to normal form. ------ 162106/17941611. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b b)) 3. ==[ beta ]==> ((a (^y.y))(b b)) 4. ==[ alpha ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 162107/17941620. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 162108/17941629. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((^z.z)(a (^x1.x1)))(^y.y)) 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. ------ 162109/17952426. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 162110/17952540. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) b)(a (a a)))) 3. ==[ eta ]==> ((^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. ------ 162111/17952810. ------ 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. ------ 162112/17953035. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162113/17953263. ------ 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. ------ 162114/17954451. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 162115/17954493. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a)) b)) 3. ==[ beta ]==> (^y.((((a a)(a a)) b)(((a a)(a a)) b))) 4. ==[ alpha ]==> (^x.((((a a)(a a)) b)(((a a)(a a)) b))) REDUCED to normal form. ------ 162116/17955189. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 162117/17955549. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 162118/17955558. ------ 1. ==[ start ]==> (((a b) c)(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.((a a)(a a)))) REDUCED to normal form. ------ 162119/17955918. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((y y)(y y)))) REDUCED to normal form. ------ 162120/17956131. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ eta ]==> (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 ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 162121/17956575. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.(^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. ------ 162122/17956584. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 162123/17956917. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^z.b)) REDUCED to normal form. ------ 162124/17956968. ------ 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 ]==> (((b a)(a (^x1.x1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((b a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 162125/17957571. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((b a) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162126/17957886. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 162127/17958384. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 162128/17958393. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(y a))) REDUCED to normal form. ------ 162129/17958672. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))((^z.z)(a a))) b) 4. ==[ beta ]==> (((^y.y)((^z.z)(a a))) b) 5. ==[ alpha ]==> (((^x.x)((^y.y)(a a))) b) 6. ==[ beta ]==> (((^y.y)(a a)) b) 7. ==[ alpha ]==> (((^x.x)(a a)) b) 8. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 162130/17958885. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((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)(a a))))) 4. ==[ alpha ]==> ((((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)(a a))))) 5. ==[ beta ]==> ((((a (^x.x))(a a))((a (^z.z))((^x1.x1)(a a))))(((a (^y1.y1))((^z1.z1)(a a)))((a (^x2.x2))((^y2.y2)(a a))))) 6. ==[ alpha ]==> ((((a (^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))))) 7. ==[ beta ]==> ((((a (^x.x))(a a))((a (^y.y))(a a)))(((a (^x1.x1))((^y1.y1)(a a)))((a (^z1.z1))((^x2.x2)(a a))))) 8. ==[ alpha ]==> ((((a (^x.x))(a a))((a (^y.y))(a a)))(((a (^z.z))((^x1.x1)(a a)))((a (^y1.y1))((^z1.z1)(a a))))) 9. ==[ beta ]==> ((((a (^x.x))(a a))((a (^y.y))(a a)))(((a (^z.z))(a a))((a (^y1.y1))((^z1.z1)(a a))))) 10. ==[ alpha ]==> ((((a (^x.x))(a a))((a (^y.y))(a a)))(((a (^z.z))(a a))((a (^x1.x1))((^y1.y1)(a a))))) 11. ==[ beta ]==> ((((a (^x.x))(a a))((a (^y.y))(a a)))(((a (^z.z))(a a))((a (^x1.x1))(a a)))) REDUCED to normal form. ------ 162131/17959167. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 162132/17959419. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 162133/17959644. ------ 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)(^y.(a a))) REDUCED to normal form. ------ 162134/17960283. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.b))) 3. ==[ beta ]==> ((b c)(^y.(^z.b))) 4. ==[ alpha ]==> ((b c)(^x.(^y.b))) REDUCED to normal form. ------ 162135/17960310. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(x x)))) REDUCED to normal form. ------ 162136/17960688. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 162137/17960859. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.((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))) REDUCED to normal form. ------ 162138/17961633. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 162139/17961768. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 162140/17961876. ------ 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. ------ 162141/17961993. ------ 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. ------ 162142/17962263. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> ((((^x.x) 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. ------ 162143/17962368. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b b)) 3. ==[ beta ]==> ((b b)((b b)(^y.y))) 4. ==[ alpha ]==> ((b b)((b b)(^x.x))) REDUCED to normal form. ------ 162144/17962617. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (a ((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 162145/17962698. ------ 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))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 162146/17962806. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 162147/17962824. ------ 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)((^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. ------ 162148/17962869. ------ 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. ------ 162149/17962896. ------ 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))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 162150/17962923. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 5. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 162151/17963112. ------ 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 (^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. ------ 162152/17963139. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 162153/17963166. ------ 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. ------ 162154/17963193. ------ 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. ------ 162155/17963283. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 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))) REDUCED to normal form. ------ 162156/17963310. ------ 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. ------ 162157/17963337. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(y1 y1)))) 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. ------ 162158/17963346. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a (a a))) REDUCED to normal form. ------ 162159/17963373. ------ 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.(^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. ------ 162160/17963391. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 162161/17963418. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 162162/17963508. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)(b a))) 3. ==[ beta ]==> ((b b)((^y.a)(b a))) 4. ==[ alpha ]==> ((b b)((^x.a)(b a))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 162163/17963553. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (a a))(^b.b))) 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. ------ 162164/17963643. ------ 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. ------ 162165/17963688. ------ 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) REDUCED to normal form. ------ 162166/17963751. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(y y))) REDUCED to normal form. ------ 162167/17963778. ------ 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. ------ 162168/17964327. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^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. ------ 162169/17964354. ------ 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.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 162170/17964381. ------ 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. ------ 162171/17964408. ------ 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. ------ 162172/17964435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 162173/17964498. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 162174/17964579. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)(^z.(^x1.x1)))) IRREDUCIBLE: cycle. ------ 162175/17964642. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 162176/17964660. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 162177/17964669. ------ 1. ==[ start ]==> (((a b) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 162178/17964687. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a) a)(^c.(^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. ------ 162179/17964696. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 162180/17964750. ------ 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 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 162181/17964768. ------ 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. ------ 162182/17964777. ------ 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. ------ 162183/17964804. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 162184/17964831. ------ 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. ------ 162185/17964849. ------ 1. ==[ start ]==> (((^a.b)(a a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a a))((b (^y.y)) a)) 3. ==[ beta ]==> (b ((b (^y.y)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 162186/17964876. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 162187/17965047. ------ 1. ==[ start ]==> (((^a.b) b)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 162188/17965254. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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 a)) REDUCED to normal form. ------ 162189/17965542. ------ 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)(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 (^x.x)) b)) REDUCED to normal form. ------ 162190/17965569. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 162191/17965695. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 162192/17965794. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 162193/17965929. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 162194/17965938. ------ 1. ==[ start ]==> (((a b) c)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.x)((a a)(a a)))) 3. ==[ beta ]==> (((a b) c)((a a)(a a))) REDUCED to normal form. ------ 162195/17965965. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.y))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 162196/17965992. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b)(^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. ------ 162197/17966073. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 162198/17966127. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162199/17966181. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 162200/17966235. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 162201/17966271. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b ((^y.y) b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 162202/17966298. ------ 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)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a ((a a)(a a)))) REDUCED to normal form. ------ 162203/17966325. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b)(a a))) 3. ==[ beta ]==> ((a (a b))(((^y.y) b)(a a))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b)(a a))) 5. ==[ beta ]==> ((a (a b))(b (a a))) REDUCED to normal form. ------ 162204/17966352. ------ 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)))) REDUCED to normal form. ------ 162205/17966379. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a)((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((b a)((^z.z) a))) 8. ==[ alpha ]==> ((^x.x)((b a)((^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. ------ 162206/17966406. ------ 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. ------ 162207/17966433. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(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. ------ 162208/17966460. ------ 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. ------ 162209/17966487. ------ 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. ------ 162210/17966514. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.x)((^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. ------ 162211/17966685. ------ 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.(^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. ------ 162212/17966748. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 162213/17966793. ------ 1. ==[ start ]==> (((^a.a)(b a))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((a b)(^y.a))) 3. ==[ beta ]==> ((b a)((a b)(^y.a))) 4. ==[ alpha ]==> ((b a)((a b)(^x.a))) REDUCED to normal form. ------ 162214/17966820. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 162215/17966856. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 162216/17966874. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 162217/17966883. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 162218/17966937. ------ 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 (^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. ------ 162219/17966955. ------ 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)(^y.y))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 162220/17966964. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z) b)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) b)) 5. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 162221/17966991. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.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. ------ 162222/17967018. ------ 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.(^y2.y2)))) 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. ------ 162223/17967243. ------ 1. ==[ start ]==> (((a b)(a (a a)))(c (b a))) REDUCED to normal form. ------ 162224/17967270. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 162225/17967297. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a b)) REDUCED to normal form. ------ 162226/17967351. ------ 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. ------ 162227/17967630. ------ 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.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. ------ 162228/17967639. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 162229/17967657. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 162230/17967684. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((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. ------ 162231/17967738. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((a b)(^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 162232/17967747. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 162233/17967774. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((a a) a))) 5. ==[ beta ]==> ((^y.b)((^z.a)((a a) a))) 6. ==[ alpha ]==> ((^x.b)((^y.a)((a a) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 162234/17967819. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 162235/17967828. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 162236/17967855. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 162237/17967882. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(b 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. ------ 162238/17967927. ------ 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))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162239/17967936. ------ 1. ==[ start ]==> (((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.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. ------ 162240/17967954. ------ 1. ==[ start ]==> ((a (^b.b))((b a) b)) 2. ==[ alpha ]==> ((a (^x.x))((b a) b)) REDUCED to normal form. ------ 162241/17968188. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b (b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (b a))) REDUCED to normal form. ------ 162242/17968242. ------ 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. ------ 162243/17968269. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 162244/17968278. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) 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. ------ 162245/17968548. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162246/17968557. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 162247/17968584. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((b a)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b a)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 162248/17968602. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(^y.(y y)))) 5. ==[ beta ]==> (b ((a b)(^y.(y y)))) 6. ==[ alpha ]==> (b ((a b)(^x.(x x)))) REDUCED to normal form. ------ 162249/17968611. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 162250/17968629. ------ 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.(^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. ------ 162251/17968683. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (a a))(^z.b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (a a))(^z.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (a a))(^z.b))) REDUCED to normal form. ------ 162252/17968719. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)((^z.z)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162253/17968746. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^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. ------ 162254/17968773. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(b a))) 3. ==[ beta ]==> (((a b)(^x.a))(b a)) REDUCED to normal form. ------ 162255/17968881. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 162256/17968908. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.a)(^b.(^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. ------ 162257/17968998. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b a))(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (b a))(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((a (b a))(c (a a))) REDUCED to normal form. ------ 162258/17969025. ------ 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 a)(^y.y)))) REDUCED to normal form. ------ 162259/17969052. ------ 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. ------ 162260/17969079. ------ 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))) REDUCED to normal form. ------ 162261/17969106. ------ 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. ------ 162262/17969133. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 162263/17969160. ------ 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. ------ 162264/17969214. ------ 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 a))((a a) a))) REDUCED to normal form. ------ 162265/17969241. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)(a b))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) a)(a b))) 5. ==[ beta ]==> ((b (a a))(a (a b))) REDUCED to normal form. ------ 162266/17969268. ------ 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. ------ 162267/17969439. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 162268/17969547. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a a)(^c.(^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. ------ 162269/17969583. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 162270/17969610. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a))(^a.(^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. ------ 162271/17969628. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a b) c)) 3. ==[ beta ]==> (((a a)(a a))((a b) c)) REDUCED to normal form. ------ 162272/17969664. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.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. ------ 162273/17969691. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 162274/17969772. ------ 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.(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. ------ 162275/17969799. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 162276/17969997. ------ 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. ------ 162277/17970024. ------ 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)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(a a))) REDUCED to normal form. ------ 162278/17970519. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b) b)) 3. ==[ beta ]==> (b ((^z.b) b)) 4. ==[ alpha ]==> (b ((^x.b) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 162279/17970663. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b (^y.b))) 3. ==[ beta ]==> ((b c)(b (^y.b))) 4. ==[ alpha ]==> ((b c)(b (^x.b))) REDUCED to normal form. ------ 162280/17970690. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(a (^x.(a a)))) REDUCED to normal form. ------ 162281/17970735. ------ 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. ------ 162282/17970762. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^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. ------ 162283/17970798. ------ 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. ------ 162284/17970816. ------ 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.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 162285/17970825. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 162286/17970897. ------ 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 b) a)) REDUCED to normal form. ------ 162287/17970906. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 162288/17970933. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 162289/17971014. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 162290/17971041. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 162291/17971068. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 162292/17971131. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 162293/17971158. ------ 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. ------ 162294/17971185. ------ 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. ------ 162295/17971212. ------ 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 (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 162296/17971239. ------ 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. ------ 162297/17971599. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.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. ------ 162298/17971680. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) d)) 3. ==[ beta ]==> (b ((^x1.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 162299/17971788. ------ 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. ------ 162300/17971905. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 162301/17971923. ------ 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. ------ 162302/17971950. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a) c)) 5. ==[ beta ]==> (((^y.y) a) c) 6. ==[ alpha ]==> (((^x.x) a) c) 7. ==[ beta ]==> (a c) REDUCED to normal form. ------ 162303/17972013. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 162304/17972085. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.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. ------ 162305/17972094. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 162306/17972121. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b (^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.(y y)))) REDUCED to normal form. ------ 162307/17972148. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 162308/17972193. ------ 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.(^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. ------ 162309/17972202. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 162310/17972229. ------ 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))((^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. ------ 162311/17972256. ------ 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. ------ 162312/17972310. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(^a.(^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. ------ 162313/17972346. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 162314/17972373. ------ 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. ------ 162315/17972400. ------ 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. ------ 162316/17972427. ------ 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 (^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)))) REDUCED to normal form. ------ 162317/17972454. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 162318/17972508. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c b)) REDUCED to normal form. ------ 162319/17972535. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b c)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b c)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b c)) 5. ==[ beta ]==> (((a a)(a a))(b c)) REDUCED to normal form. ------ 162320/17972616. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a (^x1.x1)))) REDUCED to normal form. ------ 162321/17972643. ------ 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 ]==> ((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. ------ 162322/17972670. ------ 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))) REDUCED to normal form. ------ 162323/17972742. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^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. ------ 162324/17972751. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b b)) REDUCED to normal form. ------ 162325/17972760. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)(^a.(^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. ------ 162326/17983392. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^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)))) 5. ==[ beta ]==> ((a a)((^x1.(a a))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 162327/17983593. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 162328/17983617. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^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 ]==> (^x.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 162329/17983860. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a) a)(b a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 162330/17983998. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 162331/17984310. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(^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. ------ 162332/17984742. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(a a))(^b.b))) 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 ]==> ((((^y.y)(^y.y))((^z.(z z))(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.(z z))(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 7. ==[ beta ]==> (((^y.y)((^z.(z z))(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)((^y.(y y))(^z.z)))((^x1.(x1 x1))(^y1.y1))) 9. ==[ beta ]==> (((^y.(y y))(^z.z))((^x1.(x1 x1))(^y1.y1))) 10. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.x1))) 11. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.x1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 13. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 14. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 15. ==[ beta ]==> ((^y.(y y))(^z.z)) 16. ==[ alpha ]==> ((^x.(x x))(^y.y)) 17. ==[ beta ]==> ((^y.y)(^y.y)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162333/17984835. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(x x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.a)(^y.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(^x1.x1))) 7. ==[ beta ]==> (a (^z.(^x1.x1))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 162334/17985075. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 162335/17986524. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((((^z.(a a))((a a) a))((^z.(a a))((a a) a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(a a))((a a) a))((^y.(a a))((a a) a)))(^z.z)) 5. ==[ beta ]==> (((a a)((^y.(a a))((a a) a)))(^z.z)) 6. ==[ alpha ]==> (((a a)((^x.(a 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. ------ 162336/17986707. ------ 1. ==[ start ]==> (((a b) c)(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(a a)))) REDUCED to normal form. ------ 162337/17987067. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 162338/17987733. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 162339/17988066. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 162340/17989542. ------ 1. ==[ start ]==> (((a b)(^c.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 162341/17990073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 162342/17991036. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^z.(a a))) REDUCED to normal form. ------ 162343/17991114. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 162344/17992035. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 162345/17992197. ------ 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))) REDUCED to normal form. ------ 162346/17992275. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))(^y1.a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162347/17992368. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.((z z) z))) 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. ------ 162348/17993025. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 162349/17993142. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 162350/17993250. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 162351/17993331. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 162352/17993412. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^b.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. ------ 162353/17993493. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.y))) 5. ==[ beta ]==> ((a a)(^y.(^z.y))) 6. ==[ alpha ]==> ((a a)(^x.(^y.x))) REDUCED to normal form. ------ 162354/17993517. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^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. ------ 162355/17993784. ------ 1. ==[ start ]==> ((a (a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 162356/17993865. ------ 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. ------ 162357/17993955. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(b ((^a.(^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 (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 162358/17993982. ------ 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 (^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. ------ 162359/17993991. ------ 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 (^x.x))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 162360/17994009. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 162361/17994090. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 162362/17994117. ------ 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 (^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. ------ 162363/17994171. ------ 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. ------ 162364/17994198. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(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. ------ 162365/17994252. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(b a))) REDUCED to normal form. ------ 162366/17994360. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> (((a (^y.y))(b (^z.z)))((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 162367/17994387. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.(^y1.y1)) 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. ------ 162368/17994423. ------ 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. ------ 162369/17994450. ------ 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. ------ 162370/17994477. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 162371/17994504. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(b (^z.(z z)))) REDUCED to normal form. ------ 162372/17994531. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 162373/17994558. ------ 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. ------ 162374/17994621. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 162375/17994648. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 162376/17994702. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(^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)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 162377/17994828. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) 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)) 7. ==[ beta ]==> (a ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162378/17994855. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z)) b)) REDUCED to normal form. ------ 162379/17995026. ------ 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. ------ 162380/17995053. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 162381/17995107. ------ 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. ------ 162382/17995134. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(^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. ------ 162383/17995170. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(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. ------ 162384/17995224. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a (a ((^z.(^x1.x1)) 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. ------ 162385/17995305. ------ 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. ------ 162386/17995332. ------ 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 (^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. ------ 162387/17995386. ------ 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)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))((a a) a))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 162388/17995467. ------ 1. ==[ start ]==> ((a (^a.b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 162389/17995638. ------ 1. ==[ start ]==> (((^a.b) a)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 162390/17995800. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x)(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. ------ 162391/17995827. ------ 1. ==[ start ]==> (((a b) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 162392/17995854. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 162393/17995908. ------ 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))(^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. ------ 162394/17995935. ------ 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. ------ 162395/17995962. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)((a (^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.y))(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 162396/17996016. ------ 1. ==[ start ]==> (((a b)(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 162397/17996052. ------ 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 a)) REDUCED to normal form. ------ 162398/17996079. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.a)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.a)) REDUCED to normal form. ------ 162399/17996106. ------ 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)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 162400/17996187. ------ 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. ------ 162401/17996214. ------ 1. ==[ start ]==> (((a b)(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 162402/17996331. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c ((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c ((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c ((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)(c ((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.x)(c ((^y.y) b))) 7. ==[ beta ]==> (c ((^y.y) b)) 8. ==[ alpha ]==> (c ((^x.x) b)) 9. ==[ beta ]==> (c b) REDUCED to normal form. ------ 162403/17996412. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 162404/17996421. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b) b)((^x.(a a)) b)) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 162405/17996448. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y) c)) 3. ==[ beta ]==> (((a a) a)((^y.y) c)) 4. ==[ alpha ]==> (((a a) a)((^x.x) c)) 5. ==[ beta ]==> (((a a) a) c) REDUCED to normal form. ------ 162406/17996466. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^x1.x1) a))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((^z.z) a))) 7. ==[ beta ]==> ((a a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 162407/17996493. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 162408/17996547. ------ 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)(a a))((a a) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((a a) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((a a) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a) a))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a) a))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 11. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 12. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 13. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 162409/17996628. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 162410/17996727. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.(a a)))) REDUCED to normal form. ------ 162411/17996808. ------ 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. ------ 162412/17996835. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 162413/17996853. ------ 1. ==[ start ]==> (((^a.b) c)((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 162414/17996916. ------ 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 a)) REDUCED to normal form. ------ 162415/17997096. ------ 1. ==[ start ]==> (((a b) c)((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)((a a)(^x.(a a)))) REDUCED to normal form. ------ 162416/17997123. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(a a)) a)) 3. ==[ beta ]==> (((a a) b)(((a a)(a a)) a)) REDUCED to normal form. ------ 162417/17997150. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b b)) REDUCED to normal form. ------ 162418/17997429. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^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. ------ 162419/17997762. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 162420/17997906. ------ 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 z)))) REDUCED to normal form. ------ 162421/17998014. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.(a a)))(^z.(a a))) 8. ==[ alpha ]==> ((a (^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 162422/17998041. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 162423/17998095. ------ 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))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 162424/17998122. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 162425/17998149. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b) a)) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b) a)) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b) a)) 5. ==[ beta ]==> (((a a)(^x.a))(b a)) REDUCED to normal form. ------ 162426/17998176. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1))) b)) REDUCED to normal form. ------ 162427/17998239. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 162428/17998266. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 162429/17998293. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a (a a))((^y.b)(^z.a))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(^y.a))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 162430/17998320. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.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. ------ 162431/17998347. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 162432/17998428. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 162433/17998455. ------ 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)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 162434/17998500. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 162435/17998518. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162436/17998599. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a b)((^z.z)(^x1.x1)))) 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. ------ 162437/17998680. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 162438/17998797. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 162439/17998824. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 162440/17998905. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 162441/17998932. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(^z.a))) 5. ==[ beta ]==> ((^y.b)(((a a) a)(^z.a))) 6. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 162442/17998986. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 162443/17999094. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1))) a)) REDUCED to normal form. ------ 162444/17999157. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 162445/17999184. ------ 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.(x1 x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 162446/17999211. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 162447/17999238. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 162448/17999265. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 162449/17999292. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 162450/17999319. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.a)(^c.(^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. ------ 162451/17999391. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 162452/17999436. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a (^x1.x1)))) 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. ------ 162453/17999463. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))((^x2.x2) 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. ------ 162454/17999598. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 162455/17999715. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 162456/17999742. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(a a))(^b.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. ------ 162457/17999769. ------ 1. ==[ start ]==> (((a a)(^b.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(y y)))) REDUCED to normal form. ------ 162458/17999796. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 162459/17999877. ------ 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) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162460/17999904. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 162461/17999931. ------ 1. ==[ start ]==> (((a b)(^c.a))((a a)(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 162462/17999958. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 162463/17999985. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 162464/18000102. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(^a.a))(^c.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. ------ 162465/18000129. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.b)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)(^y1.b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 162466/18000156. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 162467/18000462. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((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. ------ 162468/18000741. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 162469/18000768. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a) b)) REDUCED to normal form. ------ 162470/18000948. ------ 1. ==[ start ]==> (((^a.b)(a b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (b (b ((^y.y)(a a)))) 4. ==[ alpha ]==> (b (b ((^x.x)(a a)))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 162471/18001011. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 162472/18001056. ------ 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)((^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. ------ 162473/18001065. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a) d)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a) d)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 162474/18001182. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b (^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(a a)))) REDUCED to normal form. ------ 162475/18001236. ------ 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 a)) REDUCED to normal form. ------ 162476/18001263. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 162477/18001317. ------ 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. ------ 162478/18001344. ------ 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))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)((a a) a))((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.z))) 10. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.y))) 11. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 12. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 162479/18001371. ------ 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 a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 162480/18001425. ------ 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.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. ------ 162481/18001452. ------ 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))) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 162482/18001479. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(^a.(^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. ------ 162483/18001506. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 162484/18001677. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b)(a a))) 3. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 162485/18001785. ------ 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)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162486/18001956. ------ 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. ------ 162487/18001983. ------ 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.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. ------ 162488/18002064. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b) a)) REDUCED to normal form. ------ 162489/18002091. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a) b)) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a) b)) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a) b)) REDUCED to normal form. ------ 162490/18002397. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (^z.a))) 3. ==[ beta ]==> (((^y.y)(b a))(b (^z.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (^y.a))) 5. ==[ beta ]==> ((b a)(b (^y.a))) 6. ==[ alpha ]==> ((b a)(b (^x.a))) REDUCED to normal form. ------ 162491/18002424. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.b))) REDUCED to normal form. ------ 162492/18002451. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.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) REDUCED to normal form. ------ 162493/18002478. ------ 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 (^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. ------ 162494/18002505. ------ 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 y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 162495/18002559. ------ 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.(^x1.x1))((^y1.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. ------ 162496/18002586. ------ 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. ------ 162497/18002667. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 162498/18002757. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 162499/18002838. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (b (((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (b (((^x.x) 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. ------ 162500/18003063. ------ 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 ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162501/18003162. ------ 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. ------ 162502/18003198. ------ 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.(^x2.x2)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162503/18003243. ------ 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 (^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. ------ 162504/18003252. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 162505/18003360. ------ 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.(^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. ------ 162506/18003387. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))(^b.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. ------ 162507/18003414. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.(y y)))) REDUCED to normal form. ------ 162508/18003468. ------ 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. ------ 162509/18003504. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^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. ------ 162510/18003531. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(z z))) REDUCED to normal form. ------ 162511/18003585. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (^a.(^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. ------ 162512/18003612. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b (^b.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. ------ 162513/18003639. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.(x x)))) REDUCED to normal form. ------ 162514/18003666. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.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. ------ 162515/18003693. ------ 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)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 162516/18003720. ------ 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. ------ 162517/18003774. ------ 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.(^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. ------ 162518/18003801. ------ 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))) 5. ==[ beta ]==> ((b (a (a a)))(^y.a)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.a)) REDUCED to normal form. ------ 162519/18003882. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 162520/18003900. ------ 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))) REDUCED to normal form. ------ 162521/18003909. ------ 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)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 162522/18003918. ------ 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 ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 162523/18014769. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 162524/18014778. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 162525/18015486. ------ 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.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162526/18016431. ------ 1. ==[ start ]==> ((^a.(a b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x b))((b (^y.y))(^z.z))) 3. ==[ beta ]==> (((b (^y.y))(^z.z)) b) 4. ==[ alpha ]==> (((b (^x.x))(^y.y)) b) REDUCED to normal form. ------ 162527/18016794. ------ 1. ==[ start ]==> (((^a.b)(a a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(y (^z.z)))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 162528/18019293. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1))) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 162529/18019575. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 162530/18019872. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 162531/18019896. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^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. ------ 162532/18020178. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 162533/18022290. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a) a) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 162534/18022635. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(a b))) REDUCED to normal form. ------ 162535/18022842. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(a z))) 3. ==[ eta ]==> (((^x.b)((^y.y)(a a))) a) 4. ==[ beta ]==> (b a) REDUCED to normal form. ------ 162536/18023373. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.a))) 5. ==[ beta ]==> ((b a)(^y.(^z.a))) 6. ==[ alpha ]==> ((b a)(^x.(^y.a))) REDUCED to normal form. ------ 162537/18023544. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.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. ------ 162538/18023985. ------ 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)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162539/18024093. ------ 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. ------ 162540/18024270. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(^a.(^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. ------ 162541/18024318. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.d)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.d)) REDUCED to normal form. ------ 162542/18024507. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.a))) REDUCED to normal form. ------ 162543/18024588. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 162544/18024669. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.c)) 3. ==[ beta ]==> (((^y.y)(a a))(^z.c)) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.c)) 5. ==[ beta ]==> ((a a)(^y.c)) 6. ==[ alpha ]==> ((a a)(^x.c)) REDUCED to normal form. ------ 162545/18024693. ------ 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))) REDUCED to normal form. ------ 162546/18024978. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(a a))(^c.(^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. ------ 162547/18025149. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 162548/18025167. ------ 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)((^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. ------ 162549/18025176. ------ 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. ------ 162550/18025230. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 162551/18025311. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 162552/18025338. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b a)((a a) a))) 3. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 162553/18025365. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 162554/18025392. ------ 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))((^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. ------ 162555/18025419. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 162556/18025527. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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)))) 5. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 162557/18025734. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 162558/18025779. ------ 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. ------ 162559/18025806. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.(a a)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.(a a)))) REDUCED to normal form. ------ 162560/18025833. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 162561/18025887. ------ 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.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 162562/18025896. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(^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. ------ 162563/18025923. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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. ------ 162564/18025977. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 162565/18026112. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z z))) REDUCED to normal form. ------ 162566/18026355. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(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. ------ 162567/18026445. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b (^z.z))(a a))) 3. ==[ beta ]==> (((^y.y) b)((b (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(a a))) 5. ==[ beta ]==> (b ((b (^y.y))(a a))) 6. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 162568/18026472. ------ 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. ------ 162569/18026526. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^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. ------ 162570/18026553. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x)))((b a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))((b a)(^y.y))) REDUCED to normal form. ------ 162571/18026580. ------ 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. ------ 162572/18026607. ------ 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)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162573/18026634. ------ 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. ------ 162574/18026832. ------ 1. ==[ start ]==> ((a (a b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (a b))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 162575/18026922. ------ 1. ==[ start ]==> (((^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)))(a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(a (a a)))) IRREDUCIBLE: cycle. ------ 162576/18027003. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 162577/18027030. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 162578/18027111. ------ 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. ------ 162579/18027192. ------ 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 ((^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. ------ 162580/18027237. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(a a)) b)) REDUCED to normal form. ------ 162581/18027264. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) b) c)) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(b c)) REDUCED to normal form. ------ 162582/18027435. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162583/18027516. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.z1))) 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. ------ 162584/18027606. ------ 1. ==[ start ]==> (((a b) b)(((a a)(a a))(a a))) REDUCED to normal form. ------ 162585/18027633. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (((a a) a)(b (a (^y.y)))) 6. ==[ alpha ]==> (((a a) a)(b (a (^x.x)))) REDUCED to normal form. ------ 162586/18027660. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 162587/18027687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a)(a (a a)))) REDUCED to normal form. ------ 162588/18027741. ------ 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. ------ 162589/18027768. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(a b))) 5. ==[ beta ]==> ((^y.(y y))((a b)(a b))) 6. ==[ alpha ]==> ((^x.(x x))((a b)(a b))) 7. ==[ beta ]==> (((a b)(a b))((a b)(a b))) REDUCED to normal form. ------ 162590/18027795. ------ 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)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 162591/18027822. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((a a)(^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. ------ 162592/18027849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^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. ------ 162593/18027966. ------ 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))(^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. ------ 162594/18027993. ------ 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. ------ 162595/18028020. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (^a.(^a.a)))(^b.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))) REDUCED to normal form. ------ 162596/18028047. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 162597/18028074. ------ 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. ------ 162598/18028137. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 162599/18028272. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 162600/18028353. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b)(^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)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 162601/18028380. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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. ------ 162602/18028515. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 162603/18028668. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a)) a)) 3. ==[ beta ]==> ((a (a b))((^y.(a a)) a)) 4. ==[ alpha ]==> ((a (a b))((^x.(a a)) a)) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 162604/18028695. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.b) b)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x) b)) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 162605/18028947. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (c (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 162606/18029028. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)(a a))) 3. ==[ beta ]==> (b ((^z.z)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 162607/18029136. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 162608/18029163. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 162609/18029217. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 162610/18029298. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 162611/18029685. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 162612/18029694. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.(^y1.y1))) 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. ------ 162613/18029973. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 162614/18030000. ------ 1. ==[ start ]==> (((^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))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 162615/18030081. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a (a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a (a a)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 162616/18030162. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 162617/18030270. ------ 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))((^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. ------ 162618/18030297. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^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. ------ 162619/18030315. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a) b)) REDUCED to normal form. ------ 162620/18030342. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 162621/18030576. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(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. ------ 162622/18030585. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1))) 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. ------ 162623/18030783. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(d (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(d (^z.(a a)))) 3. ==[ beta ]==> (b (d (^z.(a a)))) 4. ==[ alpha ]==> (b (d (^x.(a a)))) REDUCED to normal form. ------ 162624/18030945. ------ 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) 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. ------ 162625/18030972. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.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. ------ 162626/18031026. ------ 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.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))((a 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. ------ 162627/18031107. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^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. ------ 162628/18031215. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 162629/18031449. ------ 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))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 162630/18031476. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 162631/18031647. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 162632/18031782. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 162633/18031890. ------ 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))((^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. ------ 162634/18031971. ------ 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.(^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. ------ 162635/18031998. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.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. ------ 162636/18032052. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(^a.a))(^b.(^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. ------ 162637/18032115. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(c (a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(c (a b))) REDUCED to normal form. ------ 162638/18032133. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 162639/18032142. ------ 1. ==[ start ]==> (((a b)(^a.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(b (a a))) REDUCED to normal form. ------ 162640/18032196. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^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. ------ 162641/18032250. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a) a)) REDUCED to normal form. ------ 162642/18032277. ------ 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. ------ 162643/18032304. ------ 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))(^x.x))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 162644/18032421. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(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. ------ 162645/18032448. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 162646/18032475. ------ 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. ------ 162647/18032502. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(y y))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(x x))) REDUCED to normal form. ------ 162648/18032529. ------ 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. ------ 162649/18032610. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a a)(^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. ------ 162650/18032637. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((b (a (^x.x)))((a a) a)) REDUCED to normal form. ------ 162651/18032664. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b) b)) REDUCED to normal form. ------ 162652/18032691. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a) c)) REDUCED to normal form. ------ 162653/18032781. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)(^y2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)(^y2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162654/18033006. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((b c)((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((b c)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 162655/18033033. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)(a b))) REDUCED to normal form. ------ 162656/18033078. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(a a))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 162657/18033159. ------ 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. ------ 162658/18033240. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 162659/18033348. ------ 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.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162660/18033384. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.a))(c (^z.z))) 6. ==[ alpha ]==> ((b (^x.a))(c (^y.y))) REDUCED to normal form. ------ 162661/18033411. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 162662/18033474. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a) b)) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 162663/18033501. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z)) c)) 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. ------ 162664/18033636. ------ 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. ------ 162665/18033663. ------ 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.(^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. ------ 162666/18033690. ------ 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. ------ 162667/18033744. ------ 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 (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 162668/18033771. ------ 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))) 5. ==[ beta ]==> ((b a)((a a)(^y.a))) 6. ==[ alpha ]==> ((b a)((a a)(^x.a))) REDUCED to normal form. ------ 162669/18033798. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 162670/18033942. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.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. ------ 162671/18034023. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (^x1.a))) 3. ==[ beta ]==> (b (d (^x1.a))) 4. ==[ alpha ]==> (b (d (^x.a))) REDUCED to normal form. ------ 162672/18034131. ------ 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. ------ 162673/18034266. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((^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. ------ 162674/18034293. ------ 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.(^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. ------ 162675/18034347. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(z z)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 162676/18034356. ------ 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. ------ 162677/18034383. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162678/18034437. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 162679/18034464. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a (^y.y)) a)) REDUCED to normal form. ------ 162680/18034491. ------ 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. ------ 162681/18034536. ------ 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 z1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162682/18034572. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c c)) 3. ==[ beta ]==> ((b (^y.(y y)))(c c)) 4. ==[ alpha ]==> ((b (^x.(x x)))(c c)) REDUCED to normal form. ------ 162683/18034671. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(^a.(^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. ------ 162684/18034743. ------ 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)) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y)) a)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x)) a)) 5. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 162685/18034770. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.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. ------ 162686/18034851. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 162687/18034878. ------ 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.(^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. ------ 162688/18034905. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.a))) REDUCED to normal form. ------ 162689/18034959. ------ 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 (^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1)) b)) REDUCED to normal form. ------ 162690/18034986. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a) c)) 3. ==[ beta ]==> ((b (a (a a)))((a a) c)) REDUCED to normal form. ------ 162691/18035013. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a) a)) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 162692/18035094. ------ 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. ------ 162693/18035103. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^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 ]==> (((^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. ------ 162694/18045981. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 162695/18045996. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (^y.((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (^x.((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (^x.(a (^z.z))) 6. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 162696/18046068. ------ 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) a))) 3. ==[ eta ]==> ((^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. ------ 162697/18046338. ------ 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. ------ 162698/18046413. ------ 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. ------ 162699/18046563. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162700/18046818. ------ 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 (^x.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 162701/18047997. ------ 1. ==[ start ]==> (((^a.b)(a a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 162702/18048006. ------ 1. ==[ start ]==> (((a b)(^a.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 162703/18048021. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b (^z.z)) a)) 3. ==[ beta ]==> (^y.(((b (^z.z)) a)((b (^z.z)) a))) 4. ==[ alpha ]==> (^x.(((b (^y.y)) a)((b (^z.z)) a))) REDUCED to normal form. ------ 162704/18049113. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^b.((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. ------ 162705/18049473. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.((y y)(y y)))) 3. ==[ beta ]==> ((a (a b))(^y.((y y)(y y)))) 4. ==[ alpha ]==> ((a (a b))(^x.((x x)(x x)))) REDUCED to normal form. ------ 162706/18049659. ------ 1. ==[ start ]==> ((^a.(b a))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(b x))(((a a) a)(a b))) 3. ==[ eta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 162707/18050139. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 162708/18050208. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 162709/18050496. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x1.(^y1.y1)))(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 162710/18050787. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 162711/18051084. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 162712/18051099. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162713/18051381. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 162714/18051390. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 162715/18051414. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 162716/18051948. ------ 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))) REDUCED to normal form. ------ 162717/18052227. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(b x))) 3. ==[ eta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 162718/18052413. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((((^y.y) a)(a b))(((^y.y) a)(a b)))((((^y.y) a)(a b))(((^y.y) a)(a b)))) 4. ==[ alpha ]==> (((((^x.x) a)(a b))(((^y.y) a)(a b)))((((^z.z) a)(a b))(((^x1.x1) a)(a b)))) 5. ==[ beta ]==> (((a (a b))(((^y.y) a)(a b)))((((^z.z) a)(a b))(((^x1.x1) a)(a b)))) 6. ==[ alpha ]==> (((a (a b))(((^x.x) a)(a b)))((((^y.y) a)(a b))(((^z.z) a)(a b)))) 7. ==[ beta ]==> (((a (a b))(a (a b)))((((^y.y) a)(a b))(((^z.z) a)(a b)))) 8. ==[ alpha ]==> (((a (a b))(a (a b)))((((^x.x) a)(a b))(((^y.y) a)(a b)))) 9. ==[ beta ]==> (((a (a b))(a (a b)))((a (a b))(((^y.y) a)(a b)))) 10. ==[ alpha ]==> (((a (a b))(a (a b)))((a (a b))(((^x.x) a)(a b)))) 11. ==[ beta ]==> (((a (a b))(a (a b)))((a (a b))(a (a b)))) REDUCED to normal form. ------ 162719/18052731. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 162720/18054045. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^z.(^x1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 162721/18054054. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(a y))) 3. ==[ eta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 162722/18055053. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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 (^x.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 162723/18055188. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162724/18055473. ------ 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. ------ 162725/18055548. ------ 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. ------ 162726/18055629. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^x.a)) REDUCED to normal form. ------ 162727/18055818. ------ 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) y))) 3. ==[ eta ]==> ((((a a)(a a))((^x.x) 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. ------ 162728/18055890. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.z))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 162729/18056199. ------ 1. ==[ start ]==> (((a a) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 162730/18056253. ------ 1. ==[ start ]==> (((^a.a) b)((^c.a)(^a.(^a.(^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))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 162731/18056280. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(^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. ------ 162732/18056307. ------ 1. ==[ start ]==> (((a a) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 162733/18056388. ------ 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)))) REDUCED to normal form. ------ 162734/18056406. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((a (^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.a))(a (^y.y))) REDUCED to normal form. ------ 162735/18056424. ------ 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. ------ 162736/18056451. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 162737/18056478. ------ 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))) 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. ------ 162738/18056487. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a)) d)) 3. ==[ beta ]==> ((^y.a)((^z.(a a)) d)) 4. ==[ alpha ]==> ((^x.a)((^y.(a a)) d)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 162739/18056667. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a) a)(b a))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(b a))) REDUCED to normal form. ------ 162740/18056694. ------ 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)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 162741/18056721. ------ 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. ------ 162742/18056748. ------ 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. ------ 162743/18056820. ------ 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. ------ 162744/18056838. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 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)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162745/18056865. ------ 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. ------ 162746/18056892. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.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. ------ 162747/18056901. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 162748/18056928. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 162749/18056946. ------ 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)))(^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. ------ 162750/18056955. ------ 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. ------ 162751/18056973. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 162752/18057063. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((b b)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b b)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 162753/18057108. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162754/18057135. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (a a))(^b.b))) 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. ------ 162755/18057198. ------ 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. ------ 162756/18057225. ------ 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 ((^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. ------ 162757/18057243. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^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) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 162758/18057270. ------ 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. ------ 162759/18057306. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 162760/18057333. ------ 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. ------ 162761/18057360. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 162762/18057882. ------ 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. ------ 162763/18057909. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(b a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(b a))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 162764/18057936. ------ 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. ------ 162765/18057963. ------ 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. ------ 162766/18057990. ------ 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 (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 162767/18058017. ------ 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. ------ 162768/18058053. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.b)((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.b)((b (^y.y))(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 162769/18058134. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) IRREDUCIBLE: cycle. ------ 162770/18058197. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(^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)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 162771/18058215. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 162772/18058224. ------ 1. ==[ start ]==> (((a b) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))(a b))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 162773/18058242. ------ 1. ==[ start ]==> (((^a.a)(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((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. ------ 162774/18058251. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 162775/18058305. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 162776/18058323. ------ 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. ------ 162777/18058332. ------ 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. ------ 162778/18058359. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.a)((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.a)((^y.a)((^z.z) b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 162779/18058386. ------ 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 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. ------ 162780/18058413. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x))(b (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 162781/18058431. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(a a)))((b (^y.y)) a)) REDUCED to normal form. ------ 162782/18058602. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 162783/18058863. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z) c)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y) c)) 5. ==[ beta ]==> ((a a)((^y.y) c)) 6. ==[ alpha ]==> ((a a)((^x.x) c)) 7. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 162784/18059097. ------ 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)(a a))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) 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. ------ 162785/18059124. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a (^y.y)) b)) REDUCED to normal form. ------ 162786/18059151. ------ 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. ------ 162787/18059250. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 162788/18059349. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((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. ------ 162789/18059484. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 162790/18059493. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 162791/18059520. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (((a a) b)((a a)(a a))) REDUCED to normal form. ------ 162792/18059565. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b) b)) 5. ==[ beta ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 162793/18059601. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.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. ------ 162794/18059682. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162795/18059709. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 162796/18059736. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 162797/18059763. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^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. ------ 162798/18059853. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b ((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b ((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b b)) REDUCED to normal form. ------ 162799/18059880. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(a ((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))(a ((a a)(a a)))) REDUCED to normal form. ------ 162800/18059907. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(b (a a))) REDUCED to normal form. ------ 162801/18059934. ------ 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)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a (^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (^x1.x1)))) 9. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.x1))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 162802/18059961. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((b a) a)) REDUCED to normal form. ------ 162803/18059988. ------ 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. ------ 162804/18060015. ------ 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. ------ 162805/18060042. ------ 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. ------ 162806/18060069. ------ 1. ==[ start ]==> ((a (b a))(((a a) a)(a b))) REDUCED to normal form. ------ 162807/18060240. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 162808/18060348. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(a a))(^b.(^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. ------ 162809/18060375. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.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. ------ 162810/18060411. ------ 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) REDUCED to normal form. ------ 162811/18060429. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (((a b)(a b))(^y.(a a))) 8. ==[ alpha ]==> (((a b)(a b))(^x.(a a))) REDUCED to normal form. ------ 162812/18060438. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))((^x1.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. ------ 162813/18060492. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 162814/18060510. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((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. ------ 162815/18060519. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(a (^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. ------ 162816/18060546. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.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. ------ 162817/18060573. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 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. ------ 162818/18060618. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a) c)) REDUCED to normal form. ------ 162819/18060852. ------ 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.(^x1.x1))))) REDUCED to normal form. ------ 162820/18060906. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 162821/18060915. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162822/18061194. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a (^z.z))) REDUCED to normal form. ------ 162823/18061212. ------ 1. ==[ start ]==> (((^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.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 162824/18061221. ------ 1. ==[ start ]==> (((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 a))) 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. ------ 162825/18061239. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 162826/18061293. ------ 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)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.(z z)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.(y y)))) 9. ==[ beta ]==> (((a a)(a a))((a a)(^y.(y y)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 162827/18061302. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 162828/18061329. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.b)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 162829/18061374. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.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. ------ 162830/18061383. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 162831/18061410. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(((^z.z)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.y)(a a)))) 9. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 162832/18061437. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 162833/18061482. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162834/18061491. ------ 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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 162835/18061509. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 162836/18061788. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 162837/18061797. ------ 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. ------ 162838/18061824. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(a a))) 3. ==[ beta ]==> ((a b)((b a)(a a))) REDUCED to normal form. ------ 162839/18062103. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162840/18062139. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 162841/18062157. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.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. ------ 162842/18062166. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 162843/18062184. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(y1 y1)))) 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. ------ 162844/18062193. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 162845/18062274. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(a b))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(a b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(a b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 162846/18062301. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.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. ------ 162847/18062319. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 162848/18062328. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 162849/18062355. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 162850/18062436. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 162851/18062463. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 162852/18062607. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b ((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))(b ((a a)(^z.z)))) 6. ==[ alpha ]==> (((^x.x)(a a))(b ((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. ------ 162853/18062634. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (b a))) REDUCED to normal form. ------ 162854/18062661. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 162855/18062688. ------ 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. ------ 162856/18062715. ------ 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.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a b) a)) REDUCED to normal form. ------ 162857/18062769. ------ 1. ==[ start ]==> (((a (^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))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^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 (^z.z)))((^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. ------ 162858/18062796. ------ 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. ------ 162859/18062823. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a (a b))) REDUCED to normal form. ------ 162860/18062994. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((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. ------ 162861/18063102. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((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. ------ 162862/18063138. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 162863/18063183. ------ 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)) 5. ==[ beta ]==> (((a a)(a a))((a a) b)) REDUCED to normal form. ------ 162864/18063210. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 162865/18063219. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 162866/18063327. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.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. ------ 162867/18063354. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 162868/18063453. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 162869/18063552. ------ 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 a) a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a ((a a) a))) REDUCED to normal form. ------ 162870/18063579. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))(a b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(a b))) REDUCED to normal form. ------ 162871/18063606. ------ 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)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 162872/18064074. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 162873/18064218. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (^y.a))) 3. ==[ beta ]==> ((b c)(c (^y.a))) 4. ==[ alpha ]==> ((b c)(c (^x.a))) REDUCED to normal form. ------ 162874/18064245. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b (^x.b))) REDUCED to normal form. ------ 162875/18064290. ------ 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))) REDUCED to normal form. ------ 162876/18064317. ------ 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.(^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. ------ 162877/18064353. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 162878/18064371. ------ 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. ------ 162879/18064380. ------ 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. ------ 162880/18064452. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.b))) 3. ==[ beta ]==> (b ((a a)(^z.b))) 4. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 162881/18064461. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(a b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a b)) REDUCED to normal form. ------ 162882/18064488. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 162883/18064569. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.(y1 y1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))(^y1.(y1 y1)))) IRREDUCIBLE: cycle. ------ 162884/18064596. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 162885/18064686. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 162886/18064713. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.y))) REDUCED to normal form. ------ 162887/18064740. ------ 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. ------ 162888/18064767. ------ 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. ------ 162889/18064794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((a (^y.y))((^z.z)(^x1.x1)))) 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. ------ 162890/18064821. ------ 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))) REDUCED to normal form. ------ 162891/18065235. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1)) c)) 3. ==[ beta ]==> (b ((^x1.(x1 x1)) c)) 4. ==[ alpha ]==> (b ((^x.(x x)) c)) 5. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 162892/18065343. ------ 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))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 162893/18065460. ------ 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 ((^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. ------ 162894/18065478. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)(((^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. ------ 162895/18065505. ------ 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. ------ 162896/18065568. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 162897/18065595. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 162898/18065640. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z)) b)) 3. ==[ beta ]==> (b ((^z.(z z)) b)) 4. ==[ alpha ]==> (b ((^x.(x x)) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 162899/18065649. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (^z.(^x1.x1)))) REDUCED to normal form. ------ 162900/18065676. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^b.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. ------ 162901/18065703. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.(z z)))) REDUCED to normal form. ------ 162902/18065748. ------ 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. ------ 162903/18065757. ------ 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 y1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(a a))) REDUCED to normal form. ------ 162904/18065784. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.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. ------ 162905/18065811. ------ 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))((^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. ------ 162906/18065865. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 162907/18065883. ------ 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. ------ 162908/18065928. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(b a)) REDUCED to normal form. ------ 162909/18065955. ------ 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. ------ 162910/18065982. ------ 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. ------ 162911/18066009. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 162912/18066036. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(b a))((a a) a)) REDUCED to normal form. ------ 162913/18066117. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b c)) REDUCED to normal form. ------ 162914/18066198. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (a (^y.y)))) 3. ==[ beta ]==> ((b (a (a a)))(b (a (^y.y)))) 4. ==[ alpha ]==> ((b (a (a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 162915/18066225. ------ 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)) 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. ------ 162916/18066279. ------ 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. ------ 162917/18066297. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a (^z.a))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 162918/18066315. ------ 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)) REDUCED to normal form. ------ 162919/18066813. ------ 1. ==[ start ]==> ((^a.(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (^x.(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 162920/18076713. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.z))) 3. ==[ beta ]==> ((^z.(^x1.z))((^z.(^x1.z))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.z))(^y1.y1))) 5. ==[ beta ]==> (^y.((^z.(^x1.z))(^y1.y1))) 6. ==[ alpha ]==> (^x.((^y.(^z.y))(^x1.x1))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 162921/18077028. ------ 1. ==[ start ]==> ((^a.b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 162922/18077109. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.y1))(^y.y)) 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. ------ 162923/18077226. ------ 1. ==[ start ]==> ((^a.(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(a (a (a (^z.z))))) 3. ==[ beta ]==> (^y.(a (a (a (^z.z))))) 4. ==[ alpha ]==> (^x.(a (a (a (^y.y))))) REDUCED to normal form. ------ 162924/18077229. ------ 1. ==[ start ]==> ((a (^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 162925/18077469. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 162926/18078351. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^y.(^z.z))(^x1.(^y1.(^z1.z1)))))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3)))))((^y3.(^z3.z3))(^x4.(^y4.(^z4.z4))))) 5. ==[ beta ]==> (((^y.y)((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3)))))((^y3.(^z3.z3))(^x4.(^y4.(^z4.z4))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1)))))((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3))))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3))))) 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. ------ 162927/18078684. ------ 1. ==[ start ]==> ((^a.(^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 162928/18079236. ------ 1. ==[ start ]==> (((a b)(^a.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 162929/18079458. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.b)(^x1.(a a)))((^z.b)(^x1.(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.b)(^z.(a a)))((^x1.b)(^y1.(a a))))) 5. ==[ beta ]==> (((^y.b)(^z.(a a)))((^x1.b)(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b)(^x1.(a a)))) 7. ==[ beta ]==> (b ((^z.b)(^x1.(a a)))) 8. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 162930/18079632. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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)))) REDUCED to normal form. ------ 162931/18080343. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 162932/18080703. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 162933/18081369. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 162934/18082620. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 162935/18083178. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 162936/18083961. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 162937/18084456. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 162938/18084672. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.((^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)))(^y.(a a))) REDUCED to normal form. ------ 162939/18084723. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 162940/18084897. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^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. ------ 162941/18085284. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 162942/18085671. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.b))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.b))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.b))) REDUCED to normal form. ------ 162943/18085833. ------ 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))) REDUCED to normal form. ------ 162944/18085884. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ eta ]==> ((^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. ------ 162945/18086778. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 162946/18086886. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 162947/18087048. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^b.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. ------ 162948/18087120. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.c)) 3. ==[ beta ]==> ((a (^y.y))(^z.c)) 4. ==[ alpha ]==> ((a (^x.x))(^y.c)) REDUCED to normal form. ------ 162949/18087126. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.a))) 3. ==[ beta ]==> ((a (^z.a))((a (^z.a))(^y.y))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.a))(^z.z))) REDUCED to normal form. ------ 162950/18087129. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.y))) REDUCED to normal form. ------ 162951/18087447. ------ 1. ==[ start ]==> ((a b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 162952/18087528. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 162953/18087618. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 162954/18087645. ------ 1. ==[ start ]==> ((a (^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(a (a (a (^y.y))))) REDUCED to normal form. ------ 162955/18087726. ------ 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) a))) 3. ==[ beta ]==> ((^y.a)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((^x.a)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 162956/18087753. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 162957/18087807. ------ 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. ------ 162958/18087834. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 162959/18087888. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 162960/18087996. ------ 1. ==[ start ]==> (((^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 a)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((((^y.y) a)((a a)(a a)))(((^y.y) a)((a a)(a a)))) 6. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)((a a)(a a)))) 8. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)((a a)(a a)))) 9. ==[ beta ]==> ((a ((a a)(a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 162961/18088023. ------ 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)((a (^x1.x1))(b (^y1.y1)))) 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. ------ 162962/18088086. ------ 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. ------ 162963/18088113. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 162964/18088140. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 162965/18088167. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 162966/18088194. ------ 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. ------ 162967/18088284. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 162968/18088302. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b b)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 162969/18088311. ------ 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. ------ 162970/18088491. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^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. ------ 162971/18088518. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b (^z.z)) b)) REDUCED to normal form. ------ 162972/18088545. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(a a)) c)) 3. ==[ beta ]==> ((a (^y.a))(((a a)(a a)) c)) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(a a)) c)) REDUCED to normal form. ------ 162973/18088689. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 162974/18088716. ------ 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. ------ 162975/18088770. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 162976/18088860. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(b (b (^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(b (b (^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(b (b (^z.z)))) 5. ==[ beta ]==> (a (b (b (^z.z)))) 6. ==[ alpha ]==> (a (b (b (^x.x)))) REDUCED to normal form. ------ 162977/18088941. ------ 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. ------ 162978/18088968. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)((^z1.z1) 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. ------ 162979/18089022. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((b a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a a)((b a)((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a a)((b a)(^y.y))) 10. ==[ alpha ]==> ((a a)((b a)(^x.x))) REDUCED to normal form. ------ 162980/18089103. ------ 1. ==[ start ]==> ((a (^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.b))((a b)(a a))) REDUCED to normal form. ------ 162981/18089436. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a) b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 162982/18089463. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(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. ------ 162983/18089490. ------ 1. ==[ start ]==> (((a a)(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a b)(^y.(a a)))) REDUCED to normal form. ------ 162984/18089571. ------ 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. ------ 162985/18089598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.a)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 162986/18089742. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^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 (^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. ------ 162987/18089769. ------ 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. ------ 162988/18089850. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 162989/18089877. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 162990/18090048. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 162991/18090102. ------ 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)))) 7. ==[ beta ]==> ((a a)(b (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(b (a (^x.x)))) REDUCED to normal form. ------ 162992/18090111. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) c)) 3. ==[ beta ]==> (((a a)(^x.(a a))) c) REDUCED to normal form. ------ 162993/18090129. ------ 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) 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 (^x.(^y.y))) a) REDUCED to normal form. ------ 162994/18090183. ------ 1. ==[ start ]==> (((^a.(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))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 11. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 12. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 13. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 14. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 162995/18090264. ------ 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.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. ------ 162996/18090363. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c (^y.y))) REDUCED to normal form. ------ 162997/18090390. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(b (^c.(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. ------ 162998/18090471. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b)(a (^a.a)))) 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. ------ 162999/18090489. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 163000/18090498. ------ 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) 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. ------ 163001/18090732. ------ 1. ==[ start ]==> (((a b) c)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b) c)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 163002/18090759. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((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. ------ 163003/18090786. ------ 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. ------ 163004/18090840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1))) c)) REDUCED to normal form. ------ 163005/18091065. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 163006/18091092. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 163007/18091119. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a (a b))(^y.(a a))) 6. ==[ alpha ]==> ((a (a b))(^x.(a a))) REDUCED to normal form. ------ 163008/18091398. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(b a))) 5. ==[ beta ]==> (b (((^z.z) a)(b a))) 6. ==[ alpha ]==> (b (((^x.x) a)(b a))) 7. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 163009/18091542. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((b a)(^y.a))) REDUCED to normal form. ------ 163010/18091650. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(^y.b))) REDUCED to normal form. ------ 163011/18091677. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.b))(^z.(a a))) 6. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(a a))) REDUCED to normal form. ------ 163012/18091758. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163013/18091785. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a a)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 163014/18091812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^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. ------ 163015/18091929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 163016/18091956. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 163017/18092010. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 163018/18092037. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 163019/18092091. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 163020/18092136. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163021/18092154. ------ 1. ==[ start ]==> (((^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 a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163022/18092235. ------ 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 a))(a (a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> ((a a)(((^z.z)(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. ------ 163023/18092316. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(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. ------ 163024/18092424. ------ 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 (^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. ------ 163025/18092460. ------ 1. ==[ start ]==> (((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.z1))) REDUCED to normal form. ------ 163026/18092541. ------ 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 z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 163027/18092568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((a b)(^y.(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 163028/18092622. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.b))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.b)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 163029/18092649. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 163030/18092676. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) a)(^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. ------ 163031/18092730. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 163032/18092766. ------ 1. ==[ start ]==> (((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))) 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. ------ 163033/18092847. ------ 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 z)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 163034/18092874. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 163035/18092928. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 163036/18092955. ------ 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 y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 163037/18092982. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 163038/18093036. ------ 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))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 163039/18093072. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 163040/18093099. ------ 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))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))(a (^x2.x2)))) 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. ------ 163041/18093234. ------ 1. ==[ start ]==> (((^a.b)(^c.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. ------ 163042/18093351. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a)(^z.z))) REDUCED to normal form. ------ 163043/18093378. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a))(^a.(^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. ------ 163044/18093405. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^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. ------ 163045/18093432. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(^y1.(y1 y1)))) REDUCED to normal form. ------ 163046/18093513. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(^z.b))) 5. ==[ beta ]==> ((^y.(a a))((a (a a))(^z.b))) 6. ==[ alpha ]==> ((^x.(a a))((a (a a))(^y.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163047/18093540. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a (^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 163048/18093567. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 163049/18093621. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a) a)) REDUCED to normal form. ------ 163050/18093738. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.a)(^b.(^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. ------ 163051/18093765. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.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. ------ 163052/18093792. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((a (b a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((a (b a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((a (b a))((^y.b)(^y.b))) 6. ==[ alpha ]==> ((a (b a))((^x.b)(^y.b))) 7. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 163053/18093819. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) a) REDUCED to normal form. ------ 163054/18094098. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((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)((a (^x1.x1))((^y1.y1)(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. ------ 163055/18094377. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a a)(^c.(^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. ------ 163056/18094404. ------ 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. ------ 163057/18094458. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b) c)) REDUCED to normal form. ------ 163058/18094584. ------ 1. ==[ start ]==> (((^a.b)(a b))(c (a b))) 2. ==[ alpha ]==> (((^x.b)(a b))(c (a b))) 3. ==[ beta ]==> (b (c (a b))) REDUCED to normal form. ------ 163059/18094647. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) 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. ------ 163060/18094692. ------ 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 (^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. ------ 163061/18094701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 163062/18094728. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a) d)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a) d)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a) d)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 163063/18094818. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c (^z.b))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (^z.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.b))) REDUCED to normal form. ------ 163064/18094845. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(b (^b.(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. ------ 163065/18094872. ------ 1. ==[ start ]==> (((a (a a))(b a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 163066/18094899. ------ 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)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 163067/18094926. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 163068/18094953. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 163069/18094980. ------ 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. ------ 163070/18095007. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.y1))) 10. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.x1))) 11. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 12. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 163071/18095061. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 163072/18095088. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(a a))) 7. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 163073/18095115. ------ 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))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 163074/18095142. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 163075/18095313. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(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. ------ 163076/18095421. ------ 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. ------ 163077/18095592. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^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. ------ 163078/18095619. ------ 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. ------ 163079/18095700. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 163080/18095727. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b) a)) 3. ==[ beta ]==> (((a a)(^y.b))((a b) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((a b) a)) REDUCED to normal form. ------ 163081/18096033. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(c (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(c (^x.(^y.y)))) REDUCED to normal form. ------ 163082/18096060. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.a))) REDUCED to normal form. ------ 163083/18096087. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 163084/18096114. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.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) REDUCED to normal form. ------ 163085/18096141. ------ 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 (^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. ------ 163086/18096195. ------ 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. ------ 163087/18096222. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x) 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)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 163088/18096249. ------ 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. ------ 163089/18096303. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 163090/18096393. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(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))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163091/18096474. ------ 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. ------ 163092/18096699. ------ 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. ------ 163093/18096798. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c ((^z.z) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c ((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c ((^z.z) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(c ((^z.z) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c ((^y.y) a))) 7. ==[ beta ]==> ((b b)(c ((^y.y) a))) 8. ==[ alpha ]==> ((b b)(c ((^x.x) a))) 9. ==[ beta ]==> ((b b)(c a)) REDUCED to normal form. ------ 163094/18096879. ------ 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. ------ 163095/18096888. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z)) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 163096/18096915. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.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. ------ 163097/18096996. ------ 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. ------ 163098/18097023. ------ 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.(^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. ------ 163099/18097050. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 163100/18097104. ------ 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. ------ 163101/18097140. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(^a.(^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. ------ 163102/18097167. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^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. ------ 163103/18097194. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^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. ------ 163104/18097275. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.a))) REDUCED to normal form. ------ 163105/18097302. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 163106/18097329. ------ 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))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 163107/18097356. ------ 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 (^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. ------ 163108/18097410. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 163109/18097437. ------ 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.(^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. ------ 163110/18097464. ------ 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))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.a)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.a)) REDUCED to normal form. ------ 163111/18097518. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^a.(^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. ------ 163112/18097545. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.a))) REDUCED to normal form. ------ 163113/18098061. ------ 1. ==[ start ]==> ((^a.(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 163114/18100086. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(z (^x1.x1)))(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (^x.((^x1.(x1 (^y1.y1)))(^z.z))) 6. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(^x1.x1))) 7. ==[ beta ]==> (^x.((^x1.x1)(^z.z))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163115/18103164. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163116/18107961. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.c)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.c)) 3. ==[ beta ]==> ((^z.c)((^z.c)(^y.y))) 4. ==[ alpha ]==> ((^x.c)((^y.c)(^z.z))) 5. ==[ beta ]==> c REDUCED to normal form. ------ 163117/18108483. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.a)(^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)))) REDUCED to normal form. ------ 163118/18108486. ------ 1. ==[ start ]==> ((a (^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 163119/18108900. ------ 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. ------ 163120/18108918. ------ 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 ]==> (((^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)))) REDUCED to normal form. ------ 163121/18109050. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163122/18109323. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.(^y1.y1)) 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. ------ 163123/18109737. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x)(^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. ------ 163124/18110115. ------ 1. ==[ start ]==> (((^a.b) a)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 163125/18110508. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.z)(b (^x1.x1)))((^z.z)(b (^x1.x1))))) 4. ==[ alpha ]==> (^x.(((^y.y)(b (^z.z)))((^x1.x1)(b (^y1.y1))))) 5. ==[ beta ]==> (^x.((b (^z.z))((^x1.x1)(b (^y1.y1))))) 6. ==[ alpha ]==> (^x.((b (^y.y))((^z.z)(b (^x1.x1))))) 7. ==[ beta ]==> (^x.((b (^y.y))(b (^x1.x1)))) 8. ==[ alpha ]==> (^x.((b (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 163126/18110511. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 163127/18110898. ------ 1. ==[ start ]==> (((a b) b)(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 163128/18111390. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((((a a)(^z.z))(^x1.(^y1.y1)))(((a a)(^z.z))(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> (((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1))))(^x2.x2)) REDUCED to normal form. ------ 163129/18112320. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^z.(^x1.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 163130/18112695. ------ 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.(^z2.z2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 163131/18112977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163132/18112983. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> (((^x1.x1) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 163133/18113292. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^a.(^b.b))) 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))) REDUCED to normal form. ------ 163134/18113586. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163135/18113589. ------ 1. ==[ start ]==> ((a (^b.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 163136/18113901. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163137/18114183. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163138/18115488. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 163139/18115929. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 163140/18115980. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163141/18116154. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 163142/18116370. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 163143/18117141. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1)) b)) 3. ==[ eta ]==> ((^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. ------ 163144/18117423. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.(^c.a))) 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. ------ 163145/18117558. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)(^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. ------ 163146/18117828. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163147/18117960. ------ 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))) REDUCED to normal form. ------ 163148/18118386. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.c)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.c)) REDUCED to normal form. ------ 163149/18118395. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.(^x1.z))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.x))(^z.z)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163150/18118722. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 163151/18118803. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 163152/18118893. ------ 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 (^x.x))(^y.y))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 163153/18118911. ------ 1. ==[ start ]==> ((a (^b.a))((^a.a)(^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)))) REDUCED to normal form. ------ 163154/18118929. ------ 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. ------ 163155/18118947. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163156/18119028. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (a (a a)))) REDUCED to normal form. ------ 163157/18119055. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^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. ------ 163158/18119082. ------ 1. ==[ start ]==> (((a a)(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((b a)((a a) a))) REDUCED to normal form. ------ 163159/18119109. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 163160/18119136. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 163161/18119244. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) 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))) 5. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 163162/18119289. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(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. ------ 163163/18119325. ------ 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. ------ 163164/18119343. ------ 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 ]==> (((^y.y)(^y.y))(a (^z.(z (^x1.x1))))) 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. ------ 163165/18119451. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 163166/18119478. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 163167/18119496. ------ 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. ------ 163168/18119523. ------ 1. ==[ start ]==> (((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.b))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 163169/18119550. ------ 1. ==[ start ]==> ((((^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))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 163170/18119577. ------ 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. ------ 163171/18119613. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 163172/18119640. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163173/18119694. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^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. ------ 163174/18119748. ------ 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.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) 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. ------ 163175/18120072. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))(^b.b))) 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)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163176/18120162. ------ 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))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 163177/18120189. ------ 1. ==[ start ]==> ((((a a) a) a)((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a) a)((b (^x.x))(a a))) REDUCED to normal form. ------ 163178/18120243. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b ((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b a)) REDUCED to normal form. ------ 163179/18120270. ------ 1. ==[ start ]==> ((((^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)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 163180/18120297. ------ 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. ------ 163181/18120324. ------ 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)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163182/18120351. ------ 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. ------ 163183/18120540. ------ 1. ==[ start ]==> (((^a.b) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 163184/18120639. ------ 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) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.x1) a))) IRREDUCIBLE: cycle. ------ 163185/18120720. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 163186/18120747. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(a b))) 3. ==[ beta ]==> ((a b)((^y.(a a))(a b))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(a b))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 163187/18120774. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^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. ------ 163188/18120828. ------ 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. ------ 163189/18120909. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 163190/18120936. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(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. ------ 163191/18120954. ------ 1. ==[ start ]==> (((a a)(a b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(a b))((b (^x.x)) a)) REDUCED to normal form. ------ 163192/18120981. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(a a)) b)) REDUCED to normal form. ------ 163193/18121008. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b) c)) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b) c)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b) c)) 7. ==[ beta ]==> ((a (^x.x))(b c)) REDUCED to normal form. ------ 163194/18121152. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163195/18121179. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 163196/18121233. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163197/18121323. ------ 1. ==[ start ]==> (((a b) b)(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(a (b (^x.x)))) REDUCED to normal form. ------ 163198/18121350. ------ 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. ------ 163199/18121377. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b)(a (^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. ------ 163200/18121404. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 163201/18121458. ------ 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. ------ 163202/18121485. ------ 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)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))((a a) a))) 7. ==[ beta ]==> ((((^y.y)(a a))((a a) a))(((^y.y)(a a))((a a) a))) 8. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a))((a a) a))) 9. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a))((a a) a))) 10. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))((a a) a))) 11. ==[ beta ]==> (((a a)((a a) a))((a a)((a a) a))) REDUCED to normal form. ------ 163203/18121512. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 163204/18121539. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 163205/18121566. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^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))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^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. ------ 163206/18121710. ------ 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. ------ 163207/18121737. ------ 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.(^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. ------ 163208/18121764. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 163209/18121791. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b a)(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 163210/18121818. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 163211/18121854. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 163212/18121989. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.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) REDUCED to normal form. ------ 163213/18122097. ------ 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.(^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. ------ 163214/18122232. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.b)(^x1.b))) 3. ==[ beta ]==> (b ((^z.b)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 163215/18122439. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.b) 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. ------ 163216/18122745. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(a (^z.(a a)))) 3. ==[ beta ]==> (b (a (^z.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 163217/18122853. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(^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)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 163218/18122880. ------ 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.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(^z1.z1)))) 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. ------ 163219/18122934. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(a b))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(a b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(a b))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 163220/18123015. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 163221/18123123. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 163222/18123141. ------ 1. ==[ start ]==> (((a a)(b a))((b a) c)) REDUCED to normal form. ------ 163223/18123402. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163224/18123411. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z) a)) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 163225/18123690. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 163226/18123699. ------ 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. ------ 163227/18123717. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (^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. ------ 163228/18123744. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 163229/18123879. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 163230/18123987. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163231/18124014. ------ 1. ==[ start ]==> ((a (^b.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^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. ------ 163232/18124032. ------ 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)) REDUCED to normal form. ------ 163233/18124059. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a) b)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a) b)) REDUCED to normal form. ------ 163234/18124293. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(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. ------ 163235/18124329. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x) 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)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 163236/18124608. ------ 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.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163237/18124662. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^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)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163238/18124689. ------ 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) 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. ------ 163239/18124824. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.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. ------ 163240/18125220. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 163241/18125364. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(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. ------ 163242/18125499. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 163243/18125607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 163244/18125715. ------ 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.(^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. ------ 163245/18125769. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 163246/18125850. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(^z.b))) 3. ==[ beta ]==> (b ((^y.a)(^z.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 163247/18125859. ------ 1. ==[ start ]==> (((a b)(^a.b))(c (a b))) 2. ==[ alpha ]==> (((a b)(^x.b))(c (a b))) REDUCED to normal form. ------ 163248/18125913. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 163249/18125967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)(a (^x1.x1)))) REDUCED to normal form. ------ 163250/18125994. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 163251/18126021. ------ 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. ------ 163252/18126165. ------ 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 a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^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. ------ 163253/18126192. ------ 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.(^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. ------ 163254/18126219. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))(((a a) a)(^x.a))) REDUCED to normal form. ------ 163255/18126246. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^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))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^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. ------ 163256/18126273. ------ 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. ------ 163257/18126327. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 163258/18126354. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 163259/18126381. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a) a)) REDUCED to normal form. ------ 163260/18126408. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b) b)) REDUCED to normal form. ------ 163261/18126498. ------ 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.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163262/18126579. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 163263/18126723. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b c)(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b c)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b c)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((b c)(a (^y.y))) 8. ==[ alpha ]==> ((b c)(a (^x.x))) REDUCED to normal form. ------ 163264/18126750. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 163265/18126795. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(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)))) REDUCED to normal form. ------ 163266/18126822. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b)(a a))) 3. ==[ beta ]==> ((^y.y)((^z.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. ------ 163267/18126876. ------ 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))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) 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. ------ 163268/18126957. ------ 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))((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. ------ 163269/18127065. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^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. ------ 163270/18127191. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b) a)) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 163271/18127245. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) c)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) c)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 163272/18127380. ------ 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. ------ 163273/18127407. ------ 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.(^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)))) 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. ------ 163274/18127461. ------ 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)(^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. ------ 163275/18127488. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 163276/18127569. ------ 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 (^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. ------ 163277/18127659. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 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. ------ 163278/18127848. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a (^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163279/18127983. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 163280/18128010. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 163281/18128064. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(^b.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. ------ 163282/18128073. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c ((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(c a)) REDUCED to normal form. ------ 163283/18128100. ------ 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. ------ 163284/18128154. ------ 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. ------ 163285/18128181. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a (a (^y.y)))) REDUCED to normal form. ------ 163286/18128208. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a (^z.z)) a)) REDUCED to normal form. ------ 163287/18128253. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163288/18128316. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c c)) REDUCED to normal form. ------ 163289/18128388. ------ 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 (^x.(x (^y.y))))((^x1.x1)(^x1.x1))) 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. ------ 163290/18128406. ------ 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. ------ 163291/18128433. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z)) c)) REDUCED to normal form. ------ 163292/18128487. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y)) a)) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y)) a)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x)) a)) 5. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 163293/18128514. ------ 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) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 163294/18128541. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 163295/18128595. ------ 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)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) 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. ------ 163296/18128622. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 163297/18128676. ------ 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) a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 163298/18128703. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (^y.y)) b)) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y)) b)) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 163299/18128784. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^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. ------ 163300/18128802. ------ 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. ------ 163301/18128820. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(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 ]==> ((a (^z.a))(^y.y)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 163302/18130974. ------ 1. ==[ start ]==> ((^a.(a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((^y.(b (^z.z))) b) 4. ==[ alpha ]==> ((^x.(b (^y.y))) b) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163303/18131361. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 163304/18133836. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> ((^x1.((^y1.y1) b))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 163305/18134439. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.(^a.(^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. ------ 163306/18134754. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163307/18139788. ------ 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. ------ 163308/18139839. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b (^z.z))(a (^x1.x1)))) 3. ==[ eta ]==> ((^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. ------ 163309/18140109. ------ 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. ------ 163310/18140211. ------ 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. ------ 163311/18140334. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163312/18140616. ------ 1. ==[ start ]==> (((a a)(^b.(^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)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 163313/18141405. ------ 1. ==[ start ]==> ((^a.(a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(b (^y.y))) b) 4. ==[ alpha ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 163314/18141408. ------ 1. ==[ start ]==> ((a (a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.(b (^y.y)))) REDUCED to normal form. ------ 163315/18141795. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 163316/18142911. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.((a a)(a a)))) REDUCED to normal form. ------ 163317/18143271. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 163318/18143430. ------ 1. ==[ start ]==> ((^a.(b a))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(b x))((a b)((a a) a))) 3. ==[ eta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 163319/18143937. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 163320/18143979. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 163321/18144261. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163322/18144267. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a ((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^x1.x1) b))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.z))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 163323/18144270. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 163324/18144585. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 163325/18144870. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)(^a.(^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. ------ 163326/18144873. ------ 1. ==[ start ]==> ((a (^b.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163327/18145185. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163328/18145188. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 163329/18145476. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 163330/18145746. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(z a))) REDUCED to normal form. ------ 163331/18146025. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(b x))) 3. ==[ eta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 163332/18146184. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((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))((a a) a)))) REDUCED to normal form. ------ 163333/18146529. ------ 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. ------ 163334/18146772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 163335/18146997. ------ 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))(^x.(a a))) REDUCED to normal form. ------ 163336/18147852. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.b)) a) 4. ==[ beta ]==> (((a a)(^y.b)) a) 5. ==[ alpha ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 163337/18148050. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(y b))) REDUCED to normal form. ------ 163338/18148212. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.((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))) REDUCED to normal form. ------ 163339/18149121. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 163340/18149229. ------ 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. ------ 163341/18149244. ------ 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. ------ 163342/18149346. ------ 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. ------ 163343/18149427. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 163344/18149667. ------ 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. ------ 163345/18149679. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.c)(^y.y)) 6. ==[ alpha ]==> ((^x.c)(^y.y)) 7. ==[ beta ]==> c REDUCED to normal form. ------ 163346/18150024. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(a a))(^c.(^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. ------ 163347/18150105. ------ 1. ==[ start ]==> (((a a) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 163348/18150222. ------ 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. ------ 163349/18150249. ------ 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 (^x.x))(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. ------ 163350/18150276. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) REDUCED to normal form. ------ 163351/18150465. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 163352/18150492. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 163353/18150519. ------ 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. ------ 163354/18150546. ------ 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. ------ 163355/18150645. ------ 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. ------ 163356/18150663. ------ 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. ------ 163357/18150690. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.(^z1.z1)))) 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. ------ 163358/18150744. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 163359/18150753. ------ 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. ------ 163360/18150771. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 163361/18150861. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 163362/18150933. ------ 1. ==[ start ]==> (((^a.(^a.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.(^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. ------ 163363/18150996. ------ 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. ------ 163364/18151023. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(b (^z.z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 163365/18151050. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 163366/18151068. ------ 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. ------ 163367/18151158. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.b)(^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. ------ 163368/18151680. ------ 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)))) 3. ==[ beta ]==> (((a a)((a a) a))((a b)(a a))) REDUCED to normal form. ------ 163369/18151707. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 163370/18151734. ------ 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. ------ 163371/18151761. ------ 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. ------ 163372/18151788. ------ 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) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(a ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 163373/18151815. ------ 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)(a a)))) REDUCED to normal form. ------ 163374/18151842. ------ 1. ==[ start ]==> ((a (a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a a)(b (^x.x)))) REDUCED to normal form. ------ 163375/18151932. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b)(^x1.a))) IRREDUCIBLE: cycle. ------ 163376/18152013. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 163377/18152022. ------ 1. ==[ start ]==> (((a b) a)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 163378/18152040. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> ((a b)((a a)(^y.b))) 6. ==[ alpha ]==> ((a b)((a a)(^x.b))) REDUCED to normal form. ------ 163379/18152049. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 163380/18152067. ------ 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)((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. ------ 163381/18152103. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 163382/18152130. ------ 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. ------ 163383/18152157. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 163384/18152184. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 163385/18152202. ------ 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 ((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 163386/18152211. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 163387/18152400. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 163388/18152688. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z) c)) 3. ==[ beta ]==> ((^y.y)((^z.z) 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. ------ 163389/18152895. ------ 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))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(b a))) REDUCED to normal form. ------ 163390/18152922. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 163391/18152949. ------ 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 (^x.x)) b)) REDUCED to normal form. ------ 163392/18152976. ------ 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)(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. ------ 163393/18153048. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b)(a (^a.a)))) 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. ------ 163394/18153147. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^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. ------ 163395/18153282. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 163396/18153291. ------ 1. ==[ start ]==> (((a b) c)((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 163397/18153318. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 163398/18153345. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a a))) REDUCED to normal form. ------ 163399/18153363. ------ 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. ------ 163400/18153390. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^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. ------ 163401/18153399. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 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. ------ 163402/18153426. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 163403/18153480. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 163404/18153507. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 163405/18153534. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 163406/18153588. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(^a.a))(^c.(^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. ------ 163407/18153678. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(b ((^y.y) b))) 3. ==[ beta ]==> ((a (a b))(b ((^y.y) b))) 4. ==[ alpha ]==> ((a (a b))(b ((^x.x) b))) 5. ==[ beta ]==> ((a (a b))(b b)) REDUCED to normal form. ------ 163408/18153705. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(a ((a a)(a a)))) REDUCED to normal form. ------ 163409/18153732. ------ 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)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(a a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a a))) 7. ==[ beta ]==> ((^y.y)(((^z.z) b)(a a))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a a))) 9. ==[ beta ]==> (((^y.y) b)(a a)) 10. ==[ alpha ]==> (((^x.x) b)(a a)) 11. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 163410/18153759. ------ 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)))) REDUCED to normal form. ------ 163411/18153786. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a b) a)((b a)((^y.y) a))) 4. ==[ alpha ]==> (((a b) a)((b a)((^x.x) a))) 5. ==[ beta ]==> (((a b) a)((b a) a)) REDUCED to normal form. ------ 163412/18153813. ------ 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))(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. ------ 163413/18153840. ------ 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)(a 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. ------ 163414/18153867. ------ 1. ==[ start ]==> ((a (b a))((a b)((a a) a))) REDUCED to normal form. ------ 163415/18154101. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 163416/18154146. ------ 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 z)))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 163417/18154173. ------ 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)))(((^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. ------ 163418/18154209. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.b)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)((a a) a))) 5. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 163419/18154227. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a) a)(^y.b))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)(^y.b))) 4. ==[ alpha ]==> (((a b)(a b))(((a a) a)(^x.b))) REDUCED to normal form. ------ 163420/18154236. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 163421/18154290. ------ 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 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. ------ 163422/18154317. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(b a))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 163423/18154344. ------ 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.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 163424/18154371. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 163425/18154416. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.(^y1.y1))) b)) REDUCED to normal form. ------ 163426/18154695. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163427/18154704. ------ 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 (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 163428/18154713. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b) 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. ------ 163429/18154794. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1)) d)) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1)) d)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) d)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 163430/18154992. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163431/18155019. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 163432/18155037. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 163433/18155091. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(^z.a))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 163434/18155100. ------ 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) 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. ------ 163435/18155127. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))(a (a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 163436/18155172. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 163437/18155181. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.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. ------ 163438/18155208. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(a b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 163439/18155235. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(a a))) REDUCED to normal form. ------ 163440/18155289. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(b 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. ------ 163441/18155307. ------ 1. ==[ start ]==> ((a (^b.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 163442/18155595. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(b (b a))) REDUCED to normal form. ------ 163443/18155622. ------ 1. ==[ start ]==> ((a ((^a.a) b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a b)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 163444/18155631. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^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. ------ 163445/18155910. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163446/18155955. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 163447/18155964. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 163448/18155982. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.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. ------ 163449/18155991. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 163450/18156036. ------ 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.(^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. ------ 163451/18156072. ------ 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.(^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 a) REDUCED to normal form. ------ 163452/18156099. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a b)(a b))) REDUCED to normal form. ------ 163453/18156117. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 163454/18156126. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 163455/18156153. ------ 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))((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. ------ 163456/18156180. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(b a)) REDUCED to normal form. ------ 163457/18156225. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 163458/18156261. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 163459/18156432. ------ 1. ==[ start ]==> ((((a a) a)(a b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 163460/18156459. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (b a))) REDUCED to normal form. ------ 163461/18156486. ------ 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.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)(^y.y))(((a a)(^z.z))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 163462/18156513. ------ 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))(a (^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. ------ 163463/18156567. ------ 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) a)(a (a a)))) REDUCED to normal form. ------ 163464/18156594. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (a a))((^x.x)((^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. ------ 163465/18156621. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (a a))((a a) a))) REDUCED to normal form. ------ 163466/18156792. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(^z.a))) 3. ==[ beta ]==> (b ((a b)(^z.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 163467/18156900. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^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. ------ 163468/18156936. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 163469/18156963. ------ 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. ------ 163470/18156981. ------ 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)) 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. ------ 163471/18157008. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(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. ------ 163472/18157017. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 163473/18157044. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(^y1.a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 163474/18157125. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 163475/18157152. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 163476/18157206. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.a)(^c.(^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. ------ 163477/18157251. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 163478/18157350. ------ 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)(^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. ------ 163479/18157377. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)((a a) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a ((a a) a))) REDUCED to normal form. ------ 163480/18157404. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (^x1.x1))(a b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(a b))) REDUCED to normal form. ------ 163481/18157431. ------ 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)))) 3. ==[ beta ]==> (((a (a a))(b a))((a a)(a a))) REDUCED to normal form. ------ 163482/18158016. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d (^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(d (^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(d (^x.(^y.y)))) REDUCED to normal form. ------ 163483/18158043. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c (^x.a))) REDUCED to normal form. ------ 163484/18158115. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((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. ------ 163485/18158151. ------ 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)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 163486/18158169. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.a)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.a)) REDUCED to normal form. ------ 163487/18158178. ------ 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))((^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. ------ 163488/18158250. ------ 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 (^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 163489/18158259. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^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. ------ 163490/18158286. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)(a b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a b))) 5. ==[ beta ]==> (((a a)(^x.b))(a b)) REDUCED to normal form. ------ 163491/18158367. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.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. ------ 163492/18158394. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.a))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 163493/18158421. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)(^b.(^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. ------ 163494/18158484. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (a b))) REDUCED to normal form. ------ 163495/18158511. ------ 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. ------ 163496/18158538. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a b)((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> ((a b)((^x.x)(a (^y.y)))) 9. ==[ beta ]==> ((a b)(a (^y.y))) 10. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 163497/18158565. ------ 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. ------ 163498/18158592. ------ 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. ------ 163499/18158619. ------ 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 (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 163500/18158646. ------ 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. ------ 163501/18159033. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163502/18159258. ------ 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. ------ 163503/18159276. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((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. ------ 163504/18159303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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 ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 163505/18159357. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a) c)) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a) c)) 7. ==[ beta ]==> ((b b)(((^y.y) a) c)) 8. ==[ alpha ]==> ((b b)(((^x.x) a) c)) 9. ==[ beta ]==> ((b b)(a c)) REDUCED to normal form. ------ 163506/18159366. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 163507/18159393. ------ 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))(^y2.(y2 y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(y2 y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163508/18159438. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 163509/18159501. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.a))) REDUCED to normal form. ------ 163510/18159555. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 163511/18159582. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(a a))) 5. ==[ beta ]==> ((b (^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 163512/18159609. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.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. ------ 163513/18159663. ------ 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. ------ 163514/18159681. ------ 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. ------ 163515/18159726. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (a (^z.z)))) REDUCED to normal form. ------ 163516/18159753. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b ((^y.y) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b ((^x.x) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(b a)) REDUCED to normal form. ------ 163517/18159780. ------ 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. ------ 163518/18159807. ------ 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. ------ 163519/18159834. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 163520/18159861. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 163521/18159915. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c b)) REDUCED to normal form. ------ 163522/18159996. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (a a))) 3. ==[ beta ]==> ((b (a (a a)))(c (a a))) REDUCED to normal form. ------ 163523/18160023. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(b (a (^x.x)))) REDUCED to normal form. ------ 163524/18160077. ------ 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))((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. ------ 163525/18160095. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^a.(^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. ------ 163526/18160104. ------ 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. ------ 163527/18165138. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^x1.(^y1.y1))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163528/18166056. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163529/18170880. ------ 1. ==[ start ]==> ((^a.b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 163530/18171078. ------ 1. ==[ start ]==> ((^a.(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.x))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (^x.(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (^x.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 163531/18171099. ------ 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. ------ 163532/18171321. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 163533/18171771. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.b)((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. ------ 163534/18172536. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 163535/18172728. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(^y.(b (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163536/18173124. ------ 1. ==[ start ]==> (((a a)(a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(x (^y.y)))) REDUCED to normal form. ------ 163537/18173310. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((^z.(a a))(^x1.b))((^z.(a a))(^x1.b)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(a a))(^z.b))((^x1.(a a))(^y1.b)))) 5. ==[ beta ]==> (((^y.(a a))(^z.b))((^x1.(a a))(^y1.b))) 6. ==[ alpha ]==> (((^x.(a a))(^y.b))((^z.(a a))(^x1.b))) 7. ==[ beta ]==> ((a a)((^z.(a a))(^x1.b))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.b))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 163538/18174582. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 163539/18174915. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^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. ------ 163540/18175578. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^x1.x1)(^y1.y1))(^y.(^z.z))) 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. ------ 163541/18175581. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 163542/18175590. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 163543/18176202. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 163544/18176496. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163545/18176499. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 163546/18176508. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^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)))) REDUCED to normal form. ------ 163547/18178551. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.((^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))(^x.(a a))) REDUCED to normal form. ------ 163548/18178575. ------ 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. ------ 163549/18178965. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(a b))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a b))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a b))) REDUCED to normal form. ------ 163550/18179163. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.b))) REDUCED to normal form. ------ 163551/18179361. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 163552/18179550. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 163553/18180018. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163554/18180315. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 163555/18180657. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 163556/18180765. ------ 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.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 163557/18180846. ------ 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))(^x1.a)) REDUCED to normal form. ------ 163558/18180978. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^a.(^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. ------ 163559/18181326. ------ 1. ==[ start ]==> ((a b)((^c.(^a.a))(^b.(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. ------ 163560/18181524. ------ 1. ==[ start ]==> ((a (^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.y))) REDUCED to normal form. ------ 163561/18181542. ------ 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. ------ 163562/18181560. ------ 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)((^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. ------ 163563/18181605. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 163564/18181632. ------ 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) 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. ------ 163565/18181641. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a)) d)) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 163566/18181686. ------ 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. ------ 163567/18181713. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 163568/18181767. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 163569/18181875. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.(y y))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.(x x))((a (a a))((^y.y) b))) 5. ==[ beta ]==> (((a (a a))((^y.y) b))((a (a a))((^y.y) b))) 6. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))((^y.y) b))) 7. ==[ beta ]==> (((a (a a)) b)((a (a a))((^y.y) b))) 8. ==[ alpha ]==> (((a (a a)) b)((a (a a))((^x.x) b))) 9. ==[ beta ]==> (((a (a a)) b)((a (a a)) b)) REDUCED to normal form. ------ 163570/18181902. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 163571/18181956. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)((^z.(^x1.x1)) 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. ------ 163572/18181992. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.(^z.z)) a)(^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. ------ 163573/18182019. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 163574/18182046. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 163575/18182073. ------ 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. ------ 163576/18182109. ------ 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. ------ 163577/18182181. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((b b)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((b b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 163578/18182190. ------ 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. ------ 163579/18182217. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 163580/18182316. ------ 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. ------ 163581/18182397. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 163582/18182424. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b (^z.z)) b)) 3. ==[ beta ]==> ((a (^y.a))((b (^z.z)) b)) 4. ==[ alpha ]==> ((a (^x.a))((b (^y.y)) b)) REDUCED to normal form. ------ 163583/18182514. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 163584/18182595. ------ 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. ------ 163585/18182622. ------ 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. ------ 163586/18182739. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c ((a a)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c ((a a)(a a)))) 5. ==[ beta ]==> (a (c ((a a)(a a)))) REDUCED to normal form. ------ 163587/18182820. ------ 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. ------ 163588/18182847. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^y1.y1)))) 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. ------ 163589/18182856. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 163590/18182901. ------ 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.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(a (a a)))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 163591/18182982. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a (^x.b))((a a)(a b))) REDUCED to normal form. ------ 163592/18183171. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.b)((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((^x.b)((a a)(b (^y.y)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163593/18183315. ------ 1. ==[ start ]==> ((((a a) a) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 163594/18183342. ------ 1. ==[ start ]==> (((a b) a)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 163595/18183369. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 163596/18183423. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 163597/18183477. ------ 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 REDUCED to normal form. ------ 163598/18183504. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 163599/18183531. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 163600/18183567. ------ 1. ==[ start ]==> (((a a)(a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(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. ------ 163601/18183648. ------ 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. ------ 163602/18183675. ------ 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.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 8. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 163603/18183729. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 163604/18183756. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 163605/18183927. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 163606/18183981. ------ 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. ------ 163607/18183990. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 163608/18184008. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 163609/18184017. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) c) REDUCED to normal form. ------ 163610/18184062. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b a)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(a (a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(a (a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(a (a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b a)(a (a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a (a a)))) 9. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 10. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 11. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 163611/18184143. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 163612/18184296. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 163613/18184368. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 163614/18184377. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b)(a (^a.a)))) 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. ------ 163615/18184404. ------ 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) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 163616/18184611. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) c)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) c)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 163617/18184638. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 163618/18184719. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) b) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b b)) REDUCED to normal form. ------ 163619/18184746. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((a (^y.b))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 163620/18184971. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 163621/18184998. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 163622/18185277. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> (b ((a (a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 163623/18185358. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a a)((^z.z) b))) 3. ==[ beta ]==> (b ((a a)((^z.z) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 163624/18185421. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 163625/18185529. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a b)(^y.a))) REDUCED to normal form. ------ 163626/18185556. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a) a)(^y.b))) REDUCED to normal form. ------ 163627/18185610. ------ 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. ------ 163628/18185664. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163629/18185691. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 163630/18185754. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 163631/18185835. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(a a))(^b.(^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. ------ 163632/18185862. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.a))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 163633/18185916. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 163634/18186024. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 163635/18186033. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 163636/18186114. ------ 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) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a a)(((a a)(^z.z))((^x1.x1) 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. ------ 163637/18186195. ------ 1. ==[ start ]==> (((^a.b)(^b.(^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. ------ 163638/18186303. ------ 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))((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. ------ 163639/18186330. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 163640/18186420. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 163641/18186447. ------ 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)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.(z z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 163642/18186501. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 163643/18186528. ------ 1. ==[ start ]==> ((((^a.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))(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.b))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(^z.b)) 8. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 163644/18186555. ------ 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.(a a)))) REDUCED to normal form. ------ 163645/18186645. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 163646/18186672. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1)))(^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. ------ 163647/18186753. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^z.(z z)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(y y)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 163648/18186780. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.b)(^b.(^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. ------ 163649/18186807. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 163650/18186834. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 163651/18186861. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 163652/18186942. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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))))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 163653/18186951. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(a (a (^z.(^x1.x1))))) 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. ------ 163654/18186978. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((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. ------ 163655/18187113. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 163656/18187221. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((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. ------ 163657/18187257. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a)(^y.y))) 3. ==[ beta ]==> ((b a)((b a)(^y.y))) 4. ==[ alpha ]==> ((b a)((b a)(^x.x))) REDUCED to normal form. ------ 163658/18187284. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 163659/18187311. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^y1.a))) REDUCED to normal form. ------ 163660/18187392. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163661/18187419. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (a a))(^y.b))) REDUCED to normal form. ------ 163662/18187446. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 163663/18187473. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 163664/18187554. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1)) b)) REDUCED to normal form. ------ 163665/18187581. ------ 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 (^x.x))((a a) c)) REDUCED to normal form. ------ 163666/18187617. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a a) b)((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 163667/18187671. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(^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))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 163668/18187698. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 163669/18187725. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.a)(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 163670/18187752. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^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. ------ 163671/18187977. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 163672/18188256. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((b b)((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 163673/18188337. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) b)) REDUCED to normal form. ------ 163674/18188364. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a b) c)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b) c)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b) c)) REDUCED to normal form. ------ 163675/18188571. ------ 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 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. ------ 163676/18188580. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 163677/18188607. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b) c)) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 163678/18188751. ------ 1. ==[ start ]==> (((a (a a))(b a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(b (^x.(a a)))) REDUCED to normal form. ------ 163679/18188805. ------ 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))(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 a)) REDUCED to normal form. ------ 163680/18188832. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 163681/18188886. ------ 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. ------ 163682/18188940. ------ 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 a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 163683/18188967. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 163684/18188994. ------ 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))((^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. ------ 163685/18189021. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 163686/18189192. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b (a b))) 3. ==[ beta ]==> (b (b (a b))) REDUCED to normal form. ------ 163687/18189300. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((^x2.x2) 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. ------ 163688/18189408. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.x)(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))) REDUCED to normal form. ------ 163689/18189471. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)(^a.(^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. ------ 163690/18189498. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.a)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 163691/18189579. ------ 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. ------ 163692/18189606. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 163693/18189804. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.b)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.b)) REDUCED to normal form. ------ 163694/18189966. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b (^y.a))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.a))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.a))) REDUCED to normal form. ------ 163695/18189993. ------ 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. ------ 163696/18190074. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^z.z) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 163697/18190101. ------ 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. ------ 163698/18190128. ------ 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.(^z.z))((^x1.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. ------ 163699/18190272. ------ 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. ------ 163700/18190353. ------ 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. ------ 163701/18190461. ------ 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)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163702/18190578. ------ 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 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. ------ 163703/18190686. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a) c)) 3. ==[ beta ]==> (((a (a a))(^x.x))(a c)) REDUCED to normal form. ------ 163704/18190758. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 163705/18190767. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 163706/18190794. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z)) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z)) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y)) b)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(b b)) REDUCED to normal form. ------ 163707/18190821. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.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. ------ 163708/18190866. ------ 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. ------ 163709/18190902. ------ 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. ------ 163710/18190929. ------ 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.(^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. ------ 163711/18190983. ------ 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 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. ------ 163712/18191019. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 163713/18191046. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.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. ------ 163714/18191073. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(^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. ------ 163715/18191100. ------ 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 z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^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. ------ 163716/18191154. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 163717/18191181. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.a))) REDUCED to normal form. ------ 163718/18191208. ------ 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.(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)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.(y y)))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.(x x)))) REDUCED to normal form. ------ 163719/18191235. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.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. ------ 163720/18191289. ------ 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. ------ 163721/18191316. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.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. ------ 163722/18191343. ------ 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.(^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. ------ 163723/18191415. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^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. ------ 163724/18191424. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.(^z.z)))) REDUCED to normal form. ------ 163725/18191433. ------ 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. ------ 163726/18201444. ------ 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. ------ 163727/18202254. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 163728/18202455. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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)))) REDUCED to normal form. ------ 163729/18202878. ------ 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. ------ 163730/18202983. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163731/18203109. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a b)(^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. ------ 163732/18203283. ------ 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. ------ 163733/18203697. ------ 1. ==[ start ]==> ((((a a) a) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((((a a) a) a)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 163734/18204441. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))((a a)(a a)))((^z.(^x1.x1))((a a)(a a))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))((a a)(a a)))((^x1.(^y1.y1))((a a)(a a))))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.(^y1.y1))((a a)(a a))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))((a a)(a a))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))((a a)(a a)))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))((a a)(a a)))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163735/18204462. ------ 1. ==[ start ]==> (((a a)(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 163736/18204858. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a a) a)(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a a) a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 163737/18205323. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b a)(^z.(z z)))) 3. ==[ beta ]==> ((((b a)(^z.(z z)))((b a)(^z.(z z))))(^y.y)) 4. ==[ alpha ]==> ((((b a)(^x.(x x)))((b a)(^y.(y y))))(^z.z)) REDUCED to normal form. ------ 163738/18205578. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^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)))) REDUCED to normal form. ------ 163739/18206628. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b)(^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. ------ 163740/18206928. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.(^b.b))) 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. ------ 163741/18207252. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^a.(^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. ------ 163742/18207519. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163743/18207846. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^b.(^a.(^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. ------ 163744/18208125. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(b a))) REDUCED to normal form. ------ 163745/18209196. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(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. ------ 163746/18209913. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 163747/18210330. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 163748/18211074. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a) a)) 3. ==[ eta ]==> ((^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. ------ 163749/18211518. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163750/18211653. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 163751/18211662. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 163752/18211770. ------ 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. ------ 163753/18211893. ------ 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. ------ 163754/18211896. ------ 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. ------ 163755/18211995. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.d)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.d)) 3. ==[ beta ]==> (((a (a a)) b)(^y.d)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.d)) REDUCED to normal form. ------ 163756/18212316. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^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. ------ 163757/18212709. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 163758/18212790. ------ 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)((^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. ------ 163759/18212907. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(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. ------ 163760/18212916. ------ 1. ==[ start ]==> (((a (^a.a))(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))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 163761/18212988. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(a a)) a)) REDUCED to normal form. ------ 163762/18213015. ------ 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)))) 5. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 163763/18213042. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.a))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 163764/18213069. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)((a a) a))) REDUCED to normal form. ------ 163765/18213096. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 163766/18213204. ------ 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 (^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)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 163767/18213285. ------ 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. ------ 163768/18213312. ------ 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. ------ 163769/18213330. ------ 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. ------ 163770/18213438. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 163771/18213456. ------ 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. ------ 163772/18213483. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) a)((b a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b a)(^y.a))) REDUCED to normal form. ------ 163773/18213510. ------ 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))) REDUCED to normal form. ------ 163774/18213537. ------ 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. ------ 163775/18213564. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 163776/18213573. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163777/18213654. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 9. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 10. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 11. ==[ beta ]==> (b ((^y.y) b)) 12. ==[ alpha ]==> (b ((^x.x) b)) 13. ==[ beta ]==> (b b) REDUCED to normal form. ------ 163778/18213708. ------ 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))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163779/18213735. ------ 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. ------ 163780/18214032. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 163781/18214086. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (a ((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163782/18214122. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(b (b (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(b (b (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (b (^y.y)))) 6. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 163783/18214149. ------ 1. ==[ start ]==> ((((a a) a) a)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) a)(a ((^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. ------ 163784/18214203. ------ 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))(a (^x1.x1)))) REDUCED to normal form. ------ 163785/18214230. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(b ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.(x x)))(b a)) REDUCED to normal form. ------ 163786/18214257. ------ 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. ------ 163787/18214284. ------ 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 a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163788/18214311. ------ 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. ------ 163789/18214500. ------ 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 (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 163790/18214707. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a 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. ------ 163791/18214734. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^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. ------ 163792/18214869. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 163793/18214896. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 163794/18214941. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b (^y.y)) a)) REDUCED to normal form. ------ 163795/18214968. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a)) b)) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 163796/18214995. ------ 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. ------ 163797/18215112. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163798/18215139. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 163799/18215274. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 163800/18215283. ------ 1. ==[ start ]==> (((a b) b)(b ((a a)(a a)))) REDUCED to normal form. ------ 163801/18215310. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(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. ------ 163802/18215337. ------ 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. ------ 163803/18215364. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b)(a (^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. ------ 163804/18215418. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a)(a (a a)))) REDUCED to normal form. ------ 163805/18215445. ------ 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 z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 9. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 10. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 11. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^y1.y1))) 12. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 163806/18215472. ------ 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. ------ 163807/18215499. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 163808/18215526. ------ 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. ------ 163809/18215697. ------ 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))) 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. ------ 163810/18215724. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 163811/18215751. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (^a.(^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))) REDUCED to normal form. ------ 163812/18215778. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 163813/18215814. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 163814/18215949. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 163815/18216030. ------ 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)(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. ------ 163816/18216111. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(^x1.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. ------ 163817/18216192. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 163818/18216426. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x) b)) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 163819/18216453. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 163820/18216705. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(b (^z.z))) 3. ==[ beta ]==> (b (b (^z.z))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 163821/18216894. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a b)(a b))((^y.b)((a a) a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.b)((a a) a))) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 163822/18216975. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.(y y))((a a)(^z.z)))) 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. ------ 163823/18217083. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b)(^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. ------ 163824/18217101. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 163825/18217128. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((b a) c)) REDUCED to normal form. ------ 163826/18217362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 163827/18217380. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a)(^b.b))) 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. ------ 163828/18217659. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(b a))) REDUCED to normal form. ------ 163829/18217677. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163830/18217686. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 163831/18217704. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(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. ------ 163832/18217839. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 163833/18217947. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163834/18217974. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 163835/18217992. ------ 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.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 163836/18218019. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 163837/18218046. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a) b)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a) b)) REDUCED to normal form. ------ 163838/18218253. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163839/18218298. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.a)(^a.(^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. ------ 163840/18218577. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(b a))) REDUCED to normal form. ------ 163841/18218703. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 163842/18218784. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 163843/18219459. ------ 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 a)) REDUCED to normal form. ------ 163844/18219567. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 163845/18219648. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 163846/18219675. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 163847/18219729. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b)(^z.a))) 3. ==[ beta ]==> (((b a)(b a))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.b)(^y.a))) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 163848/18219810. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.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. ------ 163849/18219873. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (a a))) REDUCED to normal form. ------ 163850/18219927. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(a a))) REDUCED to normal form. ------ 163851/18219954. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b)(a (^z.z)))) REDUCED to normal form. ------ 163852/18219981. ------ 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)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(((a a) a) a)) REDUCED to normal form. ------ 163853/18220152. ------ 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. ------ 163854/18220179. ------ 1. ==[ start ]==> (((a b)(a b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 163855/18220206. ------ 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. ------ 163856/18220233. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 163857/18220314. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 163858/18220341. ------ 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. ------ 163859/18220368. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(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. ------ 163860/18220458. ------ 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.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(z2 z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.(z2 z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163861/18220539. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^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. ------ 163862/18220683. ------ 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. ------ 163863/18220710. ------ 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)(^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. ------ 163864/18220755. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b (^z.b))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.b))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.b))) REDUCED to normal form. ------ 163865/18220782. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 163866/18220917. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 163867/18221178. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 163868/18221205. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a) b)) 5. ==[ beta ]==> ((a b)((^y.a) b)) 6. ==[ alpha ]==> ((a b)((^x.a) b)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 163869/18221232. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1)) c)) 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. ------ 163870/18221367. ------ 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. ------ 163871/18221421. ------ 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. ------ 163872/18221448. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((b a)(a (^y.(y y)))) 8. ==[ alpha ]==> ((b a)(a (^x.(x x)))) REDUCED to normal form. ------ 163873/18221475. ------ 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 (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 163874/18221529. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a) a)) 2. ==[ alpha ]==> ((a ((^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. ------ 163875/18221619. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(x1 x1)))) 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. ------ 163876/18221808. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163877/18221943. ------ 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. ------ 163878/18221970. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 163879/18222024. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.(y y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(^z.z)))) 9. ==[ beta ]==> ((b b)((^y.(^z.z))(^y.(^z.z)))) 10. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(^x1.x1)))) 11. ==[ beta ]==> ((b b)(^y.y)) 12. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 163880/18222105. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^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. ------ 163881/18222114. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z)(^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. ------ 163882/18222141. ------ 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. ------ 163883/18222168. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (a (^z.z)))) REDUCED to normal form. ------ 163884/18222213. ------ 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 (^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163885/18222222. ------ 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. ------ 163886/18222348. ------ 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. ------ 163887/18222366. ------ 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. ------ 163888/18222393. ------ 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. ------ 163889/18222474. ------ 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)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1)) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1)) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z)) a)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 163890/18222501. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a) b)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 163891/18222528. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^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. ------ 163892/18222582. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) 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. ------ 163893/18222636. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.a))) REDUCED to normal form. ------ 163894/18222663. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(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. ------ 163895/18222690. ------ 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)) 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. ------ 163896/18222744. ------ 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)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 163897/18222762. ------ 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 (^y.y))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 163898/18222771. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^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. ------ 163899/18222780. ------ 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 ]==> ((b (^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 163900/18233820. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^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. ------ 163901/18233829. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 163902/18233853. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.(^x1.x1)) a)(a a))) 3. ==[ eta ]==> ((^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. ------ 163903/18234123. ------ 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. ------ 163904/18234252. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 163905/18234348. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 163906/18234657. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 163907/18235419. ------ 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 ]==> (((a (^y.y))((a a)(a a))) b) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 163908/18235806. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((a (^z.z))(^x1.(a a)))((a (^z.z))(^x1.(a a))))) 4. ==[ alpha ]==> (^x.(((a (^y.y))(^z.(a a)))((a (^x1.x1))(^y1.(a a))))) REDUCED to normal form. ------ 163909/18237312. ------ 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 y1)(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.((y1 y1)(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.((x1 x1)(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((x1 x1)(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((z z)(z z)))) 7. ==[ beta ]==> ((^y.y)(^z.((z z)(z z)))) 8. ==[ alpha ]==> ((^x.x)(^y.((y y)(y y)))) 9. ==[ beta ]==> (^y.((y y)(y y))) 10. ==[ alpha ]==> (^x.((x x)(x x))) REDUCED to normal form. ------ 163910/18237444. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ eta ]==> (b (((^y.y)(a a))((^z.z)(^x1.x1)))) 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. ------ 163911/18237993. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) b) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 163912/18238281. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (a (^x1.(^y1.y1))))(^y.(^z.z))) 4. ==[ alpha ]==> ((b (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 163913/18239199. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(b (b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(b (b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 163914/18239517. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^a.(^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. ------ 163915/18240066. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x)(a a))((^y.y)(^z.z))) b) 4. ==[ beta ]==> (((a a)((^y.y)(^z.z))) b) 5. ==[ alpha ]==> (((a a)((^x.x)(^y.y))) b) 6. ==[ beta ]==> (((a a)(^y.y)) b) 7. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 163916/18240198. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((((^y.y)(^z.z))((^x1.x1)(^y1.y1)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1))))((((^y.y)(^z.z))((^x1.x1)(^y1.y1)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2))))((((^z2.z2)(^x3.x3))((^y3.y3)(^z3.z3)))(((^x4.x4)(^y4.y4))((^z4.z4)(^x5.x5))))) 5. ==[ beta ]==> ((((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2))))((((^z2.z2)(^x3.x3))((^y3.y3)(^z3.z3)))(((^x4.x4)(^y4.y4))((^z4.z4)(^x5.x5))))) 6. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2))))((((^y2.y2)(^z2.z2))((^x3.x3)(^y3.y3)))(((^z3.z3)(^x4.x4))((^y4.y4)(^z4.z4))))) 7. ==[ beta ]==> ((((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2))))((((^y2.y2)(^z2.z2))((^x3.x3)(^y3.y3)))(((^z3.z3)(^x4.x4))((^y4.y4)(^z4.z4))))) 8. ==[ alpha ]==> ((((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1))))((((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3)))(((^y3.y3)(^z3.z3))((^x4.x4)(^y4.y4))))) 9. ==[ beta ]==> (((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1))))((((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3)))(((^y3.y3)(^z3.z3))((^x4.x4)(^y4.y4))))) 10. ==[ alpha ]==> (((^x.x)(((^y.y)(^z.z))((^x1.x1)(^y1.y1))))((((^z1.z1)(^x2.x2))((^y2.y2)(^z2.z2)))(((^x3.x3)(^y3.y3))((^z3.z3)(^x4.x4))))) 11. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1)(^y1.y1)))((((^z1.z1)(^x2.x2))((^y2.y2)(^z2.z2)))(((^x3.x3)(^y3.y3))((^z3.z3)(^x4.x4))))) 12. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))(((^z2.z2)(^x3.x3))((^y3.y3)(^z3.z3))))) 13. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))(((^z2.z2)(^x3.x3))((^y3.y3)(^z3.z3))))) 14. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))(((^y2.y2)(^z2.z2))((^x3.x3)(^y3.y3))))) 15. ==[ beta ]==> (((^y.y)(^z.z))((((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))(((^y2.y2)(^z2.z2))((^x3.x3)(^y3.y3))))) 16. ==[ alpha ]==> (((^x.x)(^y.y))((((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))(((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3))))) 17. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))(((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3))))) 18. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))((^y2.y2)(^z2.z2))))) 19. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))((^y2.y2)(^z2.z2)))) 20. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 21. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 22. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 23. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 24. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 25. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 26. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 27. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.y1))) 28. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 29. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 30. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 31. ==[ beta ]==> ((^y.y)(^z.z)) 32. ==[ alpha ]==> ((^x.x)(^y.y)) 33. ==[ beta ]==> (^y.y) 34. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163917/18242091. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(y b))) REDUCED to normal form. ------ 163918/18242253. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.((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))) REDUCED to normal form. ------ 163919/18242883. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^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. ------ 163920/18243027. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 163921/18243162. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 163922/18243258. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 163923/18243387. ------ 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. ------ 163924/18243657. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.(^y.y)) a)(a a))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(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. ------ 163925/18243681. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(a a))) 3. ==[ beta ]==> (((a (^z.z))(a a))(((a (^z.z))(a a))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a (^y.y))(a a))(^z.z))) REDUCED to normal form. ------ 163926/18244092. ------ 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)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 163927/18244146. ------ 1. ==[ start ]==> (((a a) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 163928/18244173. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 163929/18244263. ------ 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. ------ 163930/18244281. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(^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))) REDUCED to normal form. ------ 163931/18244290. ------ 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. ------ 163932/18244317. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x) 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))) 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. ------ 163933/18244506. ------ 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))((^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. ------ 163934/18244533. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 163935/18244560. ------ 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. ------ 163936/18244587. ------ 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. ------ 163937/18244659. ------ 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. ------ 163938/18244713. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 163939/18244731. ------ 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)(^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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 163940/18244785. ------ 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))(^y.a))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 163941/18244812. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 163942/18244902. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(^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)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 163943/18244947. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 163944/18245028. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (a a))(^b.b))) 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. ------ 163945/18245037. ------ 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. ------ 163946/18245064. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> (a ((^y.a)((a a)(a a)))) 6. ==[ alpha ]==> (a ((^x.a)((a a)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 163947/18245091. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 163948/18245118. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 163949/18245163. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b (^z.z)) b)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b (^z.z)) b)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z)) b)) REDUCED to normal form. ------ 163950/18245721. ------ 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))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)(a b))) REDUCED to normal form. ------ 163951/18245748. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a b)(a a))) REDUCED to normal form. ------ 163952/18245775. ------ 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. ------ 163953/18245802. ------ 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. ------ 163954/18245829. ------ 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.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 163955/18245856. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) 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. ------ 163956/18245874. ------ 1. ==[ start ]==> (((^a.b) a)(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 163957/18245883. ------ 1. ==[ start ]==> ((a (a b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 163958/18245973. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(^z.(^x1.x1)))) IRREDUCIBLE: cycle. ------ 163959/18246036. ------ 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. ------ 163960/18246054. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 163961/18246081. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a 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. ------ 163962/18246090. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 163963/18246108. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 163964/18246144. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 163965/18246198. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(b a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 163966/18246225. ------ 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 (^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. ------ 163967/18246243. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 163968/18246252. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 163969/18246270. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 163970/18246657. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 163971/18246729. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 163972/18246936. ------ 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)(a a))(((^y.y)(^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))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((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. ------ 163973/18246963. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (a a))(b a))) REDUCED to normal form. ------ 163974/18246990. ------ 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))))) 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. ------ 163975/18247017. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 163976/18247044. ------ 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)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 163977/18247089. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 163978/18247188. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((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. ------ 163979/18247332. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b) c)((^x.(x x))(b a))) 3. ==[ beta ]==> (((a b) c)((b a)(b a))) REDUCED to normal form. ------ 163980/18247359. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.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) REDUCED to normal form. ------ 163981/18247386. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 163982/18247431. ------ 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)) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a)) a)) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 163983/18247440. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 163984/18247467. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 163985/18247575. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 163986/18247602. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 163987/18247719. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a b))(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a b))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 163988/18247746. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(b ((^x.x) b))) 3. ==[ beta ]==> (((a (a a))((a a) a))(b b)) REDUCED to normal form. ------ 163989/18247773. ------ 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. ------ 163990/18247800. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) b)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b (a a))) REDUCED to normal form. ------ 163991/18247827. ------ 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)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 163992/18247854. ------ 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) 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. ------ 163993/18247881. ------ 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. ------ 163994/18247908. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (b a))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (b a))((a a)(^x.x))) REDUCED to normal form. ------ 163995/18248142. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b)(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. ------ 163996/18248187. ------ 1. ==[ start ]==> (((^a.a)(b a))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((b a)(^y.a))) 3. ==[ beta ]==> ((b a)((b a)(^y.a))) 4. ==[ alpha ]==> ((b a)((b a)(^x.a))) REDUCED to normal form. ------ 163997/18248214. ------ 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)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(y1 y1)))) 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. ------ 163998/18248250. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 163999/18248268. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a b)(^y.a))) 3. ==[ beta ]==> (((a b)(a b))((a b)(^y.a))) 4. ==[ alpha ]==> (((a b)(a b))((a b)(^x.a))) REDUCED to normal form. ------ 164000/18248277. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 164001/18248331. ------ 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.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. ------ 164002/18248349. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (a a))(^c.(^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. ------ 164003/18248358. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 164004/18248385. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(b a))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 164005/18248412. ------ 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.y1))(a (^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. ------ 164006/18248457. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 164007/18248736. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 164008/18248745. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 164009/18249060. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 164010/18249132. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((b a)(^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 164011/18249168. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 164012/18249213. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 164013/18249222. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 164014/18249276. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 164015/18249330. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 164016/18249627. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.a)(^c.(^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. ------ 164017/18249663. ------ 1. ==[ start ]==> ((a ((^a.a) b))(b (b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(b (b a))) 3. ==[ beta ]==> ((a b)(b (b a))) REDUCED to normal form. ------ 164018/18249699. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2))) 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. ------ 164019/18249978. ------ 1. ==[ start ]==> ((((^a.a) b) a)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 164020/18249996. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a)(^z.z))) 3. ==[ beta ]==> (((^y.y) b)((b a)(^z.z))) 4. ==[ alpha ]==> (((^x.x) b)((b a)(^y.y))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 164021/18250023. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.(^x2.x2)))) 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. ------ 164022/18250077. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(^z.(z z)))) REDUCED to normal form. ------ 164023/18250113. ------ 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.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 164024/18250140. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 164025/18250158. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((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. ------ 164026/18250167. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a b)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 164027/18250194. ------ 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)((^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. ------ 164028/18250221. ------ 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))((a a)(^y1.y1)))) 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. ------ 164029/18250266. ------ 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))((b a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164030/18250302. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a))(^a.(^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. ------ 164031/18250473. ------ 1. ==[ start ]==> ((((a a) a)(a b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(c ((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(c (a a))) REDUCED to normal form. ------ 164032/18250500. ------ 1. ==[ start ]==> (((a b)((a a) a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 164033/18250527. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(a (b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(a (b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 164034/18250554. ------ 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))) REDUCED to normal form. ------ 164035/18250608. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b) a)) REDUCED to normal form. ------ 164036/18250635. ------ 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. ------ 164037/18250662. ------ 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)(^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. ------ 164038/18250833. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 164039/18250941. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (a a))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164040/18250977. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(a b))) 3. ==[ beta ]==> ((b b)((^y.a)(a b))) 4. ==[ alpha ]==> ((b b)((^x.a)(a b))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 164041/18251004. ------ 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)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 164042/18251049. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((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. ------ 164043/18251058. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 164044/18251085. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 164045/18251103. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b) c)) 3. ==[ beta ]==> (((b a)(b a))((a b) c)) REDUCED to normal form. ------ 164046/18251166. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(^a.a))(^b.(^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. ------ 164047/18251193. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 164048/18251247. ------ 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.(^y1.y1))(^z1.(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. ------ 164049/18251391. ------ 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)(^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. ------ 164050/18251418. ------ 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 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. ------ 164051/18251445. ------ 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) a)((a a) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a ((a a) a))) REDUCED to normal form. ------ 164052/18251472. ------ 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. ------ 164053/18251499. ------ 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)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 164054/18252192. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 164055/18252210. ------ 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.(^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. ------ 164056/18252291. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 164057/18252300. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 164058/18252327. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^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. ------ 164059/18252399. ------ 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. ------ 164060/18252435. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 164061/18252462. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 164062/18252525. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b ((a a) a))) REDUCED to normal form. ------ 164063/18252552. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (a b))) REDUCED to normal form. ------ 164064/18252579. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a)(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)(a a))) 5. ==[ beta ]==> ((a b)(((a a) a)(a a))) REDUCED to normal form. ------ 164065/18252606. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(a (^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. ------ 164066/18252633. ------ 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. ------ 164067/18252660. ------ 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. ------ 164068/18252687. ------ 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. ------ 164069/18252714. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)(a b))((a a)((a a) a))) REDUCED to normal form. ------ 164070/18253074. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> (b ((^x1.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 164071/18253299. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)((^z.z) a))) 5. ==[ beta ]==> (a ((^y.a)((^z.z) a))) 6. ==[ alpha ]==> (a ((^x.a)((^y.y) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 164072/18253317. ------ 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 ]==> (((^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)((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. ------ 164073/18253344. ------ 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)((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. ------ 164074/18253398. ------ 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. ------ 164075/18253407. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 164076/18253434. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164077/18253488. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 164078/18253596. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.(y1 y1)))) REDUCED to normal form. ------ 164079/18253623. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^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)))) REDUCED to normal form. ------ 164080/18253650. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a a)(a a))) REDUCED to normal form. ------ 164081/18253704. ------ 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.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. ------ 164082/18253722. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.(z z)))) REDUCED to normal form. ------ 164083/18253821. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(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. ------ 164084/18253848. ------ 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. ------ 164085/18253875. ------ 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. ------ 164086/18253902. ------ 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 (^z.z)))) REDUCED to normal form. ------ 164087/18253929. ------ 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)(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. ------ 164088/18254010. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b c)) REDUCED to normal form. ------ 164089/18254118. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 164090/18254145. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(a a))) REDUCED to normal form. ------ 164091/18254154. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^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 ]==> (((^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. ------ 164092/18254450. ------ 1. ==[ start ]==> (^a.((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^x.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 164093/18254451. ------ 1. ==[ start ]==> (a ((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 164094/18262203. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.((^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. ------ 164095/18263364. ------ 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. ------ 164096/18264921. ------ 1. ==[ start ]==> ((^a.a)((^b.b)(^b.(^a.a)))) 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. ------ 164097/18265173. ------ 1. ==[ start ]==> ((^a.(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(c (b (^z.z)))) 3. ==[ beta ]==> (^y.(c (b (^z.z)))) 4. ==[ alpha ]==> (^x.(c (b (^y.y)))) REDUCED to normal form. ------ 164098/18265221. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 164099/18265416. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 164100/18265866. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(a a))((^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. ------ 164101/18266298. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1))))((^x2.b)(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((b ((^x1.b)(^y1.(^z1.z1))))((^x2.b)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.(^z.z))))((^x1.b)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((b b)((^x1.b)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((b b)((^x.b)(^y.(^z.z)))) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 164102/18266472. ------ 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. ------ 164103/18266631. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 164104/18266811. ------ 1. ==[ start ]==> ((^a.(a b))(c (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(c (^y.(a a)))) 3. ==[ beta ]==> ((c (^y.(a a))) b) 4. ==[ alpha ]==> ((c (^x.(a a))) b) REDUCED to normal form. ------ 164105/18267246. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 164106/18267633. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(b (^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(b (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 164107/18268080. ------ 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) a))) 3. ==[ beta ]==> ((((^z.(^x1.(^y1.y1)))((^z1.z1) a))((^z.(^x1.(^y1.y1)))((^z1.z1) a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.(^x2.x2)))((^y2.y2) a)))(^z2.z2)) 5. ==[ beta ]==> (((^y.(^z.z))((^y1.(^z1.(^x2.x2)))((^y2.y2) a)))(^z2.z2)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a)))(^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. ------ 164108/18268704. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(a a)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 9. ==[ beta ]==> (^y.(^z.(a a))) 10. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 164109/18269673. ------ 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.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(^z1.(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164110/18270009. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^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. ------ 164111/18270324. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 164112/18270630. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(z1 (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^z1.(z1 (^x2.(^y2.y2))))) 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. ------ 164113/18272223. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^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. ------ 164114/18272670. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164115/18272673. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 164116/18273483. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.y))) REDUCED to normal form. ------ 164117/18273672. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.b))) REDUCED to normal form. ------ 164118/18273831. ------ 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. ------ 164119/18273834. ------ 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))) REDUCED to normal form. ------ 164120/18274005. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> (b (^x1.((x1 x1) x1))) 4. ==[ alpha ]==> (b (^x.((x x) x))) REDUCED to normal form. ------ 164121/18274671. ------ 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. ------ 164122/18274779. ------ 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.(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 164123/18274887. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(z z)))) REDUCED to normal form. ------ 164124/18274968. ------ 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)))(^x.a)) REDUCED to normal form. ------ 164125/18275049. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(^b.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. ------ 164126/18275394. ------ 1. ==[ start ]==> ((a a)((^b.b)(^b.(^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. ------ 164127/18275502. ------ 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. ------ 164128/18275646. ------ 1. ==[ start ]==> ((a (^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(c (b (^y.y)))) REDUCED to normal form. ------ 164129/18275691. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(^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)))) REDUCED to normal form. ------ 164130/18275727. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.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))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 164131/18275754. ------ 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))(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. ------ 164132/18275808. ------ 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. ------ 164133/18275835. ------ 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 (^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. ------ 164134/18275889. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 164135/18275997. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(a (^x1.(^y1.y1))))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 7. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 8. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 9. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 11. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 12. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 13. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 14. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 164136/18276024. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) 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. ------ 164137/18276078. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(b (^x1.x1)))) 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. ------ 164138/18276105. ------ 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. ------ 164139/18276141. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.(^x1.x1)) a)(^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. ------ 164140/18276168. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 164141/18276195. ------ 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. ------ 164142/18276231. ------ 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. ------ 164143/18276258. ------ 1. ==[ start ]==> (((a (^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)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 164144/18276303. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 164145/18276339. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 164146/18276438. ------ 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. ------ 164147/18276546. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((a (^y.a))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> ((a (^x.a))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.a))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 164148/18276573. ------ 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. ------ 164149/18276636. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 164150/18276663. ------ 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. ------ 164151/18276744. ------ 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. ------ 164152/18276771. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 164153/18276942. ------ 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. ------ 164154/18276969. ------ 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))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(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. ------ 164155/18277023. ------ 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) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) a))) 9. ==[ beta ]==> ((a a)(b ((^y.y) a))) 10. ==[ alpha ]==> ((a a)(b ((^x.x) a))) 11. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 164156/18277104. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 164157/18277284. ------ 1. ==[ start ]==> ((a (a b))(c (^c.(a a)))) 2. ==[ alpha ]==> ((a (a b))(c (^x.(a a)))) REDUCED to normal form. ------ 164158/18277293. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.b)((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 164159/18277437. ------ 1. ==[ start ]==> ((((a a) a) b)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 164160/18277464. ------ 1. ==[ start ]==> (((a b) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 164161/18277491. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 164162/18277545. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 164163/18277626. ------ 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. ------ 164164/18277653. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.x))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 164165/18277689. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 164166/18277716. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(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. ------ 164167/18277797. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.b)(^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))) 9. ==[ beta ]==> (a (^y.a)) 10. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 164168/18277824. ------ 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. ------ 164169/18278049. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((^x1.x1) b))) 3. ==[ beta ]==> (b (c ((^x1.x1) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 164170/18278103. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(a (b (^a.a)))) 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. ------ 164171/18278130. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((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. ------ 164172/18278139. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 164173/18278184. ------ 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) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))((^z1.z1) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 9. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1) a))) 10. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 11. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 12. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 13. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 164174/18278265. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 164175/18278445. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(b (^c.(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. ------ 164176/18278490. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 164177/18278499. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 164178/18278526. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b)(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)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 164179/18278553. ------ 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) 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. ------ 164180/18278733. ------ 1. ==[ start ]==> (((a b) c)((a (a a))(^d.a))) 2. ==[ alpha ]==> (((a b) c)((a (a a))(^x.a))) REDUCED to normal form. ------ 164181/18278760. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) b)(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 164182/18278787. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(^z.z))) REDUCED to normal form. ------ 164183/18278841. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 164184/18278868. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b) b)) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b) b)) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b) b)) 5. ==[ beta ]==> ((a (^x.b))(b b)) REDUCED to normal form. ------ 164185/18279066. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.(^a.a))(^c.(^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. ------ 164186/18279120. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a b))((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 164187/18279147. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.y))(^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. ------ 164188/18279399. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (b (((^z.z)(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (b ((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> (b ((^y.y)(a a))) 10. ==[ alpha ]==> (b ((^x.x)(a a))) 11. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 164189/18279480. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 164190/18279543. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (^y.y))) REDUCED to normal form. ------ 164191/18279651. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(a a))(^b.(^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. ------ 164192/18279678. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a b)(^y.a))) REDUCED to normal form. ------ 164193/18279732. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 164194/18279759. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 164195/18279813. ------ 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.x1))(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 164196/18279876. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 164197/18279903. ------ 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.(^x2.x2)))) 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. ------ 164198/18279957. ------ 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 z)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 164199/18279984. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 164200/18280011. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 164201/18280038. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(^y.b))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 164202/18280065. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 164203/18280146. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 164204/18280155. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164205/18280236. ------ 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 a))(^y.(a a)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.(a 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. ------ 164206/18280317. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a b)((^x1.x1)(^y1.y1)))) 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. ------ 164207/18280425. ------ 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))(((^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. ------ 164208/18280452. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 164209/18280479. ------ 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 (^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. ------ 164210/18280542. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 164211/18280569. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 164212/18280623. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 164213/18280677. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.b)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.b)) REDUCED to normal form. ------ 164214/18280767. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^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. ------ 164215/18280794. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(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. ------ 164216/18280821. ------ 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.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^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. ------ 164217/18280875. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 164218/18280902. ------ 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 y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 164219/18280929. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 164220/18280983. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 164221/18281037. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) a) REDUCED to normal form. ------ 164222/18281073. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(b (b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(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. ------ 164223/18281100. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(a (a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(a (a (^z1.(^x2.x2))))) 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. ------ 164224/18281235. ------ 1. ==[ start ]==> (((^a.b)(^c.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) 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. ------ 164225/18281343. ------ 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 (^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164226/18281406. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 164227/18281433. ------ 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.(^x2.x2)))) REDUCED to normal form. ------ 164228/18281514. ------ 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.(^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. ------ 164229/18281541. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(^z.a)) 6. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.a)) REDUCED to normal form. ------ 164230/18281568. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(^y.b))) REDUCED to normal form. ------ 164231/18281595. ------ 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) 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. ------ 164232/18281676. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a) a)) REDUCED to normal form. ------ 164233/18281703. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 164234/18281739. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 164235/18281766. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 164236/18281793. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.a)(^b.(^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. ------ 164237/18281820. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.z))(^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. ------ 164238/18281847. ------ 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)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.b))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.b))) 7. ==[ beta ]==> ((a a)((^y.(y y))(^z.b))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(^y.b))) 9. ==[ beta ]==> ((a a)((^y.b)(^y.b))) 10. ==[ alpha ]==> ((a a)((^x.b)(^y.b))) 11. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 164239/18281874. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.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. ------ 164240/18281901. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^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. ------ 164241/18282099. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 164242/18282378. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((b b)(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((b b)(a (^y.b))) 6. ==[ alpha ]==> ((b b)(a (^x.b))) REDUCED to normal form. ------ 164243/18282405. ------ 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. ------ 164244/18282459. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 164245/18282486. ------ 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)(a a)) b)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a)) b)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 164246/18282693. ------ 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))(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. ------ 164247/18282702. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1)) 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. ------ 164248/18282729. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a)) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 164249/18282756. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 164250/18282873. ------ 1. ==[ start ]==> (((a (a a))(b a))(c (^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))(c (^x.b))) REDUCED to normal form. ------ 164251/18282900. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(b (^z.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 164252/18282954. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(a a))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 164253/18282981. ------ 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 (^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 164254/18283062. ------ 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 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.y1))) 10. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.x1))) 11. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 12. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 164255/18283089. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.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. ------ 164256/18283116. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 164257/18283143. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^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. ------ 164258/18283314. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c ((a a) a))) 3. ==[ beta ]==> (b (c ((a a) a))) REDUCED to normal form. ------ 164259/18283422. ------ 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. ------ 164260/18283458. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z)) d)) 3. ==[ beta ]==> ((b c)((^y.(^z.z)) d)) 4. ==[ alpha ]==> ((b c)((^x.(^y.y)) d)) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 164261/18283530. ------ 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))) REDUCED to normal form. ------ 164262/18283557. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 164263/18283593. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((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))) REDUCED to normal form. ------ 164264/18283620. ------ 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. ------ 164265/18283701. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) 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. ------ 164266/18283728. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 164267/18283809. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a) b)) REDUCED to normal form. ------ 164268/18283836. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.a))((^z.z) c)) 6. ==[ alpha ]==> ((b (^x.a))((^y.y) c)) 7. ==[ beta ]==> ((b (^x.a)) c) REDUCED to normal form. ------ 164269/18283926. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 164270/18283953. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.b)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.b)) REDUCED to normal form. ------ 164271/18284088. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 164272/18284115. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 164273/18284142. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.b))) REDUCED to normal form. ------ 164274/18284196. ------ 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 (^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. ------ 164275/18284223. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((b a)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((b a)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((b a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((b a)(a ((^x.x) a))) 11. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 164276/18284250. ------ 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. ------ 164277/18284304. ------ 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. ------ 164278/18284475. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((a a) a))) 3. ==[ beta ]==> (b (a ((a a) a))) REDUCED to normal form. ------ 164279/18284583. ------ 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. ------ 164280/18284700. ------ 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))) 7. ==[ beta ]==> (a (a (^y.a))) 8. ==[ alpha ]==> (a (a (^x.a))) REDUCED to normal form. ------ 164281/18284808. ------ 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. ------ 164282/18284880. ------ 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. ------ 164283/18284916. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 164284/18284943. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(b b)) REDUCED to normal form. ------ 164285/18284988. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164286/18285051. ------ 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. ------ 164287/18285105. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 164288/18285141. ------ 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. ------ 164289/18285168. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(^x1.x1))) 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. ------ 164290/18285195. ------ 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.(^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. ------ 164291/18285222. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^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. ------ 164292/18285249. ------ 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)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 164293/18285303. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 164294/18285330. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b (^b.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. ------ 164295/18285357. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.(y y)))) REDUCED to normal form. ------ 164296/18285411. ------ 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 (^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. ------ 164297/18285438. ------ 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. ------ 164298/18285465. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.y))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 164299/18285519. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(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))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 164300/18285537. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) a)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 164301/18285555. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((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 ]==> (((a (^z.z))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 164302/18290328. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.((^a.a) b))) 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. ------ 164303/18293613. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164304/18296349. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164305/18296664. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z (^x1.x1))) a)) 3. ==[ eta ]==> ((^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. ------ 164306/18297081. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(^a.(a (^a.a))))) 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)))) REDUCED to normal form. ------ 164307/18297159. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164308/18297285. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1)(a a))(^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. ------ 164309/18298617. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (^y.(((^z.a)((^x1.x1) b))((^z.a)((^x1.x1) b)))) 4. ==[ alpha ]==> (^x.(((^y.a)((^z.z) b))((^x1.a)((^y1.y1) b)))) 5. ==[ beta ]==> (^x.(a ((^x1.a)((^y1.y1) b)))) 6. ==[ alpha ]==> (^x.(a ((^y.a)((^z.z) b)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 164310/18299061. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 164311/18299499. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((((a (^z.(^x1.x1)))(^y1.a))((a (^z.(^x1.x1)))(^y1.a)))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.a))((a (^x1.(^y1.y1)))(^z1.a)))(^x2.x2)) REDUCED to normal form. ------ 164312/18299781. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^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. ------ 164313/18300804. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1) b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 164314/18300807. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.((^a.a) b))) 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. ------ 164315/18301695. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164316/18301743. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 164317/18302049. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)(^z1.(^x2.(^y2.(^z2.z2))))) 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. ------ 164318/18302328. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(b a))) 3. ==[ beta ]==> ((b a)(^y.(b a))) 4. ==[ alpha ]==> ((b a)(^x.(b a))) REDUCED to normal form. ------ 164319/18302346. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^a.(^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. ------ 164320/18302616. ------ 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. ------ 164321/18303399. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 164322/18303642. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^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. ------ 164323/18303651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 164324/18304089. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164325/18304092. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 164326/18305424. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (b (^x1.(^y1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 164327/18305838. ------ 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. ------ 164328/18305865. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 164329/18305973. ------ 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. ------ 164330/18306069. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^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. ------ 164331/18306387. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^b.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. ------ 164332/18306486. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x (^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.z)) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 164333/18306492. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a) a)) 3. ==[ beta ]==> (((^z.a) a)(((^z.a) a)(^y.y))) 4. ==[ alpha ]==> (((^x.a) a)(((^y.a) a)(^z.z))) 5. ==[ beta ]==> (a (((^y.a) a)(^z.z))) 6. ==[ alpha ]==> (a (((^x.a) a)(^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 164334/18306831. ------ 1. ==[ start ]==> ((a (^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 164335/18307020. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(^a.a))(^b.b))) 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. ------ 164336/18307110. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(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. ------ 164337/18307146. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^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)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 164338/18307191. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 164339/18307218. ------ 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) 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. ------ 164340/18307245. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(b (a (a a)))) REDUCED to normal form. ------ 164341/18307272. ------ 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 (^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. ------ 164342/18307299. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 164343/18307407. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a) a)(b a))) 3. ==[ beta ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 164344/18307488. ------ 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. ------ 164345/18307515. ------ 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. ------ 164346/18307542. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.(^z.z)) 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. ------ 164347/18307560. ------ 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 (^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. ------ 164348/18307641. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 164349/18307659. ------ 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. ------ 164350/18307686. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 164351/18307713. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b a)(^y.a))) REDUCED to normal form. ------ 164352/18307740. ------ 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. ------ 164353/18307767. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 164354/18307776. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164355/18307803. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((a a)(^y1.y1)))) 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. ------ 164356/18307857. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164357/18307911. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.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. ------ 164358/18307938. ------ 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. ------ 164359/18308235. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^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. ------ 164360/18308289. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))(^b.b))) 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))) 7. ==[ beta ]==> (a ((^y.y)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 164361/18308325. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(c ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(c ((a a)(a a)))) 5. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 164362/18308352. ------ 1. ==[ start ]==> ((((a a) a) a)(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)(b (b (^x.x)))) REDUCED to normal form. ------ 164363/18308406. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))(a a))) REDUCED to normal form. ------ 164364/18308433. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 164365/18308460. ------ 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. ------ 164366/18308487. ------ 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 (^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164367/18308514. ------ 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. ------ 164368/18308703. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 164369/18308721. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(c (^z.(a a)))) 3. ==[ beta ]==> ((^y.b)(c (^z.(a a)))) 4. ==[ alpha ]==> ((^x.b)(c (^y.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 164370/18308883. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 164371/18308991. ------ 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. ------ 164372/18309072. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 164373/18309099. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 164374/18309117. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 164375/18309171. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z)) a)) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z)) a)) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 164376/18309198. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 164377/18309225. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b) c)) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) b) c)) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) b) c)) 7. ==[ beta ]==> (a (((^y.y) b) c)) 8. ==[ alpha ]==> (a (((^x.x) b) c)) 9. ==[ beta ]==> (a (b c)) REDUCED to normal form. ------ 164378/18309315. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(^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 a) REDUCED to normal form. ------ 164379/18309342. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 164380/18309396. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(^x2.x2)))) 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. ------ 164381/18309477. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 164382/18309486. ------ 1. ==[ start ]==> (((a b) b)(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b) b)(c ((^x.x) b))) 3. ==[ beta ]==> (((a b) b)(c b)) REDUCED to normal form. ------ 164383/18309513. ------ 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. ------ 164384/18309540. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(a (b (^y.y)))) REDUCED to normal form. ------ 164385/18309567. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(a a))(a a))) REDUCED to normal form. ------ 164386/18309621. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 164387/18309648. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(a (a a)))) 5. ==[ beta ]==> ((^y.(y y))((b a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(x x))((b a)(a (a a)))) 7. ==[ beta ]==> (((b a)(a (a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 164388/18309675. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 164389/18309702. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 164390/18309729. ------ 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. ------ 164391/18309927. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 164392/18309954. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 164393/18309981. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 164394/18310152. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 164395/18310233. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^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. ------ 164396/18310260. ------ 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)((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. ------ 164397/18310314. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((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)))) 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. ------ 164398/18310395. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 164399/18310656. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b) b)) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 164400/18310908. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 164401/18311016. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 164402/18311097. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 164403/18311178. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164404/18311286. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1) b)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) b)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 164405/18311304. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) b) a)) 3. ==[ beta ]==> (((a a)(b a))(b a)) REDUCED to normal form. ------ 164406/18311331. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 164407/18311358. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((b a) c)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a) c)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a) c)) 5. ==[ beta ]==> ((a (a a))((b a) c)) REDUCED to normal form. ------ 164408/18311583. ------ 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.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164409/18311862. ------ 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 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. ------ 164410/18311889. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.x1))(b a))) REDUCED to normal form. ------ 164411/18311907. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 164412/18311961. ------ 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.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a a))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(a a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(a a))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 164413/18312042. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 164414/18312150. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(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. ------ 164415/18312177. ------ 1. ==[ start ]==> ((a (^b.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 164416/18312222. ------ 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. ------ 164417/18312249. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 164418/18312276. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a) b)) 3. ==[ beta ]==> (((a (a a))(a a))((b a) b)) REDUCED to normal form. ------ 164419/18312303. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z)) c)) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y)) c)) 5. ==[ beta ]==> ((a b)(((a a)(^y.y)) c)) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 164420/18312528. ------ 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.z1)(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)((^z1.z1)(^x2.(^y2.(^z2.z2))))) 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. ------ 164421/18312780. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 164422/18312807. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a a)(b a))) 3. ==[ beta ]==> ((b a)((a a)(b a))) REDUCED to normal form. ------ 164423/18312825. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(a (^a.(^a.(^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. ------ 164424/18312906. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 164425/18312987. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 164426/18313095. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 164427/18313167. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a)) c)) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a)) c)) 5. ==[ beta ]==> (((a a) b)((a a) c)) REDUCED to normal form. ------ 164428/18313437. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 164429/18313662. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 164430/18313770. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 164431/18313851. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 164432/18313878. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 164433/18313932. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 164434/18314013. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(^a.a))(^b.(^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. ------ 164435/18314076. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (a b))) REDUCED to normal form. ------ 164436/18314130. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 164437/18314157. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 164438/18314184. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)(a (^y.y)))) REDUCED to normal form. ------ 164439/18314382. ------ 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. ------ 164440/18314409. ------ 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.(^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. ------ 164441/18314436. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(^z.a))) REDUCED to normal form. ------ 164442/18314490. ------ 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 (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. ------ 164443/18314517. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (^z.a))) 6. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 164444/18314544. ------ 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. ------ 164445/18314571. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 164446/18314742. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 164447/18314886. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b c)((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((b c)((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((b c)((^y.y) a)) 8. ==[ alpha ]==> ((b c)((^x.x) a)) 9. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 164448/18314913. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 164449/18314958. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (^c.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. ------ 164450/18314985. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b (^z.b))) 3. ==[ beta ]==> ((^y.y)(b (^z.b))) 4. ==[ alpha ]==> ((^x.x)(b (^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 164451/18315039. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b)(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 164452/18315120. ------ 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. ------ 164453/18315228. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> ((^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. ------ 164454/18315408. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b) a)) 5. ==[ beta ]==> ((a b)((^y.b) a)) 6. ==[ alpha ]==> ((a b)((^x.b) a)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 164455/18315462. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b a)((^y.(^z.z)) c)) 6. ==[ alpha ]==> ((b a)((^x.(^y.y)) c)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 164456/18315624. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^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. ------ 164457/18315651. ------ 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. ------ 164458/18315678. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 164459/18315822. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.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. ------ 164460/18315903. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 164461/18316011. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c (^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164462/18316146. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 164463/18316173. ------ 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. ------ 164464/18316227. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.x1))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.z))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 164465/18316308. ------ 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))(^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. ------ 164466/18316317. ------ 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. ------ 164467/18316344. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 164468/18316371. ------ 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. ------ 164469/18316425. ------ 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))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1)) a)) REDUCED to normal form. ------ 164470/18316452. ------ 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. ------ 164471/18316551. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^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. ------ 164472/18316569. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 164473/18316596. ------ 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. ------ 164474/18316623. ------ 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. ------ 164475/18316650. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y)) c)) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y)) c)) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x)) c)) REDUCED to normal form. ------ 164476/18316704. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x)) a)) 3. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 164477/18316731. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.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. ------ 164478/18316839. ------ 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.(^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. ------ 164479/18316866. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)(^b.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. ------ 164480/18316893. ------ 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)) 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. ------ 164481/18316965. ------ 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 (^y.y))(a ((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 164482/18316974. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a) a)) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 164483/18317625. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(z (z (^x1.x1))))) 3. ==[ eta ]==> ((^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. ------ 164484/18327453. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((^x.(x (x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.z)) 5. ==[ beta ]==> ((^z.z)((^z.z)(^y.y))) 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. ------ 164485/18328110. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(a (a (a (^z.z))))) 3. ==[ eta ]==> ((^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. ------ 164486/18328113. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 164487/18328380. ------ 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. ------ 164488/18328536. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 164489/18328605. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164490/18328941. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.a))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.a))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 164491/18329676. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)((^z.z) 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) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 164492/18330063. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (^y.((((^z.z) a)(^x1.x1))(((^z.z) a)(^x1.x1)))) 4. ==[ alpha ]==> (^x.((((^y.y) a)(^z.z))(((^x1.x1) a)(^y1.y1)))) 5. ==[ beta ]==> (^x.((a (^z.z))(((^x1.x1) a)(^y1.y1)))) 6. ==[ alpha ]==> (^x.((a (^y.y))(((^z.z) a)(^x1.x1)))) 7. ==[ beta ]==> (^x.((a (^y.y))(a (^x1.x1)))) 8. ==[ alpha ]==> (^x.((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 164493/18330885. ------ 1. ==[ start ]==> (((^a.b) c)(^a.(^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. ------ 164494/18331236. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 164495/18331596. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.((x x)(x x)))) REDUCED to normal form. ------ 164496/18331701. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(^y.y))(a (a a)))) 3. ==[ eta ]==> (b (((a a)(^y.y))(a (a a)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 164497/18331938. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.(y y)))) REDUCED to normal form. ------ 164498/18332250. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)(^b.b))) 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. ------ 164499/18333141. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164500/18333456. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(c ((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 164501/18333801. ------ 1. ==[ start ]==> (((a a)(^b.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 164502/18334071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 a))) REDUCED to normal form. ------ 164503/18334350. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(b y))) 3. ==[ eta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 164504/18334455. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((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)(a (a a))))) REDUCED to normal form. ------ 164505/18334845. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 164506/18334854. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 164507/18335097. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 164508/18335988. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^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. ------ 164509/18336375. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(z b))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(z b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(y b))) 5. ==[ beta ]==> ((a b)(^y.(y b))) 6. ==[ alpha ]==> ((a b)(^x.(x b))) REDUCED to normal form. ------ 164510/18337311. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 164511/18337446. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 164512/18337515. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 164513/18337671. ------ 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. ------ 164514/18337752. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 164515/18337932. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(^b.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. ------ 164516/18337938. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a ((^z.z) a))) 3. ==[ beta ]==> ((a ((^z.z) a))((a ((^z.z) a))(^y.y))) 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. ------ 164517/18337941. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.((^z.z) y))) 3. ==[ eta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 164518/18338295. ------ 1. ==[ start ]==> (((^a.a) a)((^b.b)(^b.(^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. ------ 164519/18338376. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164520/18338403. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 164521/18338484. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 164522/18338574. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 164523/18338601. ------ 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. ------ 164524/18338610. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.a)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.a)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 164525/18338790. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 164526/18338817. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(a a))) REDUCED to normal form. ------ 164527/18338844. ------ 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. ------ 164528/18338871. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a) a)(b a))) REDUCED to normal form. ------ 164529/18339024. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 164530/18339069. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 164531/18339096. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 164532/18339231. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164533/18339258. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 164534/18339312. ------ 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)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 164535/18339321. ------ 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. ------ 164536/18339348. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (a ((^y.(y y))((^z.z) b))) 6. ==[ alpha ]==> (a ((^x.(x x))((^y.y) b))) 7. ==[ beta ]==> (a (((^y.y) b)((^y.y) b))) 8. ==[ alpha ]==> (a (((^x.x) b)((^y.y) b))) 9. ==[ beta ]==> (a (b ((^y.y) b))) 10. ==[ alpha ]==> (a (b ((^x.x) b))) 11. ==[ beta ]==> (a (b b)) REDUCED to normal form. ------ 164537/18339375. ------ 1. ==[ start ]==> (((a a)(^b.(^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) REDUCED to normal form. ------ 164538/18339402. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))(b (^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. ------ 164539/18339429. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.a))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.a))(^z.z)) 8. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 164540/18339447. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 164541/18339780. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 164542/18340005. ------ 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))) REDUCED to normal form. ------ 164543/18340032. ------ 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)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a b))) REDUCED to normal form. ------ 164544/18340059. ------ 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. ------ 164545/18340086. ------ 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. ------ 164546/18340113. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 164547/18340140. ------ 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. ------ 164548/18340167. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> ((a (a b))(a ((^y.y) b))) 4. ==[ alpha ]==> ((a (a b))(a ((^x.x) b))) 5. ==[ beta ]==> ((a (a b))(a b)) REDUCED to normal form. ------ 164549/18340257. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(^x1.x1))) IRREDUCIBLE: cycle. ------ 164550/18340320. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)((^y.y) 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. ------ 164551/18340338. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 164552/18340347. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 164553/18340365. ------ 1. ==[ start ]==> (((^a.a)(a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a 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. ------ 164554/18340428. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 164555/18340446. ------ 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. ------ 164556/18340455. ------ 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. ------ 164557/18340482. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 164558/18340509. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 164559/18340527. ------ 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 a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 164560/18340536. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 164561/18340554. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 164562/18340725. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 164563/18340941. ------ 1. ==[ start ]==> (((a b) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.y))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 164564/18341067. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1) c)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1) c)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1) c)) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) c)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) c)) 9. ==[ beta ]==> ((^y.y)((^z.z) c)) 10. ==[ alpha ]==> ((^x.x)((^y.y) c)) 11. ==[ beta ]==> ((^y.y) c) 12. ==[ alpha ]==> ((^x.x) c) 13. ==[ beta ]==> c REDUCED to normal form. ------ 164565/18341220. ------ 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)(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. ------ 164566/18341247. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a b))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(^y.y))) REDUCED to normal form. ------ 164567/18341274. ------ 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. ------ 164568/18341301. ------ 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)(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. ------ 164569/18341328. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a (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. ------ 164570/18341355. ------ 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)))) 3. ==[ beta ]==> ((((a a) a) a)((a a)((a a)(a a)))) REDUCED to normal form. ------ 164571/18341373. ------ 1. ==[ start ]==> (((^a.b) c)(a (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 164572/18341472. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((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. ------ 164573/18341607. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 164574/18341616. ------ 1. ==[ start ]==> (((a b) c)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 164575/18341643. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(y y))(b a))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(b a))) 5. ==[ beta ]==> (((a a) b)((b a)(b a))) REDUCED to normal form. ------ 164576/18341670. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 164577/18341688. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.a))(^b.b))) 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))) REDUCED to normal form. ------ 164578/18341724. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(a a))) REDUCED to normal form. ------ 164579/18341751. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 164580/18341769. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b) b)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b) b)) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b b)) REDUCED to normal form. ------ 164581/18341805. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164582/18341859. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 164583/18341886. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(a a))(^c.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. ------ 164584/18341913. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 164585/18342057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b ((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b ((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b ((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z) b))) 7. ==[ beta ]==> ((^y.y)(b ((^z.z) 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. ------ 164586/18342084. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 164587/18342111. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a b) a)(((^y.y) b)(a a))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b)(a a))) 5. ==[ beta ]==> (((a b) a)(b (a a))) REDUCED to normal form. ------ 164588/18342138. ------ 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)))(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. ------ 164589/18342165. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((b a) a)) REDUCED to normal form. ------ 164590/18342192. ------ 1. ==[ start ]==> ((a (b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 164591/18342426. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(a (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (^y.(a a)))) REDUCED to normal form. ------ 164592/18342471. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 164593/18342498. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.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. ------ 164594/18342534. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 164595/18342552. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(a a))(^b.(^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. ------ 164596/18342561. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 164597/18342615. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 164598/18342633. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^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 (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 164599/18342642. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 164600/18342669. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.a))(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 164601/18342696. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 164602/18342741. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 164603/18343119. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1))) b)) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 164604/18343416. ------ 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 (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(^x1.x1))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 164605/18343425. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1)))(a 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. ------ 164606/18343497. ------ 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)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.(y1 y1)))) 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. ------ 164607/18343506. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 164608/18343533. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 164609/18343560. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 164610/18343605. ------ 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 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. ------ 164611/18343614. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(((^y1.y1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(a a))) REDUCED to normal form. ------ 164612/18343632. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^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. ------ 164613/18343911. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 164614/18343947. ------ 1. ==[ start ]==> ((a ((^a.a) b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(c ((a a)(^y.y)))) 3. ==[ beta ]==> ((a b)(c ((a a)(^y.y)))) 4. ==[ alpha ]==> ((a b)(c ((a a)(^x.x)))) REDUCED to normal form. ------ 164615/18344235. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 164616/18344289. ------ 1. ==[ start ]==> (((a a)(^b.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 164617/18344307. ------ 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)((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. ------ 164618/18344361. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^x1.a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 164619/18344397. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(a (a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 164620/18344424. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 164621/18344442. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^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. ------ 164622/18344451. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^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. ------ 164623/18344478. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 164624/18344505. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 164625/18344559. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b a)) REDUCED to normal form. ------ 164626/18344784. ------ 1. ==[ start ]==> (((a b)((a a) a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(c ((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(c (a a))) REDUCED to normal form. ------ 164627/18344811. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 164628/18344838. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(a (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (b a))) REDUCED to normal form. ------ 164629/18344892. ------ 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))(a (^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. ------ 164630/18344919. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b)((^y.y) a))) 3. ==[ beta ]==> ((b (a a))((a b)((^y.y) a))) 4. ==[ alpha ]==> ((b (a a))((a b)((^x.x) a))) 5. ==[ beta ]==> ((b (a a))((a b) a)) REDUCED to normal form. ------ 164631/18344946. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 164632/18345117. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((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. ------ 164633/18345225. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^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. ------ 164634/18345261. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((b b)((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((b b)((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((b b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 164635/18345288. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(a b))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 164636/18345306. ------ 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. ------ 164637/18345333. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a a)(^c.(^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. ------ 164638/18345342. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((a a)(^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. ------ 164639/18345387. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a)) b)) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a)) b)) 5. ==[ beta ]==> (((b a)(b a))((a a) b)) REDUCED to normal form. ------ 164640/18345450. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 164641/18345477. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(^a.a))(^b.(^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. ------ 164642/18345531. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 164643/18345585. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.y1))) REDUCED to normal form. ------ 164644/18345675. ------ 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. ------ 164645/18345702. ------ 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)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a (a a)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (a a)))) 7. ==[ beta ]==> (((a (^x.x)) b)(a (a a))) REDUCED to normal form. ------ 164646/18345729. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (a a))((^z.z)(^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. ------ 164647/18345756. ------ 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. ------ 164648/18345783. ------ 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 (^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 164649/18345810. ------ 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)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(a a))) REDUCED to normal form. ------ 164650/18346305. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164651/18346476. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(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. ------ 164652/18346494. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b)(^x1.x1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b)(^y1.y1))) REDUCED to normal form. ------ 164653/18346503. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 164654/18346575. ------ 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. ------ 164655/18346584. ------ 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. ------ 164656/18346611. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 164657/18346683. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a 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. ------ 164658/18346692. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 164659/18346719. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 164660/18346746. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(^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. ------ 164661/18346809. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(c (^y.y))) REDUCED to normal form. ------ 164662/18346836. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b ((a a) a))) REDUCED to normal form. ------ 164663/18346863. ------ 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))) 5. ==[ beta ]==> ((a b)(a (a b))) REDUCED to normal form. ------ 164664/18346890. ------ 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)(a a))) REDUCED to normal form. ------ 164665/18346917. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b a)((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> ((b a)((^x.x)(a (^y.y)))) 9. ==[ beta ]==> ((b a)(a (^y.y))) 10. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 164666/18346944. ------ 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. ------ 164667/18346971. ------ 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. ------ 164668/18346998. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 164669/18347025. ------ 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. ------ 164670/18347277. ------ 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. ------ 164671/18347583. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> (a ((^y.(y y))(a (^z.z)))) 6. ==[ alpha ]==> (a ((^x.(x x))(a (^y.y)))) 7. ==[ beta ]==> (a ((a (^y.y))(a (^y.y)))) 8. ==[ alpha ]==> (a ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 164672/18347601. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 164673/18347628. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(y1 y1)))) 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. ------ 164674/18347682. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1)) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z)) a)) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z)) a)) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y)) a)) 9. ==[ beta ]==> ((b b)((^y.y) a)) 10. ==[ alpha ]==> ((b b)((^x.x) a)) 11. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 164675/18347691. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 164676/18347718. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 164677/18347772. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^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. ------ 164678/18347799. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 164679/18347871. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.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. ------ 164680/18347880. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.a))) REDUCED to normal form. ------ 164681/18347907. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (^z.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 164682/18347934. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 164683/18347988. ------ 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)(^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. ------ 164684/18348006. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 164685/18348105. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (a (^y.y)))) 3. ==[ beta ]==> (((a (a a)) b)(c (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) b)(c (a (^x.x)))) REDUCED to normal form. ------ 164686/18348132. ------ 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 ((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b ((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b ((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(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. ------ 164687/18348159. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (a (a a)))) REDUCED to normal form. ------ 164688/18348186. ------ 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. ------ 164689/18348213. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^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)))) REDUCED to normal form. ------ 164690/18348240. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a a) a)) REDUCED to normal form. ------ 164691/18348321. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b c)) 3. ==[ beta ]==> ((b (a (a a)))(b c)) REDUCED to normal form. ------ 164692/18348402. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (a (^y.y)))) 5. ==[ beta ]==> ((a a)(b (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(b (a (^x.x)))) REDUCED to normal form. ------ 164693/18348420. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.a)) 6. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 164694/18348429. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a ((^y.y) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 164695/18348438. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^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 ]==> (((^z.a) a)(^y.y)) 6. ==[ alpha ]==> (((^x.a) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 164696/18349089. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ eta ]==> ((^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. ------ 164697/18358917. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^b.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. ------ 164698/18359286. ------ 1. ==[ start ]==> ((^a.(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1)))) 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. ------ 164699/18359313. ------ 1. ==[ start ]==> ((^a.b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 164700/18359394. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.(a a))(^x1.(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((a a)(^x1.x1)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 164701/18359583. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(^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))) REDUCED to normal form. ------ 164702/18359586. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 164703/18359595. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((^y.a)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 164704/18359754. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b a)((a a) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 164705/18360636. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((^y.(a a))(^z.(a a)))((^y.(a a))(^z.(a a))))((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((^x.(a a))(^y.(a a)))((^z.(a a))(^x1.(a a))))((^y1.(a a))(^z1.(a a)))) 5. ==[ beta ]==> (((a a)((^z.(a a))(^x1.(a a))))((^y1.(a a))(^z1.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(a a))))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^z.(a a))(^x1.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 164706/18360837. ------ 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.(^x2.x2)) y1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 164707/18360969. ------ 1. ==[ start ]==> ((^a.(^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 164708/18361611. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^b.(b (^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 (^y.y))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 164709/18361998. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.(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. ------ 164710/18362418. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.b)(a (^a.a)))) 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. ------ 164711/18362709. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 164712/18363069. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.(a a)))) REDUCED to normal form. ------ 164713/18363744. ------ 1. ==[ start ]==> (((a a)(b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((^y.y) x))) 3. ==[ eta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 164714/18364689. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 164715/18364929. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.a)(^c.(^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. ------ 164716/18365265. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(b a))) 3. ==[ beta ]==> (((^y.y) b)(^z.(b a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(b a))) 5. ==[ beta ]==> (b (^y.(b a))) 6. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 164717/18366327. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 164718/18366822. ------ 1. ==[ start ]==> (((a b)(a b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 164719/18367008. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164720/18367848. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.z))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.y))) 5. ==[ beta ]==> ((a b)(^y.(^z.y))) 6. ==[ alpha ]==> ((a b)(^x.(^y.x))) REDUCED to normal form. ------ 164721/18368169. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ eta ]==> ((^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. ------ 164722/18368343. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 164723/18369036. ------ 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. ------ 164724/18369144. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 164725/18369333. ------ 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)(^x.a)) REDUCED to normal form. ------ 164726/18369411. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(^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 REDUCED to normal form. ------ 164727/18369414. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.a))) REDUCED to normal form. ------ 164728/18369423. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164729/18369786. ------ 1. ==[ start ]==> ((a (a a))((^b.b)(^b.(^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. ------ 164730/18369813. ------ 1. ==[ start ]==> ((a b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 164731/18369894. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(a a))(^c.(^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. ------ 164732/18370083. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(^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)))) REDUCED to normal form. ------ 164733/18370092. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.a)(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.a)(a (a (a (^y.y))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 164734/18370119. ------ 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)(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. ------ 164735/18370173. ------ 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. ------ 164736/18370182. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a)) d)) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 164737/18370200. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 164738/18370254. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b a)((a a) a))) REDUCED to normal form. ------ 164739/18370362. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.(y y))(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.(x x))(((a a) a)(b a))) 5. ==[ beta ]==> ((((a a) a)(b a))(((a a) a)(b a))) REDUCED to normal form. ------ 164740/18370389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 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. ------ 164741/18370443. ------ 1. ==[ start ]==> (((^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)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) 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. ------ 164742/18370470. ------ 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. ------ 164743/18370497. ------ 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.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.(^y1.y1)) 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. ------ 164744/18370533. ------ 1. ==[ start ]==> ((((^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.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. ------ 164745/18370560. ------ 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. ------ 164746/18370623. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a (a a))) REDUCED to normal form. ------ 164747/18370650. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 164748/18370668. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b a)(^y.a))) 3. ==[ beta ]==> ((b b)((b a)(^y.a))) 4. ==[ alpha ]==> ((b b)((b a)(^x.a))) REDUCED to normal form. ------ 164749/18370803. ------ 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. ------ 164750/18370830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (a a))(^b.b))) 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. ------ 164751/18370857. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 164752/18370938. ------ 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. ------ 164753/18370965. ------ 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) REDUCED to normal form. ------ 164754/18371028. ------ 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. ------ 164755/18371055. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 164756/18371136. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 164757/18371307. ------ 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. ------ 164758/18371334. ------ 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.(^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)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 164759/18371388. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> ((a a)(((a a)(a a))(a (^y.y)))) 8. ==[ alpha ]==> ((a a)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 164760/18371397. ------ 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. ------ 164761/18371469. ------ 1. ==[ start ]==> ((a (^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.b))((b a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.b))((b a)(^y.y))) REDUCED to normal form. ------ 164762/18371658. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 164763/18371802. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) 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. ------ 164764/18371829. ------ 1. ==[ start ]==> (((a b) a)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 164765/18371856. ------ 1. ==[ start ]==> (((a a)(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 164766/18371910. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a 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. ------ 164767/18371937. ------ 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. ------ 164768/18371964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 164769/18372018. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 164770/18372054. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 164771/18372081. ------ 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))((a a)(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. ------ 164772/18372108. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(b (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(b (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 164773/18372189. ------ 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. ------ 164774/18372216. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 164775/18372468. ------ 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. ------ 164776/18372495. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(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. ------ 164777/18372549. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a (^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a (^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 11. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 12. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 13. ==[ beta ]==> (b (a (^y.y))) 14. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 164778/18372558. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) c) REDUCED to normal form. ------ 164779/18372630. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 164780/18372837. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 164781/18372918. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.b)(a (^a.a)))) 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. ------ 164782/18373098. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) c)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) c)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 164783/18373152. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) 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. ------ 164784/18373206. ------ 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. ------ 164785/18373233. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(a a)) a)) 3. ==[ beta ]==> ((a (^y.b))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(a a)) a)) REDUCED to normal form. ------ 164786/18373287. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1))) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1))) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1))) c)) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1))) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164787/18373458. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 164788/18373512. ------ 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.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))((a a) a)) a) REDUCED to normal form. ------ 164789/18373539. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.z1))) 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. ------ 164790/18373764. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(a b))) 5. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 164791/18373845. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (b (((^z.z) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 164792/18374016. ------ 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)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 164793/18374043. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(a a))(^b.(^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. ------ 164794/18374097. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(^z.b))) REDUCED to normal form. ------ 164795/18374124. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(a a))) 6. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 164796/18374151. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 164797/18374241. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)((^y.y) b))) 3. ==[ beta ]==> (((a a)(b a))((^y.y) b)) 4. ==[ alpha ]==> (((a a)(b a))((^x.x) b)) 5. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 164798/18374268. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(^x1.x1))) 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. ------ 164799/18374295. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 164800/18374376. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 164801/18374403. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 164802/18374457. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.(a 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. ------ 164803/18374601. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 164804/18374682. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(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. ------ 164805/18374790. ------ 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 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. ------ 164806/18374817. ------ 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) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((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. ------ 164807/18374844. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 164808/18374907. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 164809/18374934. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((b a)(^y.(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 164810/18374988. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 164811/18375015. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 164812/18375042. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a) a)(^z.a))) REDUCED to normal form. ------ 164813/18375096. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(^x1.(a a)))) REDUCED to normal form. ------ 164814/18375132. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 164815/18375159. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 164816/18375186. ------ 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)(^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 164817/18375213. ------ 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.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))(^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. ------ 164818/18375294. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 164819/18375321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 164820/18375402. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 164821/18375429. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.a)(^c.(^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)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 164822/18375438. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(c ((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(^z.z)))) 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. ------ 164823/18375465. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(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. ------ 164824/18375600. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(a (a a)))) 3. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 164825/18375708. ------ 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)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((^x2.x2)(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. ------ 164826/18375762. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(b a))) 3. ==[ beta ]==> (((^y.y) b)((a a)(b a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(b a))) 5. ==[ beta ]==> (b ((a a)(b a))) REDUCED to normal form. ------ 164827/18375798. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a)(^y1.y1))) REDUCED to normal form. ------ 164828/18375879. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))((a b)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.(a a))((a b)(^y.(y y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 164829/18375906. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 164830/18375933. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.a)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.a)) REDUCED to normal form. ------ 164831/18375960. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 164832/18375987. ------ 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) a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (^z.(a a)))) REDUCED to normal form. ------ 164833/18376068. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a) a)) 3. ==[ beta ]==> ((b (^y.y))((b a) a)) 4. ==[ alpha ]==> ((b (^x.x))((b a) a)) REDUCED to normal form. ------ 164834/18376104. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 164835/18376131. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 164836/18376158. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a (b a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((a (b a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 164837/18376212. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.a))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.a))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 164838/18376239. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(x x))(^y.b))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.b)(^y.b))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 164839/18376266. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.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. ------ 164840/18376464. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^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)(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 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. ------ 164841/18376743. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (a a))(^y.a))) 3. ==[ beta ]==> ((b b)((a (a a))(^y.a))) 4. ==[ alpha ]==> ((b b)((a (a a))(^x.a))) REDUCED to normal form. ------ 164842/18376770. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) 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. ------ 164843/18376824. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 164844/18376851. ------ 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.y1)) a)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 164845/18377058. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(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. ------ 164846/18377094. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 164847/18377121. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 164848/18377292. ------ 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. ------ 164849/18377319. ------ 1. ==[ start ]==> (((a b)(a b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 164850/18377346. ------ 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 a)) REDUCED to normal form. ------ 164851/18377373. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 164852/18377427. ------ 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. ------ 164853/18377454. ------ 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 z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b (a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.z))) 11. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 12. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 164854/18377481. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 164855/18377508. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^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. ------ 164856/18377787. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((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. ------ 164857/18377823. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a) c)) 3. ==[ beta ]==> ((b c)((^y.a) c)) 4. ==[ alpha ]==> ((b c)((^x.a) c)) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 164858/18377895. ------ 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 (^x.x))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 164859/18377922. ------ 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 (^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. ------ 164860/18377985. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b)(^x1.x1))) REDUCED to normal form. ------ 164861/18378066. ------ 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. ------ 164862/18378093. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.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. ------ 164863/18378174. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b) a)) REDUCED to normal form. ------ 164864/18378201. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a) b)) 3. ==[ beta ]==> ((b (^y.a))(((a a) a) b)) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a) b)) REDUCED to normal form. ------ 164865/18378291. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 164866/18378345. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.b))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.b))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.b))) 7. ==[ beta ]==> ((a b)(^y.b)) 8. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 164867/18378480. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 164868/18378507. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.a))) REDUCED to normal form. ------ 164869/18378588. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 164870/18378615. ------ 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))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 164871/18378669. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 164872/18378840. ------ 1. ==[ start ]==> (((^a.b)(^c.(^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)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 164873/18378948. ------ 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)((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164874/18379065. ------ 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. ------ 164875/18379110. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c d)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c d)) 3. ==[ beta ]==> ((^y.y)(c d)) 4. ==[ alpha ]==> ((^x.x)(c d)) 5. ==[ beta ]==> (c d) REDUCED to normal form. ------ 164876/18379173. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 164877/18379200. ------ 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. ------ 164878/18379245. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c ((^z.z) a))) 3. ==[ beta ]==> (b (c ((^z.z) a))) 4. ==[ alpha ]==> (b (c ((^x.x) a))) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 164879/18379254. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a)) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z)) d)) REDUCED to normal form. ------ 164880/18379308. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1)) 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. ------ 164881/18379353. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164882/18379362. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 164883/18379470. ------ 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.(^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. ------ 164884/18379506. ------ 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.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. ------ 164885/18379533. ------ 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. ------ 164886/18379560. ------ 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 y))(^z.z))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^y.y))) 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. ------ 164887/18379587. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.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. ------ 164888/18379614. ------ 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.(^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. ------ 164889/18379641. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.(y y))) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.(x x))) REDUCED to normal form. ------ 164890/18379722. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.a))) REDUCED to normal form. ------ 164891/18379776. ------ 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))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 164892/18379803. ------ 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 (^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. ------ 164893/18379830. ------ 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. ------ 164894/18379884. ------ 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.(^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. ------ 164895/18379911. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)(^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. ------ 164896/18379920. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(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 ]==> ((a ((^z.z) a))(^y.y)) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 164897/18391011. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (^x.((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> (^x.((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (^x.((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 164898/18391095. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 164899/18391509. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 164900/18391704. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.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. ------ 164901/18391932. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^z.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 164902/18392346. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 164903/18393036. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(((^z.(z z))(a (^x1.(^y1.y1))))((^z.(z z))(a (^x1.(^y1.y1)))))) 4. ==[ alpha ]==> (^x.(((^y.(y y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2)))))) 5. ==[ beta ]==> (^x.(((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2)))))) 6. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))(a (^x1.(^y1.y1))))((^z1.(z1 z1))(a (^x2.(^y2.y2)))))) 7. ==[ beta ]==> (^x.(((a (^y.(^z.z)))(a (^x1.(^y1.y1))))((a (^x2.(^y2.y2)))(a (^x2.(^y2.y2)))))) 8. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))(a (^x1.(^y1.y1))))((a (^z1.(^x2.x2)))(a (^y2.(^z2.z2)))))) REDUCED to normal form. ------ 164904/18393507. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 164905/18393858. ------ 1. ==[ start ]==> (((^a.b) c)(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(^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. ------ 164906/18393918. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((((^z.z) b)(^x1.(^y1.y1)))(((^z.z) b)(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) b)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1))))(^x2.x2)) 5. ==[ beta ]==> (((b (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1))))(^x2.x2)) 6. ==[ alpha ]==> (((b (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1))))(^z1.z1)) 7. ==[ beta ]==> (((b (^x.(^y.y)))(b (^x1.(^y1.y1))))(^z1.z1)) 8. ==[ alpha ]==> (((b (^x.(^y.y)))(b (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 164907/18394911. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^y.b)) REDUCED to normal form. ------ 164908/18395223. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 164909/18395244. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 164910/18395901. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^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))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 164911/18396114. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164912/18396774. ------ 1. ==[ start ]==> (((a a)(^b.b))(^c.(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(b a))) REDUCED to normal form. ------ 164913/18396792. ------ 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.(^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. ------ 164914/18398097. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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)))) REDUCED to normal form. ------ 164915/18398508. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 164916/18398961. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a b))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a b))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a b))) REDUCED to normal form. ------ 164917/18398979. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.(y1 y1)))) REDUCED to normal form. ------ 164918/18399168. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(a (a a))) 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. ------ 164919/18399669. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 164920/18400167. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)(^x.(^z.z))) 10. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 164921/18400311. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 164922/18400419. ------ 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. ------ 164923/18400488. ------ 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))) REDUCED to normal form. ------ 164924/18400536. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 164925/18400644. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.d)) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.d)) REDUCED to normal form. ------ 164926/18400923. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^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 ]==> ((^z.(^x1.a))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.a))(^z.z)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 164927/18401304. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.b)(^b.(^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. ------ 164928/18401412. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 164929/18401493. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 164930/18401520. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 164931/18401556. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(c (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(c (b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(c (b (^y.y)))) 5. ==[ beta ]==> (c (b (^y.y))) 6. ==[ alpha ]==> (c (b (^x.x))) REDUCED to normal form. ------ 164932/18401601. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(^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. ------ 164933/18401637. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x)) 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. ------ 164934/18401664. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b (^a.a))(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)))) REDUCED to normal form. ------ 164935/18401691. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 164936/18401718. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 164937/18401745. ------ 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.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. ------ 164938/18401853. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a b)((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. ------ 164939/18401934. ------ 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. ------ 164940/18401961. ------ 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. ------ 164941/18401988. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 164942/18402015. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)((^z.(^x1.x1)) 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. ------ 164943/18402105. ------ 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. ------ 164944/18402132. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (^z.(z z)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(y y)))) REDUCED to normal form. ------ 164945/18402159. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a (^a.(^a.a)))(^b.(^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)))) REDUCED to normal form. ------ 164946/18402186. ------ 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. ------ 164947/18402213. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 164948/18402222. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(^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. ------ 164949/18402249. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(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. ------ 164950/18402357. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 9. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 10. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 11. ==[ beta ]==> (b ((^y.y) b)) 12. ==[ alpha ]==> (b ((^x.x) b)) 13. ==[ beta ]==> (b b) REDUCED to normal form. ------ 164951/18402384. ------ 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. ------ 164952/18402438. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 164953/18402681. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 164954/18402735. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 164955/18402852. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^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))(^y.(^z.z)))(a (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 164956/18402879. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b (^z.z))(a a))) 3. ==[ beta ]==> ((a (^y.(y y)))((b (^z.z))(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(a a))) REDUCED to normal form. ------ 164957/18402906. ------ 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. ------ 164958/18402933. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 164959/18402960. ------ 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. ------ 164960/18403149. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 164961/18403329. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 164962/18403356. ------ 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. ------ 164963/18403437. ------ 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. ------ 164964/18403518. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 164965/18403545. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.(a a)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 164966/18403563. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.x))) REDUCED to normal form. ------ 164967/18403644. ------ 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. ------ 164968/18403671. ------ 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)(a a)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(a a)) b)) 5. ==[ beta ]==> (((^y.y) a)(((a a)(a a)) b)) 6. ==[ alpha ]==> (((^x.x) a)(((a a)(a a)) b)) 7. ==[ beta ]==> (a (((a a)(a a)) b)) REDUCED to normal form. ------ 164969/18403698. ------ 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. ------ 164970/18403788. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 164971/18403842. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(a a)))) 7. ==[ beta ]==> ((^y.b)(^z.(a a))) 8. ==[ alpha ]==> ((^x.b)(^y.(a a))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 164972/18403923. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 164973/18403986. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 164974/18404013. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (b (^z.z)))) REDUCED to normal form. ------ 164975/18404067. ------ 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)(a (^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. ------ 164976/18404094. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (((a (^y.(^z.z)))((^x1.x1) a))((a (^y.(^z.z)))((^x1.x1) a))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.(^y1.y1)))((^z1.z1) a))) 9. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.(^y1.y1)))((^z1.z1) a))) 10. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))((^y1.y1) a))) 11. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 164977/18404121. ------ 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. ------ 164978/18404148. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 164979/18404175. ------ 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. ------ 164980/18404364. ------ 1. ==[ start ]==> (((^a.b) c)((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 164981/18404400. ------ 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. ------ 164982/18404427. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) b)(^a.(^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. ------ 164983/18404463. ------ 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) 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. ------ 164984/18404598. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 164985/18404679. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.a)(a (^a.(^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) REDUCED to normal form. ------ 164986/18404706. ------ 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.(^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. ------ 164987/18405102. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b) a)((^y.(a a)) a)) 4. ==[ alpha ]==> (((a b) a)((^x.(a a)) a)) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 164988/18405129. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(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 (^x.x))) b) REDUCED to normal form. ------ 164989/18405417. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a) b)) REDUCED to normal form. ------ 164990/18405462. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(a a))) 3. ==[ beta ]==> ((b a)((^y.y)(a a))) 4. ==[ alpha ]==> ((b a)((^x.x)(a a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 164991/18405489. ------ 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)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 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. ------ 164992/18405543. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 164993/18405624. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(a b))) 3. ==[ beta ]==> (b ((^y.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 164994/18405732. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^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. ------ 164995/18405750. ------ 1. ==[ start ]==> (((a a)(b a))((a a)(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 164996/18405777. ------ 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 (^x.x))((a a)(^y.y)))(b a)) REDUCED to normal form. ------ 164997/18405804. ------ 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.(^x1.x1))) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a 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)) REDUCED to normal form. ------ 164998/18405831. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a) c)) REDUCED to normal form. ------ 164999/18406308. ------ 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. ------ 165000/18406335. ------ 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) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 165001/18406353. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c (^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(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. ------ 165002/18406407. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(a (^z.z))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(a (^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a (^z.z))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 165003/18406488. ------ 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) 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. ------ 165004/18406596. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 165005/18406623. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 165006/18406695. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165007/18406722. ------ 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)) REDUCED to normal form. ------ 165008/18406749. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a) b)) 3. ==[ beta ]==> (((^y.y)(a b))((b a) b)) 4. ==[ alpha ]==> (((^x.x)(a b))((b a) b)) 5. ==[ beta ]==> ((a b)((b a) b)) REDUCED to normal form. ------ 165009/18406947. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.a)(^c.(^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 165010/18407226. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (a a))) REDUCED to normal form. ------ 165011/18407253. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((b a)((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b a)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 165012/18407280. ------ 1. ==[ start ]==> (((a a)(^b.b))((a a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)(b a))) REDUCED to normal form. ------ 165013/18407298. ------ 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.(^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. ------ 165014/18407433. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 165015/18407541. ------ 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.(^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. ------ 165016/18407613. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y)) b)) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 165017/18407910. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a)) c)) 3. ==[ beta ]==> ((b (a a))((^y.(a a)) c)) 4. ==[ alpha ]==> ((b (a a))((^x.(a a)) c)) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 165018/18408216. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.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. ------ 165019/18408297. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(a b))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 165020/18408324. ------ 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))((^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. ------ 165021/18408378. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 165022/18408459. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 165023/18408567. ------ 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.(^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. ------ 165024/18408576. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(b (a a))) REDUCED to normal form. ------ 165025/18408603. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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. ------ 165026/18408630. ------ 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))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a)(a a))) REDUCED to normal form. ------ 165027/18408666. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b) c)) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 165028/18408693. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a) d)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a) d)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a) d)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a) d)) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 165029/18408855. ------ 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. ------ 165030/18408882. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 165031/18408936. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^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. ------ 165032/18408963. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 165033/18409017. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 165034/18409107. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165035/18409188. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 165036/18409332. ------ 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. ------ 165037/18409359. ------ 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))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)((^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. ------ 165038/18409467. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 165039/18409485. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a (^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.(a a)))) REDUCED to normal form. ------ 165040/18409566. ------ 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))((^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. ------ 165041/18409674. ------ 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. ------ 165042/18409881. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b) a)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 165043/18409908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a) b)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a) b)) 5. ==[ beta ]==> ((b a)((^y.a) b)) 6. ==[ alpha ]==> ((b a)((^x.a) b)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 165044/18409935. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z)) c)) 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. ------ 165045/18410070. ------ 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. ------ 165046/18410097. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((b a)(^y.(^z.z))) 10. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 165047/18410124. ------ 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. ------ 165048/18410178. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 165049/18410268. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 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. ------ 165050/18410349. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^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. ------ 165051/18410592. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 165052/18410619. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1) 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. ------ 165053/18410673. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^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 b)((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)((^y.y)(^z.z))) 10. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 11. ==[ beta ]==> ((b b)(^y.y)) 12. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 165054/18410754. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 165055/18410763. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(c a)) REDUCED to normal form. ------ 165056/18410790. ------ 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. ------ 165057/18410817. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 165058/18410871. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a (^y1.y1)))) REDUCED to normal form. ------ 165059/18410898. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))((a (^y.y)) a)) REDUCED to normal form. ------ 165060/18410925. ------ 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. ------ 165061/18410997. ------ 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 (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 165062/18411015. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 165063/18411042. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 165064/18411069. ------ 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. ------ 165065/18411096. ------ 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. ------ 165066/18411177. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y)) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 165067/18411204. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a) b)) 5. ==[ beta ]==> (((a a)(a a))((^y.a) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.a) b)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 165068/18411231. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^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. ------ 165069/18411285. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(^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. ------ 165070/18411312. ------ 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. ------ 165071/18411339. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 165072/18411393. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) REDUCED to normal form. ------ 165073/18411411. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (a (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(b (a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 165074/18411429. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^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 ]==> (((^z.z)(^x1.a))(^y.y)) 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. ------ 165075/18422610. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(b ((^z.(^x1.x1)) a))) 3. ==[ eta ]==> ((^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. ------ 165076/18422880. ------ 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. ------ 165077/18423063. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 165078/18423105. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165079/18423468. ------ 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. ------ 165080/18424176. ------ 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 ]==> (((a (a a))(a (^y.(^z.z)))) b) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 165081/18424563. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(((a (a a))(^z.(^x1.(^y1.y1))))((a (a a))(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> (^x.(((a (a a))(^y.(^z.(^x1.x1))))((a (a a))(^y1.(^z1.(^x2.x2)))))) REDUCED to normal form. ------ 165082/18425385. ------ 1. ==[ start ]==> (((^a.b) c)(^d.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 165083/18425394. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 165084/18425763. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 165085/18426123. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.((y y)(y y)))) 3. ==[ beta ]==> (((a b) a)(^y.((y y)(y y)))) 4. ==[ alpha ]==> (((a b) a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 165086/18426201. ------ 1. ==[ start ]==> ((^a.(b a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b x))((b a)((^y.y) a))) 3. ==[ eta ]==> (b ((b a)((^y.y) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 165087/18426750. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 165088/18427437. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 165089/18427641. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165090/18428328. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) REDUCED to normal form. ------ 165091/18428598. ------ 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))) REDUCED to normal form. ------ 165092/18428955. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a b)((^y.y) a))((a b)((^y.y) a)))(((a b)((^y.y) a))((a b)((^y.y) a)))) 4. ==[ alpha ]==> ((((a b)((^x.x) a))((a b)((^y.y) a)))(((a b)((^z.z) a))((a b)((^x1.x1) a)))) 5. ==[ beta ]==> ((((a b) a)((a b)((^y.y) a)))(((a b)((^z.z) a))((a b)((^x1.x1) a)))) 6. ==[ alpha ]==> ((((a b) a)((a b)((^x.x) a)))(((a b)((^y.y) a))((a b)((^z.z) a)))) 7. ==[ beta ]==> ((((a b) a)((a b) a))(((a b)((^y.y) a))((a b)((^z.z) a)))) 8. ==[ alpha ]==> ((((a b) a)((a b) a))(((a b)((^x.x) a))((a b)((^y.y) a)))) 9. ==[ beta ]==> ((((a b) a)((a b) a))(((a b) a)((a b)((^y.y) a)))) 10. ==[ alpha ]==> ((((a b) a)((a b) a))(((a b) a)((a b)((^x.x) a)))) 11. ==[ beta ]==> ((((a b) a)((a b) a))(((a b) a)((a b) a))) REDUCED to normal form. ------ 165093/18429381. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 165094/18429624. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^b.(^c.(^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. ------ 165095/18429849. ------ 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))(^x.(a a))) REDUCED to normal form. ------ 165096/18430515. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.(x1 x1)))) REDUCED to normal form. ------ 165097/18430704. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(a x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 165098/18430902. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(z b))) REDUCED to normal form. ------ 165099/18431694. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 165100/18431703. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^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. ------ 165101/18431838. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 165102/18432015. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 165103/18432198. ------ 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. ------ 165104/18432438. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (a (^z.z)))) 3. ==[ beta ]==> ((b (a (^z.z)))((b (a (^z.z)))(^y.y))) 4. ==[ alpha ]==> ((b (a (^x.x)))((b (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 165105/18432849. ------ 1. ==[ start ]==> (((a a) a)((^b.b)(^b.(^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. ------ 165106/18432957. ------ 1. ==[ start ]==> (((a a) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 165107/18433038. ------ 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 (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 165108/18433128. ------ 1. ==[ start ]==> ((a ((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))(b ((^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. ------ 165109/18433164. ------ 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)((^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. ------ 165110/18433317. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b a)((a a) a))) 3. ==[ beta ]==> (((a a) a)((b a)((a a) a))) REDUCED to normal form. ------ 165111/18433344. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 165112/18433371. ------ 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. ------ 165113/18433398. ------ 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. ------ 165114/18433578. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 165115/18433596. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 165116/18433623. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 165117/18433713. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 165118/18433758. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165119/18433785. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(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. ------ 165120/18433848. ------ 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. ------ 165121/18433875. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^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)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 165122/18433893. ------ 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. ------ 165123/18433902. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b ((^x1.x1) b))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((^z.z) b))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 165124/18433929. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 165125/18433956. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 165126/18433983. ------ 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. ------ 165127/18434307. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a a))(^b.b))) 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))) 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. ------ 165128/18434334. ------ 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) a) REDUCED to normal form. ------ 165129/18434532. ------ 1. ==[ start ]==> (((a a)((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a)((a a) a))((b a)(^y.y))) 4. ==[ alpha ]==> (((a a)((a a) a))((b a)(^x.x))) REDUCED to normal form. ------ 165130/18434559. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 165131/18434586. ------ 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. ------ 165132/18434613. ------ 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. ------ 165133/18434640. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 165134/18434667. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^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. ------ 165135/18434694. ------ 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. ------ 165136/18434847. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 165137/18434865. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 165138/18434874. ------ 1. ==[ start ]==> (((a b) a)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b) a)((^x.x)((^y.y) 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. ------ 165139/18434892. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 165140/18434901. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 165141/18434919. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 165142/18434955. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 165143/18434973. ------ 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. ------ 165144/18434982. ------ 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. ------ 165145/18435009. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 165146/18435063. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 165147/18435081. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165148/18435252. ------ 1. ==[ start ]==> (((^a.b) b)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 165149/18435468. ------ 1. ==[ start ]==> (((a b) b)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) b)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 165150/18435495. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.y))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 165151/18435522. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 165152/18435747. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(a a))((a b)(a b))) REDUCED to normal form. ------ 165153/18435774. ------ 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.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(((a a) a)(a a))) REDUCED to normal form. ------ 165154/18435801. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y)(^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))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((a a) a))((^x.x)((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. ------ 165155/18435828. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 165156/18435855. ------ 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)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) 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. ------ 165157/18435882. ------ 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 (^x.x)) b)) REDUCED to normal form. ------ 165158/18435900. ------ 1. ==[ start ]==> (((^a.b) c)(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(b (^y.(a a)))) 3. ==[ beta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 165159/18435909. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 165160/18435999. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 165161/18436134. ------ 1. ==[ start ]==> (((^a.b)(^b.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. ------ 165162/18436143. ------ 1. ==[ start ]==> (((a b) c)((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 165163/18436170. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 165164/18436197. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a)(b a))) REDUCED to normal form. ------ 165165/18436215. ------ 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)(^x.x))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165166/18436242. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((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. ------ 165167/18436251. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 165168/18436278. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.b))((a a)(a a))) REDUCED to normal form. ------ 165169/18436296. ------ 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)) REDUCED to normal form. ------ 165170/18436332. ------ 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.(^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. ------ 165171/18436359. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.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. ------ 165172/18436440. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 165173/18436611. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(b ((^x.x) b))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b b)) REDUCED to normal form. ------ 165174/18436638. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 165175/18436665. ------ 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)(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. ------ 165176/18436692. ------ 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 (^x1.x1)))) REDUCED to normal form. ------ 165177/18436719. ------ 1. ==[ start ]==> ((a (b a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((a (b a))((b a)((^x.x) a))) 3. ==[ beta ]==> ((a (b a))((b a) a)) REDUCED to normal form. ------ 165178/18436953. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (^y.y))) REDUCED to normal form. ------ 165179/18436998. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> ((b a)(((^y.y) b)(^z.z))) 4. ==[ alpha ]==> ((b a)(((^x.x) b)(^y.y))) 5. ==[ beta ]==> ((b a)(b (^y.y))) 6. ==[ alpha ]==> ((b a)(b (^x.x))) REDUCED to normal form. ------ 165180/18437025. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 165181/18437079. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 165182/18437088. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 165183/18437142. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 165184/18437160. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((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. ------ 165185/18437169. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(a b))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 165186/18437196. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 165187/18437223. ------ 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 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^y1.y1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 165188/18437268. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 165189/18437646. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z) a)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z) a)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z) a)) 5. ==[ beta ]==> ((a a)((^z.z) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 165190/18437727. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^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. ------ 165191/18437952. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 165192/18437979. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 165193/18438024. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 165194/18438033. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 165195/18438060. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 165196/18438087. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 165197/18438132. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165198/18438141. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 165199/18438159. ------ 1. ==[ start ]==> ((a (^b.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 165200/18438438. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^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. ------ 165201/18438645. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a)) d)) 3. ==[ beta ]==> (b ((^z.(a a)) d)) 4. ==[ alpha ]==> (b ((^x.(a a)) d)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 165202/18438789. ------ 1. ==[ start ]==> ((((^a.a) b) a)(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b a)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b a)(c (^x.(^y.y)))) REDUCED to normal form. ------ 165203/18438843. ------ 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.(^x2.x2))))) REDUCED to normal form. ------ 165204/18438888. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 165205/18438924. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a))((^z.z) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165206/18438951. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 165207/18438969. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a) a)(^b.(^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. ------ 165208/18438978. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 165209/18439005. ------ 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.(^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. ------ 165210/18439032. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(z z))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(a b))) REDUCED to normal form. ------ 165211/18439086. ------ 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.(^z1.z1))((a 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. ------ 165212/18439113. ------ 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 (^x.x))(b a)) REDUCED to normal form. ------ 165213/18439365. ------ 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 a)(^y.y)))) REDUCED to normal form. ------ 165214/18439419. ------ 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))(a a))) REDUCED to normal form. ------ 165215/18439446. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(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. ------ 165216/18439473. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a b)((^x.x) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a b) a)) REDUCED to normal form. ------ 165217/18439752. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((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. ------ 165218/18439788. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 165219/18439815. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 165220/18439833. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) 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. ------ 165221/18439860. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 165222/18439869. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))((^y1.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. ------ 165223/18439896. ------ 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)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^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. ------ 165224/18439914. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y)) a)) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 165225/18439977. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b)(^b.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. ------ 165226/18440004. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 165227/18440058. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 165228/18440112. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(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. ------ 165229/18440139. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.a)(^c.(^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. ------ 165230/18440202. ------ 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. ------ 165231/18440229. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(((a a) a) a)) REDUCED to normal form. ------ 165232/18440256. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a (a a)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 165233/18440283. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))((^x.x)(^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. ------ 165234/18440310. ------ 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)((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((a a) a))) REDUCED to normal form. ------ 165235/18440337. ------ 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. ------ 165236/18440364. ------ 1. ==[ start ]==> (((a b)(a b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(a a))) REDUCED to normal form. ------ 165237/18440643. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b) b)) 5. ==[ beta ]==> ((^y.(^z.z))((a b) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((a b) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165238/18440832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165239/18441003. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.b))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.b))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.b))) REDUCED to normal form. ------ 165240/18441030. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.(a a)))) REDUCED to normal form. ------ 165241/18441102. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^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. ------ 165242/18441111. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^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)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 165243/18441138. ------ 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. ------ 165244/18441210. ------ 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)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165245/18441219. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a b)) REDUCED to normal form. ------ 165246/18441246. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.a))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.a))((^y.b)(^z.z))) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 165247/18441390. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b ((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(b ((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b ((a a) a))) 5. ==[ beta ]==> ((a b)(b ((a a) a))) REDUCED to normal form. ------ 165248/18441417. ------ 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. ------ 165249/18441444. ------ 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. ------ 165250/18441471. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^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)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 165251/18441498. ------ 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. ------ 165252/18441525. ------ 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. ------ 165253/18441552. ------ 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. ------ 165254/18441804. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1)) 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. ------ 165255/18441993. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165256/18442110. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 165257/18442128. ------ 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. ------ 165258/18442155. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.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. ------ 165259/18442209. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b b)((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 165260/18442218. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 165261/18442245. ------ 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.(^x2.x2))(^y2.y2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165262/18442290. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z) a) c)) 3. ==[ beta ]==> (b (((^z.z) a) c)) 4. ==[ alpha ]==> (b (((^x.x) a) c)) 5. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 165263/18442299. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 165264/18442326. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 165265/18442353. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 165266/18442398. ------ 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 z1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165267/18442434. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^b.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. ------ 165268/18442461. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.(y y)))) REDUCED to normal form. ------ 165269/18442515. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 165270/18442533. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(^a.(^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. ------ 165271/18442686. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b ((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(b a)) REDUCED to normal form. ------ 165272/18442713. ------ 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. ------ 165273/18442740. ------ 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. ------ 165274/18442767. ------ 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 (^z.z)))) REDUCED to normal form. ------ 165275/18442848. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c b)) 3. ==[ beta ]==> ((b (a (a a)))(c b)) REDUCED to normal form. ------ 165276/18442875. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b c)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b c)) 3. ==[ beta ]==> ((((a a)(a a)) a)(b c)) REDUCED to normal form. ------ 165277/18442947. ------ 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 ]==> ((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. ------ 165278/18442956. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (a (^y.y)))) REDUCED to normal form. ------ 165279/18453894. ------ 1. ==[ start ]==> ((^a.b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 165280/18454203. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 165281/18454335. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 165282/18455550. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 165283/18456219. ------ 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. ------ 165284/18456324. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))((^z1.(^x2.(^y2.y2)))(^z2.(z2 z2))))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))((^z1.(^x2.(^y2.y2)))(^z2.(z2 z2)))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 7. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165285/18457317. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 165286/18457677. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 165287/18458352. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 165288/18458685. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^a.((^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. ------ 165289/18459297. ------ 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 (^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))))) REDUCED to normal form. ------ 165290/18459510. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 165291/18460152. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 165292/18460683. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^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. ------ 165293/18461589. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.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. ------ 165294/18461871. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.((^z1.z1)(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1)(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165295/18462456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.z))) REDUCED to normal form. ------ 165296/18462645. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.b))) REDUCED to normal form. ------ 165297/18462750. ------ 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. ------ 165298/18463257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 165299/18463644. ------ 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. ------ 165300/18463752. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 165301/18463860. ------ 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.(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 165302/18463992. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^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. ------ 165303/18464421. ------ 1. ==[ start ]==> ((a b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 165304/18464700. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.a)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.a)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 165305/18464727. ------ 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)(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. ------ 165306/18464736. ------ 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)(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.y))) REDUCED to normal form. ------ 165307/18464781. ------ 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. ------ 165308/18464808. ------ 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) 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. ------ 165309/18464862. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 165310/18464970. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.(y y))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.(x x))((a b)((a a)(^y.y)))) 5. ==[ beta ]==> (((a b)((a a)(^y.y)))((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 165311/18464997. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 165312/18465051. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))((^z.z) 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. ------ 165313/18465078. ------ 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. ------ 165314/18465105. ------ 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)((a (^x1.x1))(b (^y1.y1)))) 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. ------ 165315/18465168. ------ 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. ------ 165316/18465258. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.b)(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. ------ 165317/18465276. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b b)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 165318/18465285. ------ 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. ------ 165319/18465438. ------ 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.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 165320/18465465. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 165321/18465573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^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) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 165322/18465663. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) 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)))) 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. ------ 165323/18465690. ------ 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. ------ 165324/18465942. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(b (b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 165325/18465996. ------ 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 ]==> ((((^y.y) a)((^y.y) a))((b (^z.z))(a a))) 4. ==[ alpha ]==> ((((^x.x) a)((^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 a)((b (^y.y))(a a))) 8. ==[ alpha ]==> ((a a)((b (^x.x))(a a))) REDUCED to normal form. ------ 165326/18466077. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 165327/18466266. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.b)((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.b)((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 165328/18466347. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(b (^z.z)))) IRREDUCIBLE: cycle. ------ 165329/18466410. ------ 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. ------ 165330/18466437. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) b)(^y.a))) 3. ==[ beta ]==> (((a b) a)(b (^y.a))) 4. ==[ alpha ]==> (((a b) a)(b (^x.a))) REDUCED to normal form. ------ 165331/18466464. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 165332/18466518. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 165333/18466545. ------ 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. ------ 165334/18466572. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a b)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)((a b)(^z.(a a)))) 6. ==[ alpha ]==> ((^x.a)((a b)(^y.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 165335/18466662. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a b))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a b))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 165336/18466689. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 165337/18466716. ------ 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)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 165338/18466743. ------ 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. ------ 165339/18466815. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b) b)(((^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. ------ 165340/18466824. ------ 1. ==[ start ]==> (((a b)(a a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b)(a a))(^y.a)) 4. ==[ alpha ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 165341/18466851. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 165342/18467103. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(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. ------ 165343/18467157. ------ 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))(a a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a a))) 9. ==[ beta ]==> ((^y.y)(((a a)(a a))(a a))) 10. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 11. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 165344/18467166. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 165345/18467193. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z) c)) 5. ==[ beta ]==> ((^y.(y y))((^z.z) c)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) c)) 7. ==[ beta ]==> (((^y.y) c)((^y.y) c)) 8. ==[ alpha ]==> (((^x.x) c)((^y.y) c)) 9. ==[ beta ]==> (c ((^y.y) c)) 10. ==[ alpha ]==> (c ((^x.x) c)) 11. ==[ beta ]==> (c c) REDUCED to normal form. ------ 165346/18467238. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 165347/18467472. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 165348/18467706. ------ 1. ==[ start ]==> (((a b) c)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) c)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 165349/18467733. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^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)))) 7. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 165350/18467814. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 165351/18467841. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 165352/18467895. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b) b)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b) b)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165353/18468039. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 165354/18468093. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 165355/18468147. ------ 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)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> a REDUCED to normal form. ------ 165356/18468174. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))(^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. ------ 165357/18468201. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b) a)(^y.(a a))) 6. ==[ alpha ]==> (((a b) a)(^x.(a a))) REDUCED to normal form. ------ 165358/18468372. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a b)((a a) a))) 5. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 165359/18468453. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 165360/18468624. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((b a)(^z.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.a))) REDUCED to normal form. ------ 165361/18468651. ------ 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 z)))) REDUCED to normal form. ------ 165362/18468705. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 165363/18468732. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a) a)(^y.b))) REDUCED to normal form. ------ 165364/18468759. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.a))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 165365/18468849. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 165366/18468876. ------ 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)(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 165367/18468903. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b)(^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))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 165368/18468930. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 165369/18469011. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 165370/18469038. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.a))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 165371/18469209. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(a ((^z.z) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(a ((^z.z) b))) 5. ==[ beta ]==> ((a a)(a ((^z.z) b))) 6. ==[ alpha ]==> ((a a)(a ((^x.x) b))) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 165372/18469290. ------ 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) a))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 165373/18469398. ------ 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))(((^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. ------ 165374/18469425. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((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. ------ 165375/18469452. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 165376/18469506. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a (^y.(^z.z))))) 8. ==[ alpha ]==> (((a a)(a a))((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 165377/18469542. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 165378/18469596. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 165379/18469623. ------ 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)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 165380/18469650. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 165381/18469704. ------ 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)))(^z.z))((^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. ------ 165382/18469740. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 165383/18469767. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 165384/18469794. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^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. ------ 165385/18469821. ------ 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 (^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. ------ 165386/18469848. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 165387/18469902. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 165388/18469929. ------ 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 z)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 165389/18469956. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 165390/18470010. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 165391/18470037. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 165392/18470208. ------ 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) 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. ------ 165393/18470316. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((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. ------ 165394/18470370. ------ 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)))) REDUCED to normal form. ------ 165395/18470397. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((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. ------ 165396/18470487. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165397/18470514. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)(^y.(y y)))) REDUCED to normal form. ------ 165398/18470541. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 165399/18470568. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.a))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.a)) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 165400/18470595. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (a a))(^z.b))) REDUCED to normal form. ------ 165401/18470766. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (b a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 165402/18470793. ------ 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.(z z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 165403/18470847. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(^a.a))(^c.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. ------ 165404/18470874. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))(^y.b))) 3. ==[ beta ]==> (((a b)((a a) a))((^y.b)(^y.b))) 4. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 165405/18470901. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 165406/18471072. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 165407/18471207. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 165408/18471351. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^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. ------ 165409/18471432. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 165410/18471540. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b) c)) REDUCED to normal form. ------ 165411/18471927. ------ 1. ==[ start ]==> (((a b)(a b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(b (^x.(a a)))) REDUCED to normal form. ------ 165412/18471981. ------ 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))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 165413/18472062. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 165414/18472089. ------ 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.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))(a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a)(a a))(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 10. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 165415/18472116. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.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. ------ 165416/18472395. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(a ((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165417/18472431. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b) b)) 3. ==[ beta ]==> ((b c)((^y.b) b)) 4. ==[ alpha ]==> ((b c)((^x.b) b)) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 165418/18472458. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a) c)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a) c)) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 165419/18472503. ------ 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. ------ 165420/18472530. ------ 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)((^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. ------ 165421/18472584. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(a b))) REDUCED to normal form. ------ 165422/18472674. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(^z.a)) 6. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 165423/18472701. ------ 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. ------ 165424/18472782. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^x1.b))) REDUCED to normal form. ------ 165425/18472809. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b) a)) 3. ==[ beta ]==> ((b (^y.a))((a b) a)) 4. ==[ alpha ]==> ((b (^x.a))((a b) a)) REDUCED to normal form. ------ 165426/18472836. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a) a) b)) REDUCED to normal form. ------ 165427/18472899. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 165428/18472926. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 165429/18472953. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 165430/18472980. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.b)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 165431/18473169. ------ 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. ------ 165432/18473196. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.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) REDUCED to normal form. ------ 165433/18473223. ------ 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 (^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. ------ 165434/18473277. ------ 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. ------ 165435/18473448. ------ 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. ------ 165436/18473556. ------ 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. ------ 165437/18473673. ------ 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 ((^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. ------ 165438/18473781. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 165439/18473808. ------ 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)(^x2.x2)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1)) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165440/18473862. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a c)) REDUCED to normal form. ------ 165441/18473961. ------ 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. ------ 165442/18473970. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b b)) REDUCED to normal form. ------ 165443/18473997. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a) c)) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 165444/18474078. ------ 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. ------ 165445/18474114. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 165446/18474141. ------ 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))((^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. ------ 165447/18474168. ------ 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. ------ 165448/18474195. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(^y.y))) 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. ------ 165449/18474222. ------ 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.(^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. ------ 165450/18474249. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^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. ------ 165451/18474276. ------ 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 z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.(z z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 165452/18474330. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 165453/18474384. ------ 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 (^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 165454/18474411. ------ 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))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 165455/18474438. ------ 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 (^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. ------ 165456/18474492. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.y))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 165457/18474510. ------ 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 (^y.y))((a (^z.z)) b)) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 165458/18474519. ------ 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))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 165459/18474528. ------ 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 ]==> ((b (a (^z.z)))(^y.y)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 165460/18474887. ------ 1. ==[ start ]==> (^a.((b (^a.a)) c)) 2. ==[ alpha ]==> (^x.((b (^y.y)) c)) REDUCED to normal form. ------ 165461/18474888. ------ 1. ==[ start ]==> (a ((b (^a.a)) c)) 2. ==[ alpha ]==> (a ((b (^x.x)) c)) REDUCED to normal form. ------ 165462/18485421. ------ 1. ==[ start ]==> ((^a.a)((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 3. ==[ beta ]==> ((b (^y.y)) c) 4. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 165463/18485673. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165464/18485784. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 165465/18485793. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 165466/18486216. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(^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. ------ 165467/18486366. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b a)(^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. ------ 165468/18487035. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(y y)))(^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))) REDUCED to normal form. ------ 165469/18487698. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(b a))((^z.(^x1.x1))(b a)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(b a))((^x1.(^y1.y1))(b a)))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.(^y1.y1))(b a)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(b a)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(b a))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(b a))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165470/18488580. ------ 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. ------ 165471/18488916. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 165472/18489336. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1))) c)) 3. ==[ eta ]==> (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. ------ 165473/18489618. ------ 1. ==[ start ]==> (((^a.a)(b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((b a)(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 165474/18489885. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(b a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 165475/18490266. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 165476/18490572. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 165477/18490776. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165478/18492090. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a)) c)) 3. ==[ beta ]==> ((((^y.(a a)) c)((^y.(a a)) c))(((^y.(a a)) c)((^y.(a a)) c))) 4. ==[ alpha ]==> ((((^x.(a a)) c)((^y.(a a)) c))(((^z.(a a)) c)((^x1.(a a)) c))) 5. ==[ beta ]==> (((a a)((^y.(a a)) c))(((^z.(a a)) c)((^x1.(a a)) c))) 6. ==[ alpha ]==> (((a a)((^x.(a a)) c))(((^y.(a a)) c)((^z.(a a)) c))) 7. ==[ beta ]==> (((a a)(a a))(((^y.(a a)) c)((^z.(a a)) c))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a)) c)((^y.(a a)) c))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^y.(a a)) c))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a)) c))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 165479/18492534. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 165480/18492786. ------ 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. ------ 165481/18493170. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 165482/18493452. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 165483/18494331. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165484/18495150. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 165485/18495333. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.d)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.d)) REDUCED to normal form. ------ 165486/18495573. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z)) b)) 3. ==[ beta ]==> (((a (^z.z)) b)(((a (^z.z)) b)(^y.y))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a (^y.y)) b)(^z.z))) REDUCED to normal form. ------ 165487/18495957. ------ 1. ==[ start ]==> ((a a)((b (^a.a)) c)) 2. ==[ alpha ]==> ((a a)((b (^x.x)) c)) REDUCED to normal form. ------ 165488/18496020. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.b)(^b.(^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. ------ 165489/18496128. ------ 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)((^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. ------ 165490/18496209. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 165491/18496317. ------ 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 (^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. ------ 165492/18496326. ------ 1. ==[ start ]==> (((a (^a.a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(a (a (a (^y.y))))) REDUCED to normal form. ------ 165493/18496353. ------ 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))) 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. ------ 165494/18496380. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 165495/18496407. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a)) a)) REDUCED to normal form. ------ 165496/18496434. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 165497/18496542. ------ 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)(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(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. ------ 165498/18496623. ------ 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. ------ 165499/18496650. ------ 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. ------ 165500/18496677. ------ 1. ==[ start ]==> (((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 a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 165501/18496704. ------ 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)))) REDUCED to normal form. ------ 165502/18496731. ------ 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.(^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. ------ 165503/18496749. ------ 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))(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 165504/18496794. ------ 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. ------ 165505/18496821. ------ 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))(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 165506/18496848. ------ 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 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(b (^z.(z z)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 165507/18496875. ------ 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. ------ 165508/18496902. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 165509/18496992. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.b)((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 165510/18497046. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165511/18497073. ------ 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. ------ 165512/18497127. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(b (^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. ------ 165513/18497199. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b (^z.z)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 165514/18497370. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(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. ------ 165515/18497424. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.a))) 5. ==[ beta ]==> (a ((^z.a)(^x1.a))) 6. ==[ alpha ]==> (a ((^x.a)(^y.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165516/18497505. ------ 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. ------ 165517/18497541. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (b (^x1.x1)))) REDUCED to normal form. ------ 165518/18497568. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a ((^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. ------ 165519/18497595. ------ 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. ------ 165520/18497622. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165521/18497649. ------ 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)(^x.x))(b ((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b ((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b a)) REDUCED to normal form. ------ 165522/18497838. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 165523/18498018. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 165524/18498045. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.b)((^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)((^y.y) a)) 6. ==[ alpha ]==> ((a b)((^x.x) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 165525/18498072. ------ 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.(^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. ------ 165526/18498207. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 165527/18498234. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 165528/18498252. ------ 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. ------ 165529/18498279. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) 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. ------ 165530/18498360. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z)) a)) 5. ==[ beta ]==> (((^y.y) a)((b (^z.z)) a)) 6. ==[ alpha ]==> (((^x.x) a)((b (^y.y)) a)) 7. ==[ beta ]==> (a ((b (^y.y)) a)) 8. ==[ alpha ]==> (a ((b (^x.x)) a)) REDUCED to normal form. ------ 165531/18498387. ------ 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. ------ 165532/18498414. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) b) c)) 3. ==[ beta ]==> (((a b)(a a))(b c)) REDUCED to normal form. ------ 165533/18498450. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165534/18498531. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.b))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 7. ==[ beta ]==> ((^y.(a a))(^z.b)) 8. ==[ alpha ]==> ((^x.(a a))(^y.b)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165535/18498666. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.y))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 165536/18498675. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c ((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(c b)) REDUCED to normal form. ------ 165537/18498693. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 165538/18498702. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b ((a a)(a a)))) REDUCED to normal form. ------ 165539/18498756. ------ 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. ------ 165540/18498783. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> ((((^y.y) b)(a (^z.z)))(((^y.y) b)(a (^z.z)))) 8. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) b)(a (^x1.x1)))) 9. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) b)(a (^x1.x1)))) 10. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) b)(a (^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. ------ 165541/18498810. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 165542/18498837. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(a (a a)))) REDUCED to normal form. ------ 165543/18498864. ------ 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. ------ 165544/18499053. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 165545/18499116. ------ 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. ------ 165546/18499152. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.b)(a (^a.a)))) 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. ------ 165547/18499287. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 165548/18499368. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a)(^x.x))((b a)(b a))) REDUCED to normal form. ------ 165549/18499395. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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 REDUCED to normal form. ------ 165550/18499449. ------ 1. ==[ start ]==> (((^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)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((a a)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 165551/18499530. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 165552/18499845. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b) 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. ------ 165553/18499872. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 165554/18500106. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 165555/18500151. ------ 1. ==[ start ]==> (((^a.a)(b a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b 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. ------ 165556/18500178. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 165557/18500313. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^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. ------ 165558/18500421. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(b a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 165559/18500439. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165560/18500466. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 165561/18500493. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) b) a)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) b) a)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^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. ------ 165562/18500520. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 165563/18500547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((b a) c)) 3. ==[ beta ]==> (((^y.y)((a a) a))((b a) c)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((b a) c)) 5. ==[ beta ]==> (((a a) a)((b a) c)) REDUCED to normal form. ------ 165564/18500799. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 165565/18500997. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a b)) REDUCED to normal form. ------ 165566/18501024. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a (a a))(a a))) REDUCED to normal form. ------ 165567/18501096. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 165568/18501105. ------ 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. ------ 165569/18501312. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 165570/18501330. ------ 1. ==[ start ]==> (((a a)(a (^a.(^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. ------ 165571/18501357. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y) 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. ------ 165572/18501411. ------ 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. ------ 165573/18501438. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z))) a)) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z))) a)) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 165574/18501465. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((b a) b)) REDUCED to normal form. ------ 165575/18501492. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z)) c)) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 165576/18501636. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(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. ------ 165577/18501663. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.a)(^x2.(^y2.y2)))) 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. ------ 165578/18501915. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (a a))(a b))) REDUCED to normal form. ------ 165579/18501942. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x) 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. ------ 165580/18501960. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(c (^c.(^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. ------ 165581/18501969. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 165582/18501996. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(b a))) REDUCED to normal form. ------ 165583/18502122. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 165584/18502230. ------ 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)((^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. ------ 165585/18502302. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a) a)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a) a)) 3. ==[ beta ]==> (((a a) b)((b a) a)) REDUCED to normal form. ------ 165586/18502329. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a)(^x1.x1)) b)) REDUCED to normal form. ------ 165587/18502356. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((a (b a))(((^y.y)(a a)) c)) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(a a)) c)) 5. ==[ beta ]==> ((a (b a))((a a) c)) REDUCED to normal form. ------ 165588/18502599. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^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)) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 165589/18502626. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a)) c)) 3. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 165590/18502797. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 165591/18502905. ------ 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) 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. ------ 165592/18502986. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 165593/18503013. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 165594/18503067. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (((b a)(b a))((a a)(^y.y))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 165595/18503148. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b)(^z.a))) 3. ==[ beta ]==> (b ((^y.b)(^z.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 165596/18503256. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 165597/18503265. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (a b))) REDUCED to normal form. ------ 165598/18503292. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b ((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 165599/18503319. ------ 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. ------ 165600/18503355. ------ 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 a)) REDUCED to normal form. ------ 165601/18503382. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b) c)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b) c)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b) c)) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 165602/18503571. ------ 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. ------ 165603/18503625. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a) a)(^z.a))) REDUCED to normal form. ------ 165604/18503652. ------ 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)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.(z z))) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 165605/18503679. ------ 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. ------ 165606/18503706. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 165607/18503796. ------ 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. ------ 165608/18503877. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 165609/18503985. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.y1)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165610/18504021. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(a a))) 3. ==[ beta ]==> ((b c)((a b)(a a))) REDUCED to normal form. ------ 165611/18504048. ------ 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. ------ 165612/18504156. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 165613/18504174. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (^x1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (^y1.b))) REDUCED to normal form. ------ 165614/18504183. ------ 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. ------ 165615/18504255. ------ 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)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 165616/18504363. ------ 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 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. ------ 165617/18504597. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b) a)) 5. ==[ beta ]==> ((b a)((^y.b) a)) 6. ==[ alpha ]==> ((b a)((^x.b) a)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 165618/18504651. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 165619/18504786. ------ 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. ------ 165620/18504813. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^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 (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 165621/18504867. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 165622/18504957. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.x1))) 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. ------ 165623/18505038. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 165624/18505281. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((^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. ------ 165625/18505308. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a (^y1.y1)))) 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. ------ 165626/18505362. ------ 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. ------ 165627/18505443. ------ 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.(^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. ------ 165628/18505452. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (a (^z.z)))) REDUCED to normal form. ------ 165629/18505479. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(c a)) REDUCED to normal form. ------ 165630/18505506. ------ 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. ------ 165631/18505560. ------ 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. ------ 165632/18505587. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (a (^z.z)))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 165633/18505614. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a (^y.y)) a)) REDUCED to normal form. ------ 165634/18505686. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a a)(a a))) REDUCED to normal form. ------ 165635/18505704. ------ 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)))) 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. ------ 165636/18505731. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 165637/18505758. ------ 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. ------ 165638/18505785. ------ 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. ------ 165639/18505812. ------ 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. ------ 165640/18505839. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x)) c)) REDUCED to normal form. ------ 165641/18505893. ------ 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)) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z)) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y)) a)) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y)) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x)) a)) 7. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 165642/18505920. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.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. ------ 165643/18506001. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) 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. ------ 165644/18506028. ------ 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)))) 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. ------ 165645/18506082. ------ 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. ------ 165646/18506109. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y)) b)) REDUCED to normal form. ------ 165647/18506118. ------ 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.(^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. ------ 165648/18517038. ------ 1. ==[ start ]==> ((^a.(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z)) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165649/18517401. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 165650/18517623. ------ 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. ------ 165651/18517833. ------ 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. ------ 165652/18517848. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165653/18518238. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.(^y1.y1)) 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. ------ 165654/18518919. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z))(b a))) 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. ------ 165655/18520893. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 165656/18520944. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z)))(a (^x1.x1)))) 3. ==[ eta ]==> (b ((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 165657/18522207. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^a.(^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. ------ 165658/18522384. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165659/18523647. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 165660/18523698. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> (((((^y.y)(a a))(a (^z.z)))(((^y.y)(a a))(a (^z.z))))((((^y.y)(a a))(a (^z.z)))(((^y.y)(a a))(a (^z.z))))) 4. ==[ 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 (^y2.y2))))) 5. ==[ 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 (^y2.y2))))) 6. ==[ 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))))) 7. ==[ beta ]==> ((((a a)(a (^x.x)))((a a)(a (^z.z))))((((^x1.x1)(a a))(a (^y1.y1)))(((^z1.z1)(a a))(a (^x2.x2))))) 8. ==[ 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))))) 9. ==[ beta ]==> ((((a a)(a (^x.x)))((a a)(a (^y.y))))(((a a)(a (^x1.x1)))(((^y1.y1)(a a))(a (^z1.z1))))) 10. ==[ alpha ]==> ((((a a)(a (^x.x)))((a a)(a (^y.y))))(((a a)(a (^z.z)))(((^x1.x1)(a a))(a (^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. ------ 165661/18524142. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 165662/18524394. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 165663/18525474. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) b)(^y.a)) a) 4. ==[ beta ]==> ((b (^y.a)) a) 5. ==[ alpha ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 165664/18525672. ------ 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))) REDUCED to normal form. ------ 165665/18526473. ------ 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.((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165666/18526743. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.(^b.(^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. ------ 165667/18526758. ------ 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. ------ 165668/18526968. ------ 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. ------ 165669/18527583. ------ 1. ==[ start ]==> ((a (^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 165670/18527646. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 165671/18527673. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x) b)((^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. ------ 165672/18527727. ------ 1. ==[ start ]==> (((a a) b)((^c.(^a.a))(^b.(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. ------ 165673/18527754. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 165674/18527862. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(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. ------ 165675/18527943. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^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)))) REDUCED to normal form. ------ 165676/18528087. ------ 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)))((^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. ------ 165677/18528114. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 165678/18528141. ------ 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. ------ 165679/18528168. ------ 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. ------ 165680/18528321. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 165681/18528375. ------ 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. ------ 165682/18528393. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^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. ------ 165683/18528483. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(a (a a)))) 3. ==[ beta ]==> ((b b)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((b b)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((b b)(a (a a))) REDUCED to normal form. ------ 165684/18528528. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 165685/18528555. ------ 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))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.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. ------ 165686/18528609. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a b)(^y1.(^z1.z1)))) 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. ------ 165687/18528618. ------ 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. ------ 165688/18528663. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 165689/18528672. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(^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)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 165690/18528690. ------ 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. ------ 165691/18528699. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b ((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b ((^z.z) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b b)) REDUCED to normal form. ------ 165692/18528726. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 165693/18528753. ------ 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. ------ 165694/18528780. ------ 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.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) 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. ------ 165695/18529077. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(^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. ------ 165696/18529104. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(^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. ------ 165697/18529302. ------ 1. ==[ start ]==> (((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)))) REDUCED to normal form. ------ 165698/18529329. ------ 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 a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((b a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(^z.z))) REDUCED to normal form. ------ 165699/18529356. ------ 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. ------ 165700/18529383. ------ 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. ------ 165701/18529410. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 165702/18529437. ------ 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. ------ 165703/18529464. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> ((a (a b))((^y.y)(b a))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(b a))) 5. ==[ beta ]==> ((a (a b))(b a)) REDUCED to normal form. ------ 165704/18529635. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 165705/18529644. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 165706/18529662. ------ 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))) 5. ==[ beta ]==> ((a b)(b (^y.a))) 6. ==[ alpha ]==> ((a b)(b (^x.a))) REDUCED to normal form. ------ 165707/18529671. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z) 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. ------ 165708/18529689. ------ 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.(^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. ------ 165709/18529779. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(a b))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(a b))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(a b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 165710/18529806. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 165711/18529824. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 165712/18529833. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 165713/18530022. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 165714/18530265. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 165715/18530292. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 165716/18530319. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 165717/18530517. ------ 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)(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. ------ 165718/18530544. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a b)(a b))) REDUCED to normal form. ------ 165719/18530571. ------ 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)))) 5. ==[ beta ]==> ((a ((a a) a))(((a a) a)(a a))) REDUCED to normal form. ------ 165720/18530598. ------ 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))((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. ------ 165721/18530625. ------ 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))(b a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))(b a))) 5. ==[ beta ]==> ((a (a a))((a (a a))(b a))) REDUCED to normal form. ------ 165722/18530652. ------ 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 (^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))))) 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. ------ 165723/18530670. ------ 1. ==[ start ]==> (((^a.b) c)(c (^b.b))) 2. ==[ alpha ]==> (((^x.b) c)(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 165724/18530679. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 165725/18530706. ------ 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. ------ 165726/18530769. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 165727/18530904. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(^z.b))) 3. ==[ beta ]==> (b ((a b)(^z.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 165728/18530913. ------ 1. ==[ start ]==> (((a b) c)((^a.b)(a b))) 2. ==[ alpha ]==> (((a b) c)((^x.b)(a b))) 3. ==[ beta ]==> (((a b) c) b) REDUCED to normal form. ------ 165729/18530940. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 165730/18530967. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))((a 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. ------ 165731/18531012. ------ 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)(^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. ------ 165732/18531021. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.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) REDUCED to normal form. ------ 165733/18531048. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 165734/18531102. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 165735/18531129. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 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. ------ 165736/18531147. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((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. ------ 165737/18531156. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 165738/18531408. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b) a)(b ((^y.y) b))) 4. ==[ alpha ]==> (((a b) a)(b ((^x.x) b))) 5. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 165739/18531435. ------ 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)))) REDUCED to normal form. ------ 165740/18531462. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (a a))) REDUCED to normal form. ------ 165741/18531489. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 165742/18531723. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165743/18531795. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^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. ------ 165744/18531831. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 165745/18531849. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b))((b a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a b))((b a)(^x.a))) REDUCED to normal form. ------ 165746/18531912. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 165747/18531930. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a b)(^y.a))) 3. ==[ beta ]==> (b ((a b)(^y.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 165748/18531939. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 165749/18531966. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(a b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(a b))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 165750/18531993. ------ 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))((^z1.z1)(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. ------ 165751/18532317. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 165752/18532722. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 165753/18532749. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 165754/18532794. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 165755/18532857. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 165756/18532929. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 165757/18533208. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 165758/18533415. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 165759/18533586. ------ 1. ==[ start ]==> (((a a)(^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 165760/18533658. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 165761/18533694. ------ 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))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165762/18533721. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 165763/18533739. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((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. ------ 165764/18533748. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 165765/18533775. ------ 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.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 165766/18533802. ------ 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.(^x1.x1))((a a) 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. ------ 165767/18533847. ------ 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) 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. ------ 165768/18533856. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 165769/18533883. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 165770/18534189. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(a (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (b a))) REDUCED to normal form. ------ 165771/18534216. ------ 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))) REDUCED to normal form. ------ 165772/18534243. ------ 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)))) 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. ------ 165773/18534522. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((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. ------ 165774/18534558. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(a (a a)))) 3. ==[ beta ]==> ((b b)((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((b b)((^x.a)(a (a a)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 165775/18534585. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^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)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 165776/18534630. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.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. ------ 165777/18534639. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 165778/18534666. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 165779/18534684. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a a)(^c.(^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. ------ 165780/18534747. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 165781/18534765. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((a b) c)) 3. ==[ beta ]==> (b ((a b) c)) REDUCED to normal form. ------ 165782/18534774. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 165783/18534828. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(^b.(^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. ------ 165784/18534882. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 165785/18534909. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 165786/18534972. ------ 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))(a a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 165787/18534999. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)(a (^y.y)))) REDUCED to normal form. ------ 165788/18535026. ------ 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) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(((a a) a) a)) REDUCED to normal form. ------ 165789/18535053. ------ 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 (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)))) 5. ==[ beta ]==> (((a (a a))(b a))(a (a a))) REDUCED to normal form. ------ 165790/18535080. ------ 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 a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 165791/18535107. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(a a))(a ((a a) a))) REDUCED to normal form. ------ 165792/18535134. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(a b))) REDUCED to normal form. ------ 165793/18535161. ------ 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)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 165794/18535413. ------ 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)(a a)) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a)) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a)) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(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. ------ 165795/18535773. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (^z.a))) 3. ==[ beta ]==> ((a (^y.y))(c (^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(c (^y.a))) REDUCED to normal form. ------ 165796/18535800. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (^x1.b))) REDUCED to normal form. ------ 165797/18535872. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 165798/18535881. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 165799/18535908. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 165800/18535989. ------ 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.(^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. ------ 165801/18536016. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(a b))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(a b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(a b))) 5. ==[ beta ]==> ((b (^x.a))(a b)) REDUCED to normal form. ------ 165802/18536043. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 165803/18536160. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)(c ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)(c ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)(c (^y.y))) 8. ==[ alpha ]==> ((a b)(c (^x.x))) REDUCED to normal form. ------ 165804/18536187. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b ((a a) a))) REDUCED to normal form. ------ 165805/18536214. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 165806/18536241. ------ 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))) REDUCED to normal form. ------ 165807/18536268. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(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. ------ 165808/18536295. ------ 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. ------ 165809/18536322. ------ 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. ------ 165810/18536376. ------ 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. ------ 165811/18536574. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(^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. ------ 165812/18536655. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a) d)) 3. ==[ beta ]==> (b (((^x1.x1) a) d)) 4. ==[ alpha ]==> (b (((^x.x) a) d)) 5. ==[ beta ]==> (b (a d)) REDUCED to normal form. ------ 165813/18536763. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^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. ------ 165814/18536898. ------ 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.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 165815/18536925. ------ 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. ------ 165816/18536979. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((b b)((a (^y.y))(^z.(z z)))) 8. ==[ alpha ]==> ((b b)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 165817/18536988. ------ 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. ------ 165818/18537015. ------ 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)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 165819/18537060. ------ 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. ------ 165820/18537069. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(^a.(^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. ------ 165821/18537096. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 165822/18537123. ------ 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))(^y1.(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. ------ 165823/18537168. ------ 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.(^x2.x2)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165824/18537231. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.a))) REDUCED to normal form. ------ 165825/18537285. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 165826/18537303. ------ 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. ------ 165827/18537348. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c c)) REDUCED to normal form. ------ 165828/18537456. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (a (^x.x)))) REDUCED to normal form. ------ 165829/18537483. ------ 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)(^x.x)))(b a)) REDUCED to normal form. ------ 165830/18537510. ------ 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. ------ 165831/18537537. ------ 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. ------ 165832/18537591. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a) a)) REDUCED to normal form. ------ 165833/18537717. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 165834/18537735. ------ 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 ]==> ((^y.(y (^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z)) b)) 5. ==[ beta ]==> (((a (^z.z)) b)(^y.y)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 165835/18548718. ------ 1. ==[ start ]==> ((^a.b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 165836/18549159. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 165837/18549609. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165838/18550296. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(x x))((^y.y) a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(^x1.x1))) 5. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((^x.x) a)((^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. ------ 165839/18550374. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 165840/18551070. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^b.(b (^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. ------ 165841/18551148. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.a))((^z.z)(^x1.a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.a))((^x1.x1)(^y1.a)))) 5. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.a))) 7. ==[ beta ]==> ((^y.a)((^z.z)(^x1.a))) 8. ==[ alpha ]==> ((^x.a)((^y.y)(^z.a))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 165842/18551457. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(b (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(b (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(b (^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(b (^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(^z.(b (^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 11. ==[ beta ]==> (^y.(b (^z.z))) 12. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 165843/18552528. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 165844/18552861. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.((^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. ------ 165845/18553203. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) a)((^y.y)(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. ------ 165846/18553416. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(^z1.(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 165847/18554148. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(^y.(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 165848/18554334. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 165849/18555012. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^b.(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(y a))) 3. ==[ beta ]==> (((a a) b)(^y.(y a))) 4. ==[ alpha ]==> (((a a) b)(^x.(x a))) REDUCED to normal form. ------ 165850/18556413. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 165851/18557109. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.b))) REDUCED to normal form. ------ 165852/18557307. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.y))) 5. ==[ beta ]==> ((b a)(^y.(^z.y))) 6. ==[ alpha ]==> ((b a)(^x.(^y.x))) REDUCED to normal form. ------ 165853/18557496. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.b))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.b))) 5. ==[ beta ]==> ((b a)(^y.(^z.b))) 6. ==[ alpha ]==> ((b a)(^x.(^y.b))) REDUCED to normal form. ------ 165854/18557574. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165855/18558261. ------ 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.((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 165856/18558495. ------ 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. ------ 165857/18558603. ------ 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.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 165858/18558711. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 165859/18558792. ------ 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)(^x.a)) REDUCED to normal form. ------ 165860/18558816. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)(^a.a))) 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. ------ 165861/18559236. ------ 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. ------ 165862/18559272. ------ 1. ==[ start ]==> ((a b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 165863/18559488. ------ 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. ------ 165864/18559551. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(c (b (^z.z)))) 3. ==[ beta ]==> ((^y.a)(c (b (^z.z)))) 4. ==[ alpha ]==> ((^x.a)(c (b (^y.y)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 165865/18559578. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 165866/18559614. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y (^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)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 165867/18559632. ------ 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. ------ 165868/18559659. ------ 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))(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. ------ 165869/18559713. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(b (a (a a)))) REDUCED to normal form. ------ 165870/18559821. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((((^y.y)(a a))((^z.z)(a a)))(((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(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)(a a))(((^y.y)(a a))((^z.z)(a a)))) 10. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((^y.y)(a a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(a a)))) 12. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(a a)))) 13. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 165871/18559848. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^x1.x1)))) 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. ------ 165872/18559902. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 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. ------ 165873/18559929. ------ 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. ------ 165874/18559956. ------ 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) 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. ------ 165875/18560010. ------ 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)((^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. ------ 165876/18560127. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((b b)(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> ((b b)(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> ((b b)(b (^y.(y y)))) 6. ==[ alpha ]==> ((b b)(b (^x.(x x)))) REDUCED to normal form. ------ 165877/18560136. ------ 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. ------ 165878/18560163. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 165879/18560262. ------ 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. ------ 165880/18560316. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^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. ------ 165881/18560343. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 165882/18560370. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a (^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 165883/18560541. ------ 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. ------ 165884/18560568. ------ 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. ------ 165885/18560847. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(a ((^z.(^x1.x1)) 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 a)(a ((^y.(^z.z)) a))) 8. ==[ alpha ]==> ((a a)(a ((^x.(^y.y)) a))) 9. ==[ beta ]==> ((a a)(a (^y.y))) 10. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 165886/18560928. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.b))(b ((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.b))(b ((^y.y) a))) 5. ==[ beta ]==> ((a (^x.b))(b a)) REDUCED to normal form. ------ 165887/18561117. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 165888/18561198. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))((a a)(a a)))) IRREDUCIBLE: cycle. ------ 165889/18561261. ------ 1. ==[ start ]==> ((((a a) a) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a) b)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 165890/18561288. ------ 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. ------ 165891/18561315. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.a))) REDUCED to normal form. ------ 165892/18561369. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 165893/18561423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 165894/18561450. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 165895/18561477. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 165896/18561513. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 165897/18561540. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 165898/18561567. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 165899/18561594. ------ 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. ------ 165900/18561621. ------ 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)))) 9. ==[ beta ]==> (a (b (^y.y))) 10. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 165901/18561666. ------ 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 a)) b)) REDUCED to normal form. ------ 165902/18561675. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 165903/18561702. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a))) 5. ==[ beta ]==> ((a (a a))(^y.a)) 6. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 165904/18561954. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c ((^z.z) b))) 3. ==[ beta ]==> ((^y.y)(c ((^z.z) 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. ------ 165905/18562008. ------ 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)(^z.z))((^y.y)(^z.z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a (b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a (b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (b (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (b (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (b (^z.z)))) 9. ==[ beta ]==> ((^y.y)(a (b (^z.z)))) 10. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 11. ==[ beta ]==> (a (b (^y.y))) 12. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 165906/18562071. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y) c)) 3. ==[ beta ]==> ((((a a) a)(^x.a)) c) REDUCED to normal form. ------ 165907/18562089. ------ 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) 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. ------ 165908/18562323. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(c (^y.y))) REDUCED to normal form. ------ 165909/18562350. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(b (^c.(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. ------ 165910/18562557. ------ 1. ==[ start ]==> (((a b) c)((a b)(^a.b))) 2. ==[ alpha ]==> (((a b) c)((a b)(^x.b))) REDUCED to normal form. ------ 165911/18562584. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) 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. ------ 165912/18562665. ------ 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)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 165913/18562692. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 165914/18562746. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 165915/18562773. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b b)) REDUCED to normal form. ------ 165916/18562800. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 165917/18562890. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.(a a))(^c.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. ------ 165918/18562917. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 165919/18562944. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 165920/18562971. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(^a.a))(^c.(^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. ------ 165921/18563025. ------ 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.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) a) REDUCED to normal form. ------ 165922/18563052. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) 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))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 165923/18563223. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (b (((^x.x)(a 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. ------ 165924/18563304. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((^y1.y1)(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. ------ 165925/18563412. ------ 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))) 5. ==[ beta ]==> ((b a)((a a) b)) REDUCED to normal form. ------ 165926/18563475. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 165927/18563502. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a)(^y.a))) REDUCED to normal form. ------ 165928/18563556. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 165929/18563583. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)(^y.a))) REDUCED to normal form. ------ 165930/18563610. ------ 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. ------ 165931/18563637. ------ 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)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(a a))) REDUCED to normal form. ------ 165932/18563700. ------ 1. ==[ start ]==> (((a a)(b a))((^b.a)(b a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(b a))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 165933/18563727. ------ 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.x1))(a (^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. ------ 165934/18563754. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^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. ------ 165935/18563781. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 165936/18563808. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 165937/18563862. ------ 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 z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 165938/18563889. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 165939/18563916. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 165940/18563970. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^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. ------ 165941/18564060. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(b (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 165942/18564141. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 165943/18564249. ------ 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 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. ------ 165944/18564276. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^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. ------ 165945/18564303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 165946/18564357. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.z))(b a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(b a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(b a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(b a))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.y))(b a))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(b a))) REDUCED to normal form. ------ 165947/18564447. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 165948/18564474. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 165949/18564501. ------ 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)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.(z z)))) REDUCED to normal form. ------ 165950/18564591. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(^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)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 165951/18564618. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(b a))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(b a))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a (^x.x))(b a))((a a)(a a))) REDUCED to normal form. ------ 165952/18564645. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 165953/18564672. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 165954/18564699. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((^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. ------ 165955/18564726. ------ 1. ==[ start ]==> ((((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))) 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. ------ 165956/18564807. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 165957/18564888. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 165958/18565059. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 165959/18565167. ------ 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)(^x2.x2))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))((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. ------ 165960/18565221. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^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)))) 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. ------ 165961/18565248. ------ 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 (^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))((a a)(^z1.z1)))) 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. ------ 165962/18565338. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 165963/18565365. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(a a))(^b.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. ------ 165964/18565392. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(^y.(y y)))) REDUCED to normal form. ------ 165965/18565419. ------ 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.(^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. ------ 165966/18565500. ------ 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) a)(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(a a)))) REDUCED to normal form. ------ 165967/18565527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((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. ------ 165968/18565563. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.y)(b a))) 3. ==[ beta ]==> (((a a) b)((^y.y)(b a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(b a))) 5. ==[ beta ]==> (((a a) b)(b a)) REDUCED to normal form. ------ 165969/18565617. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a))(^a.(^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)))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 165970/18565644. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 165971/18565671. ------ 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)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.(z z)))) 7. ==[ beta ]==> ((a a)((^y.b)(^z.(z z)))) 8. ==[ alpha ]==> ((a a)((^x.b)(^y.(y y)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 165972/18565698. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.a)(^b.(^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. ------ 165973/18565725. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^a.a))(^c.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. ------ 165974/18565752. ------ 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)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 165975/18565779. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) a) REDUCED to normal form. ------ 165976/18565923. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((a b)((^x1.x1) 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. ------ 165977/18566058. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 165978/18566202. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> ((b b)(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> ((b b)(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 165979/18566229. ------ 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.(^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. ------ 165980/18566283. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.b))) REDUCED to normal form. ------ 165981/18566310. ------ 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 (^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 165982/18566391. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) b)) REDUCED to normal form. ------ 165983/18566418. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((a b) c)) REDUCED to normal form. ------ 165984/18566778. ------ 1. ==[ start ]==> (((a b)(a b))(c (^a.b))) 2. ==[ alpha ]==> (((a b)(a b))(c (^x.b))) REDUCED to normal form. ------ 165985/18566805. ------ 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. ------ 165986/18566886. ------ 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)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 165987/18566913. ------ 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) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 165988/18566940. ------ 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. ------ 165989/18566967. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (b (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (b (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 10. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 165990/18567246. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 165991/18567282. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a)) a)) 3. ==[ beta ]==> ((b c)((^y.(a a)) a)) 4. ==[ alpha ]==> ((b c)((^x.(a a)) a)) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 165992/18567309. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b) b)) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 165993/18567354. ------ 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 (^x.x))((^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. ------ 165994/18567381. ------ 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. ------ 165995/18567435. ------ 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 (^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))((a a) a))) REDUCED to normal form. ------ 165996/18567525. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 165997/18567552. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.b))(^z.a)) 8. ==[ alpha ]==> (((a a)(^x.b))(^y.a)) REDUCED to normal form. ------ 165998/18567660. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(^z.b))) 3. ==[ beta ]==> ((b (^y.a))((a a)(^z.b))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(^y.b))) REDUCED to normal form. ------ 165999/18567687. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 166000/18567750. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 166001/18567777. ------ 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 y))(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 166002/18567804. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 166003/18567858. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))((^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. ------ 166004/18568020. ------ 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. ------ 166005/18568047. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^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. ------ 166006/18568128. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 166007/18568299. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d ((^x1.x1) a))) 3. ==[ beta ]==> (b (d ((^x1.x1) a))) 4. ==[ alpha ]==> (b (d ((^x.x) a))) 5. ==[ beta ]==> (b (d a)) REDUCED to normal form. ------ 166008/18568407. ------ 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. ------ 166009/18568623. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c d)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c d)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c d)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c d)) 5. ==[ beta ]==> ((b ((^y.y) b))(c d)) 6. ==[ alpha ]==> ((b ((^x.x) b))(c d)) 7. ==[ beta ]==> ((b b)(c d)) REDUCED to normal form. ------ 166010/18568632. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 166011/18568659. ------ 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))))((a a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166012/18568713. ------ 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. ------ 166013/18568740. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a) c)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a c)) REDUCED to normal form. ------ 166014/18568812. ------ 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 ((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166015/18568821. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1)) 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. ------ 166016/18568848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z)) b)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z)) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y)) b)) 5. ==[ beta ]==> ((b (^x.(x x)))(b b)) REDUCED to normal form. ------ 166017/18568875. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 166018/18568965. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 166019/18568992. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 166020/18569019. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 166021/18569046. ------ 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. ------ 166022/18569073. ------ 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 y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^x1.x1))) 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. ------ 166023/18569100. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.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. ------ 166024/18569127. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^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. ------ 166025/18569154. ------ 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 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^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. ------ 166026/18569235. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (^b.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. ------ 166027/18569262. ------ 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. ------ 166028/18569289. ------ 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))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 166029/18569343. ------ 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. ------ 166030/18569361. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^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 (^x.x))(a a)) REDUCED to normal form. ------ 166031/18569370. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.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. ------ 166032/18569765. ------ 1. ==[ start ]==> (^a.(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (^x.(((^y.(^z.z)) x) b)) 3. ==[ beta ]==> (^x.((^z.z) b)) 4. ==[ alpha ]==> (^x.((^y.y) b)) 5. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 166033/18569766. ------ 1. ==[ start ]==> (a (((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (a (((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (a ((^y.y) b)) 4. ==[ alpha ]==> (a ((^x.x) b)) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 166034/18570588. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^a.(^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. ------ 166035/18579498. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 166036/18580320. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b) a) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b) a) 3. ==[ beta ]==> (((^y.y) b) a) 4. ==[ alpha ]==> (((^x.x) b) a) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 166037/18580326. ------ 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. ------ 166038/18580353. ------ 1. ==[ start ]==> ((^a.(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) c)) 3. ==[ beta ]==> (((b (^y.y)) c)((b (^y.y)) c)) 4. ==[ alpha ]==> (((b (^x.x)) c)((b (^y.y)) c)) REDUCED to normal form. ------ 166039/18580416. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 166040/18580578. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 166041/18580725. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 166042/18581145. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166043/18581148. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 166044/18581271. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (^x1.(^y1.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. ------ 166045/18581967. ------ 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. ------ 166046/18582603. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.a)((a a)(^x1.x1)))((^z.a)((a a)(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((^y.a)((a a)(^z.z)))((^x1.a)((a a)(^y1.y1))))) 5. ==[ beta ]==> (^x.(a ((^x1.a)((a a)(^y1.y1))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)((a a)(^z.z))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 166047/18582810. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) b) c)) 3. ==[ beta ]==> ((^y.y)((((^z.z) b) c)(((^z.z) b) c))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) b) c)(((^z.z) b) c))) 5. ==[ beta ]==> ((((^y.y) b) c)(((^z.z) b) c)) 6. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) b) c)) 7. ==[ beta ]==> ((b c)(((^y.y) b) c)) 8. ==[ alpha ]==> ((b c)(((^x.x) b) c)) 9. ==[ beta ]==> ((b c)(b c)) REDUCED to normal form. ------ 166048/18583128. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 166049/18584241. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b) b)) 2. ==[ alpha ]==> ((^x.(b x))((^y.y) b)) 3. ==[ eta ]==> (b ((^y.y) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 166050/18584790. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 166051/18585504. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 166052/18585681. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166053/18585810. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 166054/18586413. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 166055/18586674. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(^z.a))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.a))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.a))) REDUCED to normal form. ------ 166056/18588075. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166057/18588168. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((^y2.y2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((^y2.y2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166058/18588393. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((b c)(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> ((b c)(^x.((^y.y)(x x)))) 5. ==[ beta ]==> ((b c)(^x.(x x))) REDUCED to normal form. ------ 166059/18589236. ------ 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. ------ 166060/18589329. ------ 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)) REDUCED to normal form. ------ 166061/18589923. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166062/18589932. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 166063/18590055. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 166064/18590058. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 166065/18590157. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 166066/18590478. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> ((((^z.z) a) a)((((^z.z) a) a)(^y.y))) 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. ------ 166067/18590877. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166068/18590889. ------ 1. ==[ start ]==> ((a a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> ((a a)((^y.y) b)) 4. ==[ alpha ]==> ((a a)((^x.x) b)) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 166069/18590916. ------ 1. ==[ start ]==> ((a (a a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (a a))((b (^x.x)) c)) REDUCED to normal form. ------ 166070/18590979. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 166071/18591087. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(a a))(^c.(^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. ------ 166072/18591141. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 166073/18591258. ------ 1. ==[ start ]==> (((a (^a.a)) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.y))) REDUCED to normal form. ------ 166074/18591285. ------ 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. ------ 166075/18591312. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 166076/18591339. ------ 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))(a (^y1.y1)))) REDUCED to normal form. ------ 166077/18591366. ------ 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) 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. ------ 166078/18591474. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 166079/18591555. ------ 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. ------ 166080/18591582. ------ 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. ------ 166081/18591609. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a (a a)) b)) REDUCED to normal form. ------ 166082/18591636. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 166083/18591663. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^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. ------ 166084/18591690. ------ 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. ------ 166085/18591708. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 166086/18591726. ------ 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. ------ 166087/18591753. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 166088/18591780. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 166089/18591807. ------ 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. ------ 166090/18591834. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 166091/18591843. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166092/18591924. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166093/18592005. ------ 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. ------ 166094/18592059. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 166095/18592131. ------ 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)(^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) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 166096/18592158. ------ 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. ------ 166097/18592302. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.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. ------ 166098/18592356. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 166099/18592437. ------ 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. ------ 166100/18592464. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(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. ------ 166101/18592473. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c ((a a)(a a)))) REDUCED to normal form. ------ 166102/18592500. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(b (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))(b (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (b (^y.y)))) REDUCED to normal form. ------ 166103/18592527. ------ 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. ------ 166104/18592554. ------ 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.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166105/18592581. ------ 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. ------ 166106/18592770. ------ 1. ==[ start ]==> (((^a.b) a)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 166107/18592977. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 166108/18593004. ------ 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) 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. ------ 166109/18593139. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 166110/18593166. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 166111/18593211. ------ 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.(^z.(^x1.x1))))) REDUCED to normal form. ------ 166112/18593238. ------ 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) a)(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 166113/18593319. ------ 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. ------ 166114/18593346. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 166115/18593373. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b) c)) 3. ==[ beta ]==> ((a (a a))(((^y.y) b) c)) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b) c)) 5. ==[ beta ]==> ((a (a a))(b c)) REDUCED to normal form. ------ 166116/18593382. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166117/18593409. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 166118/18593463. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.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. ------ 166119/18593544. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.a)(^c.(^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. ------ 166120/18593598. ------ 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 z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 166121/18593625. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 166122/18593634. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(c b)) REDUCED to normal form. ------ 166123/18593688. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 166124/18593715. ------ 1. ==[ start ]==> ((((^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 a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(a a))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(a a))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(a a))) 7. ==[ beta ]==> ((((a a)(a a))(a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 166125/18593742. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b)(a (^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. ------ 166126/18593769. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 166127/18593796. ------ 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. ------ 166128/18593985. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 166129/18594084. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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 a) REDUCED to normal form. ------ 166130/18594219. ------ 1. ==[ start ]==> (((^a.b)(^b.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. ------ 166131/18594300. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 166132/18594327. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 166133/18594381. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 166134/18594462. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 166135/18594804. ------ 1. ==[ start ]==> ((a (b a))((^b.b) b)) 2. ==[ alpha ]==> ((a (b a))((^x.x) b)) 3. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 166136/18595038. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (b a))) REDUCED to normal form. ------ 166137/18595083. ------ 1. ==[ start ]==> (((^a.a)(b a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.x)(b a))(b (^y.y))) 3. ==[ beta ]==> ((b a)(b (^y.y))) 4. ==[ alpha ]==> ((b a)(b (^x.x))) REDUCED to normal form. ------ 166138/18595164. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 166139/18595245. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 166140/18595353. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((a a)(^y1.y1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 166141/18595398. ------ 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.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 166142/18595425. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a a)(^b.b))) 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. ------ 166143/18595452. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) b) a)) 3. ==[ beta ]==> (((a (a a))(a b))(b a)) REDUCED to normal form. ------ 166144/18595479. ------ 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.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.x)((a a) 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)) REDUCED to normal form. ------ 166145/18595506. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 166146/18595650. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166147/18595731. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 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. ------ 166148/18595929. ------ 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. ------ 166149/18595956. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 166150/18596037. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.y))(b a))) REDUCED to normal form. ------ 166151/18596064. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a a)(a (^a.(^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. ------ 166152/18596109. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(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. ------ 166153/18596217. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166154/18596244. ------ 1. ==[ start ]==> ((a (^b.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 166155/18596262. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(^x1.b))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.b)) 6. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 166156/18596289. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 166157/18596370. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((a a)(^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. ------ 166158/18596397. ------ 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)) REDUCED to normal form. ------ 166159/18596424. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((b a) b)) 3. ==[ beta ]==> (((a b)(^y.y))((b a) b)) 4. ==[ alpha ]==> (((a b)(^x.x))((b a) b)) REDUCED to normal form. ------ 166160/18596568. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 166161/18596595. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(z1 z1))(^x2.(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. ------ 166162/18596847. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a) a)) REDUCED to normal form. ------ 166163/18596874. ------ 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. ------ 166164/18596901. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a) a)((^a.a)(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. ------ 166165/18596928. ------ 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 (^y1.y1))((a a)(^z1.z1)))) REDUCED to normal form. ------ 166166/18596973. ------ 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.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 166167/18597054. ------ 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) 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. ------ 166168/18597162. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^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. ------ 166169/18597261. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((b a) a)) REDUCED to normal form. ------ 166170/18597288. ------ 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)) REDUCED to normal form. ------ 166171/18597729. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(c (^z.(a a)))) 3. ==[ beta ]==> (b (c (^z.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 166172/18597837. ------ 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))(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. ------ 166173/18597918. ------ 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))((^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))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 166174/18597945. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 166175/18597999. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 166176/18598080. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 166177/18598224. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (a b))) REDUCED to normal form. ------ 166178/18598251. ------ 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)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(b (a a))) REDUCED to normal form. ------ 166179/18598314. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a)) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a)) b)) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 166180/18598341. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b) c)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b) c)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b) c)) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 166181/18598368. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a) d)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a) d)) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 166182/18598557. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 166183/18598584. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a) a)(^b.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. ------ 166184/18598611. ------ 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)(^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. ------ 166185/18598638. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 166186/18598728. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.x2)((^y2.y2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.x2)((^y2.y2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166187/18598809. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a 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. ------ 166188/18598917. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 166189/18598953. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((b c)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b c)(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((b c)(a (a a))) REDUCED to normal form. ------ 166190/18598980. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(a a))) REDUCED to normal form. ------ 166191/18599088. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^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. ------ 166192/18599115. ------ 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 a) a))) REDUCED to normal form. ------ 166193/18599187. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 166194/18599295. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^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. ------ 166195/18599421. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z) c)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y) c)) 5. ==[ beta ]==> (((a a)(b (^x.x))) c) REDUCED to normal form. ------ 166196/18599556. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b) a)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 166197/18599583. ------ 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)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 166198/18599610. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 166199/18599745. ------ 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. ------ 166200/18599799. ------ 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. ------ 166201/18599889. ------ 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. ------ 166202/18599970. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.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. ------ 166203/18600195. ------ 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. ------ 166204/18600240. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166205/18600294. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)((^z.z) a))) 7. ==[ beta ]==> ((b b)((^y.a)((^z.z) a))) 8. ==[ alpha ]==> ((b b)((^x.a)((^y.y) a))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 166206/18600303. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c d)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c d)) REDUCED to normal form. ------ 166207/18600375. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 166208/18600438. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(c a)) REDUCED to normal form. ------ 166209/18600483. ------ 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.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166210/18600492. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) REDUCED to normal form. ------ 166211/18600519. ------ 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. ------ 166212/18600546. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 166213/18600600. ------ 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. ------ 166214/18600618. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 166215/18600636. ------ 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. ------ 166216/18600663. ------ 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.(^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. ------ 166217/18600690. ------ 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))(^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))) REDUCED to normal form. ------ 166218/18600717. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a 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. ------ 166219/18600744. ------ 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. ------ 166220/18600771. ------ 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. ------ 166221/18600798. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y)) c)) REDUCED to normal form. ------ 166222/18600852. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 166223/18600960. ------ 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))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) 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. ------ 166224/18601014. ------ 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. ------ 166225/18601041. ------ 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. ------ 166226/18601050. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (((^z.a)(^x1.x1))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(^y.y))(^z.z)) 7. ==[ beta ]==> (a (^z.z)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 166227/18601437. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 166228/18612000. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b) b) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b) b) 3. ==[ beta ]==> (((^y.y) b) b) 4. ==[ alpha ]==> (((^x.x) b) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 166229/18612024. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166230/18612414. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 166231/18612609. ------ 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. ------ 166232/18613725. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a)) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 166233/18613905. ------ 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 ]==> ((((a a) a)((a a)(^y.y))) b) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 166234/18614292. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.((((a a) a)(^z.(^x1.x1)))(((a a) a)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.((((a a) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1))))) REDUCED to normal form. ------ 166235/18615174. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((((a 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 a))))(^x.x)) REDUCED to normal form. ------ 166236/18615546. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166237/18615906. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.((y y)(y y)))) REDUCED to normal form. ------ 166238/18615930. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b)(a a))) 3. ==[ eta ]==> (b (((^y.y) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 166239/18617370. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166240/18618660. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(b y))) 3. ==[ eta ]==> ((((^x.x) b)(a a)) b) 4. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 166241/18618684. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> (((((a a)(^y.y))(a a))(((a a)(^y.y))(a a)))((((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)))((((a a)(^z.z))(a a))(((a a)(^x1.x1))(a a)))) REDUCED to normal form. ------ 166242/18619416. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 166243/18620082. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(^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. ------ 166244/18620487. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(a z))) 3. ==[ eta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 166245/18620685. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(y b))) REDUCED to normal form. ------ 166246/18620847. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.((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))) REDUCED to normal form. ------ 166247/18621018. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.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. ------ 166248/18621621. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 166249/18621981. ------ 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. ------ 166250/18622062. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.((^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)))(^x.a)) REDUCED to normal form. ------ 166251/18622161. ------ 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))(^y.a)) REDUCED to normal form. ------ 166252/18622566. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166253/18622596. ------ 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)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 166254/18622623. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 166255/18622686. ------ 1. ==[ start ]==> (((^a.a) b)((^b.b)(^b.(^a.a)))) 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)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 166256/18622794. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 166257/18622875. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 166258/18622983. ------ 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)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 166259/18623001. ------ 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. ------ 166260/18623100. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 166261/18623127. ------ 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 (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 166262/18623154. ------ 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. ------ 166263/18623181. ------ 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. ------ 166264/18623496. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 166265/18623541. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 166266/18623568. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.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. ------ 166267/18623622. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 166268/18623631. ------ 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. ------ 166269/18623658. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (a ((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> (a ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 166270/18623685. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 166271/18623703. ------ 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. ------ 166272/18623712. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 166273/18623739. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.a))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.a))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.a))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.a))(b b)) REDUCED to normal form. ------ 166274/18623766. ------ 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. ------ 166275/18623793. ------ 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))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166276/18624090. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 166277/18624117. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 166278/18624171. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 166279/18624297. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 166280/18624315. ------ 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) a))) 3. ==[ beta ]==> (((a a)((a a) a))(b ((^y.y) a))) 4. ==[ alpha ]==> (((a a)((a a) a))(b ((^x.x) a))) 5. ==[ beta ]==> (((a a)((a a) a))(b a)) REDUCED to normal form. ------ 166281/18624342. ------ 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 (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 166282/18624369. ------ 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. ------ 166283/18624396. ------ 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. ------ 166284/18624423. ------ 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)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 166285/18624450. ------ 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)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a b)(a a))) REDUCED to normal form. ------ 166286/18624477. ------ 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. ------ 166287/18624648. ------ 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 ((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 166288/18624675. ------ 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. ------ 166289/18624684. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 166290/18624702. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 166291/18624738. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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. ------ 166292/18624756. ------ 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. ------ 166293/18624792. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 166294/18624819. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 166295/18624837. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((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. ------ 166296/18624846. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 166297/18624864. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 166298/18625080. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) b) c)) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) b) c)) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) b) c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166299/18625251. ------ 1. ==[ start ]==> (((a b) b)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 166300/18625305. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 166301/18625332. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 166302/18625458. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 166303/18625530. ------ 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)(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. ------ 166304/18625557. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a a)((a a) a))) REDUCED to normal form. ------ 166305/18625584. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a b)(a b))) 3. ==[ beta ]==> ((a ((a a) a))((a b)(a b))) REDUCED to normal form. ------ 166306/18625611. ------ 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.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. ------ 166307/18625638. ------ 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))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^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)))) 9. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 10. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 166308/18625665. ------ 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. ------ 166309/18625683. ------ 1. ==[ start ]==> (((^a.b) c)(d (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(d (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b (d (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (d (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 166310/18625692. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 166311/18625719. ------ 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 (^x.x)) b)) REDUCED to normal form. ------ 166312/18625746. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 166313/18625782. ------ 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))(^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. ------ 166314/18625917. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 166315/18625926. ------ 1. ==[ start ]==> (((a b) c)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 166316/18625953. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.b)(a b))) 3. ==[ beta ]==> (((a a) b)((^y.b)(a b))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(a b))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 166317/18626034. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((b a)(b a))) REDUCED to normal form. ------ 166318/18626061. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.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) REDUCED to normal form. ------ 166319/18626079. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (^a.a))(^b.b))) 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. ------ 166320/18626115. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((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. ------ 166321/18626160. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^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. ------ 166322/18626169. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 166323/18626196. ------ 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.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.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. ------ 166324/18626421. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) a)(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) a)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 166325/18626448. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 166326/18626475. ------ 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. ------ 166327/18626502. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b)(a a))) 3. ==[ beta ]==> ((a (b a))(b (a a))) REDUCED to normal form. ------ 166328/18626844. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(a a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 166329/18626862. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 166330/18626871. ------ 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)))(a (^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. ------ 166331/18626925. ------ 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. ------ 166332/18626943. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(a a))(^b.(^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. ------ 166333/18626952. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 166334/18626979. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 166335/18627510. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1))) 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. ------ 166336/18627735. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(c (^d.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(c (^y.a))) REDUCED to normal form. ------ 166337/18627762. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)(b (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 166338/18627807. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 166339/18627816. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(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. ------ 166340/18627870. ------ 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) 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. ------ 166341/18627915. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(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. ------ 166342/18627924. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 166343/18627942. ------ 1. ==[ start ]==> ((a (^b.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 166344/18628221. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 166345/18628428. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a) b)) 3. ==[ beta ]==> (b ((^z.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 166346/18628734. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(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. ------ 166347/18628752. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(a a))(^b.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. ------ 166348/18628761. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 166349/18628788. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 166350/18628860. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 166351/18628869. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(a b))) REDUCED to normal form. ------ 166352/18628896. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 166353/18629202. ------ 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 a)(^x1.x1)))) REDUCED to normal form. ------ 166354/18629229. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(a (b a))) 3. ==[ beta ]==> ((b (a a))(a (b a))) REDUCED to normal form. ------ 166355/18629256. ------ 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))) REDUCED to normal form. ------ 166356/18629292. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 166357/18629535. ------ 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.(^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. ------ 166358/18629571. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((b b)((^y.b)((^z.z) a))) 4. ==[ alpha ]==> ((b b)((^x.b)((^y.y) a))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 166359/18629616. ------ 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)(^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))((^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. ------ 166360/18629643. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 166361/18629652. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^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. ------ 166362/18629679. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(a b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 166363/18629697. ------ 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 a)(b a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 166364/18629760. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a))(^a.a))) 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. ------ 166365/18629778. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (b (((^y.y)(a a)) b)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) b)) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 166366/18629787. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 166367/18629841. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 166368/18629895. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 166369/18629922. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 166370/18629949. ------ 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))(^x1.(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. ------ 166371/18629985. ------ 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. ------ 166372/18630012. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(a a))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(a a))) REDUCED to normal form. ------ 166373/18630039. ------ 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)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(a (^z.z)))) REDUCED to normal form. ------ 166374/18630066. ------ 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. ------ 166375/18630093. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 166376/18630120. ------ 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))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))((^x.x)(^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. ------ 166377/18630147. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)((a a) a))) 3. ==[ beta ]==> (((a b)(a b))(a ((a a) a))) REDUCED to normal form. ------ 166378/18630174. ------ 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. ------ 166379/18630201. ------ 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)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 166380/18630426. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a a)(^x2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166381/18630507. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 166382/18630651. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((b c)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((b c)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((b c)(^y.(a a))) 6. ==[ alpha ]==> ((b c)(^x.(a a))) REDUCED to normal form. ------ 166383/18630723. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) c)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 166384/18630885. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b)(^z.z))) 3. ==[ beta ]==> (b ((a b)(^z.z))) 4. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 166385/18630894. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 166386/18630921. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.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) REDUCED to normal form. ------ 166387/18630993. ------ 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) 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. ------ 166388/18631002. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 166389/18631029. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^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. ------ 166390/18631056. ------ 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. ------ 166391/18631227. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(b ((a a) a))) 5. ==[ beta ]==> ((b a)(b ((a a) a))) REDUCED to normal form. ------ 166392/18631254. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (a b))) REDUCED to normal form. ------ 166393/18631281. ------ 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. ------ 166394/18631308. ------ 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 (^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. ------ 166395/18631335. ------ 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. ------ 166396/18631389. ------ 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 (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 166397/18631416. ------ 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))) 5. ==[ beta ]==> ((b a)((a a)((a a) a))) REDUCED to normal form. ------ 166398/18631587. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(^z.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. ------ 166399/18631668. ------ 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. ------ 166400/18631776. ------ 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))((^z1.a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166401/18631893. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166402/18631938. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 166403/18631992. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(^z.a))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(^z.a))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.a))) 9. ==[ beta ]==> ((b b)(a (^y.a))) 10. ==[ alpha ]==> ((b b)(a (^x.a))) REDUCED to normal form. ------ 166404/18632001. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 166405/18632028. ------ 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. ------ 166406/18632073. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 166407/18632082. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(^a.a))) 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. ------ 166408/18632109. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 166409/18632136. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 166410/18632190. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 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. ------ 166411/18632298. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166412/18632496. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (a (^y.y)))) REDUCED to normal form. ------ 166413/18632523. ------ 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 ((^z.z) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(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. ------ 166414/18632550. ------ 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. ------ 166415/18632604. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 166416/18632631. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)((^y.y) a))) 3. ==[ beta ]==> ((b (a (a a)))((a a)((^y.y) a))) 4. ==[ alpha ]==> ((b (a (a a)))((a a)((^x.x) a))) 5. ==[ beta ]==> ((b (a (a a)))((a a) a)) REDUCED to normal form. ------ 166417/18632712. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b c)) 3. ==[ beta ]==> (((^y.y)(a a))(b c)) 4. ==[ alpha ]==> (((^x.x)(a a))(b c)) 5. ==[ beta ]==> ((a a)(b c)) REDUCED to normal form. ------ 166418/18632730. ------ 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. ------ 166419/18632748. ------ 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 ]==> ((((^z.z) a) a)(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a) a)(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 166420/18633135. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 166421/18633152. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (^x.((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166422/18633153. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (a ((^z.z)(^y.y))) 4. ==[ alpha ]==> (a ((^x.x)(^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 166423/18633975. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^c.((^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. ------ 166424/18643308. ------ 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) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 166425/18643707. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b) c) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b) c) 3. ==[ beta ]==> (((^y.y) b) c) 4. ==[ alpha ]==> (((^x.x) b) c) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 166426/18643725. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a)) a) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z)) a) 3. ==[ beta ]==> (((^z.z)(^y.y)) 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. ------ 166427/18643731. ------ 1. ==[ start ]==> ((^a.a)((^a.(a (^a.a)))(^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 ]==> ((^z.z)(^y.y)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166428/18644148. ------ 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. ------ 166429/18644226. ------ 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) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 166430/18644550. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166431/18644553. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 166432/18644571. ------ 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. ------ 166433/18644676. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.b)(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)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166434/18644976. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 166435/18645108. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3))))((^y3.(^z3.(^x4.x4)))(^y4.(^z4.z4)))) 5. ==[ beta ]==> (((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3))))((^y3.(^z3.(^x4.x4)))(^y4.(^z4.z4)))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2))))((^y2.(^z2.(^x3.x3)))(^y3.(^z3.z3)))) 7. ==[ beta ]==> ((^y.y)((^y2.(^z2.(^x3.x3)))(^y3.(^z3.z3)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166436/18645441. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 166437/18646164. ------ 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. ------ 166438/18646890. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> (((b (^z.(a a)))(b (^z.(a a))))(^y.y)) 4. ==[ alpha ]==> (((b (^x.(a a)))(b (^y.(a a))))(^z.z)) REDUCED to normal form. ------ 166439/18647262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166440/18647622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 166441/18648297. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.((^y.y) x))) 3. ==[ eta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 166442/18649242. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 166443/18649401. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 166444/18650106. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(x1 a))) REDUCED to normal form. ------ 166445/18651132. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 166446/18651480. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166447/18652401. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 166448/18652590. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 166449/18652641. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 166450/18652923. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 166451/18653460. ------ 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. ------ 166452/18653481. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 166453/18653589. ------ 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. ------ 166454/18653697. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(z z)))) REDUCED to normal form. ------ 166455/18653805. ------ 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 z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 166456/18653883. ------ 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. ------ 166457/18653886. ------ 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))))(^y.a)) REDUCED to normal form. ------ 166458/18654282. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.a)) 3. ==[ beta ]==> (((^y.y) b)(^z.a)) 4. ==[ alpha ]==> (((^x.x) b)(^y.a)) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 166459/18654300. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.x1)) 3. ==[ beta ]==> (((^z.z)(^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. ------ 166460/18654312. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a a)((^z.z)(^y.y))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 166461/18654330. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (a (((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> (a (((^x.(^y.y)) a) b)) 5. ==[ beta ]==> (a ((^y.y) b)) 6. ==[ alpha ]==> (a ((^x.x) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 166462/18654357. ------ 1. ==[ start ]==> (((a a) a)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a) a)((b (^x.x)) c)) REDUCED to normal form. ------ 166463/18654420. ------ 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. ------ 166464/18654609. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 166465/18654726. ------ 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. ------ 166466/18654735. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a a)(^x.a))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 166467/18654753. ------ 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)(((^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. ------ 166468/18654807. ------ 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) a))) 3. ==[ beta ]==> ((a (^x.(x x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 166469/18654915. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(a b))) 5. ==[ beta ]==> ((((a a)(^y.y))(a b))(((a a)(^y.y))(a b))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 166470/18654942. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(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. ------ 166471/18654996. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((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. ------ 166472/18655023. ------ 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. ------ 166473/18655050. ------ 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))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) 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. ------ 166474/18655104. ------ 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 (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 166475/18655131. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.(^x1.x1)) 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. ------ 166476/18655149. ------ 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. ------ 166477/18655221. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(a a))(^y.a))) 3. ==[ beta ]==> ((b b)(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> ((b b)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 166478/18655257. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^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. ------ 166479/18655356. ------ 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. ------ 166480/18655383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 166481/18655437. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 166482/18655464. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))(^b.b))) 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. ------ 166483/18655554. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 166484/18655662. ------ 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. ------ 166485/18655689. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))(^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. ------ 166486/18655941. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(b (b (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(b (b (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b (b (^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))(b (b (^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(b (b (^y.y)))) 7. ==[ beta ]==> ((a a)(b (b (^y.y)))) 8. ==[ alpha ]==> ((a a)(b (b (^x.x)))) REDUCED to normal form. ------ 166487/18656022. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 166488/18656211. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.b)(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.b)(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 166489/18656292. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)((^x1.x1) b))) IRREDUCIBLE: cycle. ------ 166490/18656382. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b) a)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 166491/18656409. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 166492/18656463. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 166493/18656490. ------ 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. ------ 166494/18656517. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 166495/18656544. ------ 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))(^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. ------ 166496/18656571. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 166497/18656607. ------ 1. ==[ start ]==> (((a a)(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 166498/18656634. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z))(b 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. ------ 166499/18656661. ------ 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)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 166500/18656688. ------ 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. ------ 166501/18656715. ------ 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))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> (a ((^y.(^z.z))((a a)(a a)))) 8. ==[ alpha ]==> (a ((^x.(^y.y))((a a)(a a)))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 166502/18656742. ------ 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. ------ 166503/18656760. ------ 1. ==[ start ]==> (((^a.b) b)((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b) b)((b (^y.y)) a)) 3. ==[ beta ]==> (b ((b (^y.y)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 166504/18657102. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b ((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b ((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b ((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b ((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 11. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 166505/18657165. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 166506/18657183. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 166507/18657192. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) c) REDUCED to normal form. ------ 166508/18657471. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 166509/18657651. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a b) c)((a a)(^y.a))) 4. ==[ alpha ]==> (((a b) c)((a a)(^x.a))) REDUCED to normal form. ------ 166510/18657678. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a b)(^y.b))) 3. ==[ beta ]==> (((a a) b)((a b)(^y.b))) 4. ==[ alpha ]==> (((a a) b)((a b)(^x.b))) REDUCED to normal form. ------ 166511/18657705. ------ 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. ------ 166512/18657786. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.b))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 166513/18657840. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166514/18657867. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 166515/18657894. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) b) b)) 3. ==[ beta ]==> (((a b)(^x.a))(b b)) REDUCED to normal form. ------ 166516/18658011. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 166517/18658038. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.b)(^z.b))) 3. ==[ beta ]==> ((a (a b))((^y.b)(^z.b))) 4. ==[ alpha ]==> ((a (a b))((^x.b)(^y.b))) 5. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 166518/18658092. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 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. ------ 166519/18658146. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 166520/18658173. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 166521/18658317. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> (b (((a a)(^z.z))(a (a a)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 166522/18658398. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a) a)(a b))) 3. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 166523/18658506. ------ 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))))) REDUCED to normal form. ------ 166524/18658533. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((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)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 166525/18658569. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a)))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.y))) REDUCED to normal form. ------ 166526/18658596. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 166527/18658650. ------ 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))(^x1.(x1 x1)))) REDUCED to normal form. ------ 166528/18658677. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(a a))(^b.(^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. ------ 166529/18658704. ------ 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. ------ 166530/18658731. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^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. ------ 166531/18658794. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(b a))(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 166532/18658821. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 166533/18658848. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 166534/18658875. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.y) b)) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.x) b)) 5. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 166535/18658902. ------ 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))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 166536/18658929. ------ 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.(^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. ------ 166537/18659010. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 166538/18659154. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(c (b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(c (b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(c (b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(c (b a))) 5. ==[ beta ]==> ((a a)(c (b a))) REDUCED to normal form. ------ 166539/18659235. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 166540/18659343. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 166541/18659370. ------ 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 a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 166542/18659397. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 166543/18659451. ------ 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) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((a a)(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((a a)(^y.y)))) 9. ==[ beta ]==> (((a a)(a a))(a ((a a)(^y.y)))) 10. ==[ alpha ]==> (((a a)(a a))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 166544/18659541. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 166545/18659568. ------ 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. ------ 166546/18659595. ------ 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. ------ 166547/18659649. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 166548/18659712. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 166549/18659739. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(((^z.z)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)((^y.y)(a a)))) 9. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 166550/18659766. ------ 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) REDUCED to normal form. ------ 166551/18659793. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(b a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(b a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 166552/18659820. ------ 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 (^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. ------ 166553/18659847. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 166554/18659955. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 166555/18659982. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 166556/18660153. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 166557/18660261. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166558/18660315. ------ 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. ------ 166559/18660342. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1)(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. ------ 166560/18660396. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a a)(b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a a)(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(b a))) REDUCED to normal form. ------ 166561/18660432. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(^z.z))) 5. ==[ beta ]==> ((^y.(a a))((b a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((b a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166562/18660459. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 166563/18660486. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a 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. ------ 166564/18660513. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 166565/18660540. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 166566/18660594. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(^y1.b))) REDUCED to normal form. ------ 166567/18660621. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.(a a)))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 166568/18660657. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 166569/18660684. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(b a)) REDUCED to normal form. ------ 166570/18660765. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.a))) 7. ==[ beta ]==> ((a a)((^y.(a a))(^z.a))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 166571/18660792. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 166572/18660819. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.a)(^b.(^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. ------ 166573/18660846. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 166574/18660873. ------ 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 y))(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((^z.b)(^z.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.b)(^z.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 166575/18661017. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(a (^y1.y1)))) 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. ------ 166576/18661152. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 166577/18661296. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)(^y.a))) 3. ==[ beta ]==> ((b b)((a b)(^y.a))) 4. ==[ alpha ]==> ((b b)((a b)(^x.a))) REDUCED to normal form. ------ 166578/18661323. ------ 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. ------ 166579/18661377. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.a))) REDUCED to normal form. ------ 166580/18661404. ------ 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) a)(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.b))) REDUCED to normal form. ------ 166581/18661485. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 166582/18661512. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.b))((a a) b)) REDUCED to normal form. ------ 166583/18661926. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(a a)))) REDUCED to normal form. ------ 166584/18661980. ------ 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))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 166585/18662007. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 166586/18662061. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 166587/18662403. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(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. ------ 166588/18662448. ------ 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. ------ 166589/18662475. ------ 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) 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. ------ 166590/18662529. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.y1))) REDUCED to normal form. ------ 166591/18662619. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(^y.y))) REDUCED to normal form. ------ 166592/18662646. ------ 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.(^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. ------ 166593/18662727. ------ 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) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 166594/18662754. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 166595/18662781. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 166596/18662844. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 166597/18662871. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.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. ------ 166598/18662898. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> ((a b)((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 166599/18662925. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.a)(^b.(^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. ------ 166600/18662952. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 166601/18662979. ------ 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)(^x.x)))(^z.b)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 166602/18663141. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(b (^c.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))) 5. ==[ beta ]==> ((b a)(b (^y.a))) 6. ==[ alpha ]==> ((b a)(b (^x.a))) REDUCED to normal form. ------ 166603/18663168. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 166604/18663222. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 166605/18663501. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 166606/18663636. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((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. ------ 166607/18663726. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 166608/18663753. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 166609/18663807. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^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. ------ 166610/18663834. ------ 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. ------ 166611/18663861. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a c)) REDUCED to normal form. ------ 166612/18663906. ------ 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. ------ 166613/18663942. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 166614/18663969. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(b b)) REDUCED to normal form. ------ 166615/18664041. ------ 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. ------ 166616/18664059. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 166617/18664086. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(a a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a a)(a a))) REDUCED to normal form. ------ 166618/18664113. ------ 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)))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 166619/18664140. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 166620/18664167. ------ 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. ------ 166621/18664194. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(^y.y))) 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. ------ 166622/18664221. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.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. ------ 166623/18664248. ------ 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.(^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. ------ 166624/18664275. ------ 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 z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.(z z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(y y))) REDUCED to normal form. ------ 166625/18664356. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (^b.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. ------ 166626/18664383. ------ 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)))) 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. ------ 166627/18664437. ------ 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)(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. ------ 166628/18664455. ------ 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 (^y.y))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 166629/18664464. ------ 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. ------ 166630/18664860. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 166631/18664878. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 166632/18664886. ------ 1. ==[ start ]==> (^a.((a (a (^a.a))) a)) 2. ==[ alpha ]==> (^x.((x (x (^y.y))) x)) REDUCED to normal form. ------ 166633/18664887. ------ 1. ==[ start ]==> (a ((a (a (^a.a))) a)) 2. ==[ alpha ]==> (a ((a (a (^x.x))) a)) REDUCED to normal form. ------ 166634/18675459. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a)) b) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z)) b) 3. ==[ beta ]==> (((^z.z)(^y.y)) 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. ------ 166635/18675468. ------ 1. ==[ start ]==> (((a (a (^a.a))) a) a) 2. ==[ alpha ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 166636/18675474. ------ 1. ==[ start ]==> ((^a.a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a (a (^y.y))) a) 4. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 166637/18675483. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166638/18675501. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((((^y.(^z.z)) a) b)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> (((^y.y) b)(((^z.(^x1.x1)) a) b)) 6. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a) b)) 7. ==[ beta ]==> (b (((^y.(^z.z)) a) b)) 8. ==[ alpha ]==> (b (((^x.(^y.y)) a) b)) 9. ==[ beta ]==> (b ((^y.y) b)) 10. ==[ alpha ]==> (b ((^x.x) b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 166639/18675528. ------ 1. ==[ start ]==> ((^a.b)((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.b)((b (^y.y)) c)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 166640/18675891. ------ 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. ------ 166641/18675900. ------ 1. ==[ start ]==> (((a a)(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 166642/18676419. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(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. ------ 166643/18677142. ------ 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.(^x2.x2)) y1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^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. ------ 166644/18677520. ------ 1. ==[ start ]==> ((((a a) a) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 166645/18677751. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(((^z.b)((^x1.x1)(a a)))((^z.b)((^x1.x1)(a a))))) 4. ==[ alpha ]==> (^x.(((^y.b)((^z.z)(a a)))((^x1.b)((^y1.y1)(a a))))) 5. ==[ beta ]==> (^x.(b ((^x1.b)((^y1.y1)(a a))))) 6. ==[ alpha ]==> (^x.(b ((^y.b)((^z.z)(a a))))) 7. ==[ beta ]==> (^x.(b b)) REDUCED to normal form. ------ 166646/18677958. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.y)((((a a)(a a)) b)(((a a)(a a)) b))) 4. ==[ alpha ]==> ((^x.x)((((a a)(a a)) b)(((a a)(a a)) b))) 5. ==[ beta ]==> ((((a a)(a a)) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 166647/18678303. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(b (^z.z)))) 7. ==[ beta ]==> ((^y.(b (^z.z)))(^y.(b (^z.z)))) 8. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(b (^x1.x1)))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166648/18679389. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(a a)) a)) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a)) a)) 3. ==[ eta ]==> (b ((^y.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 166649/18679938. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 166650/18680040. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 166651/18680697. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^a.(^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. ------ 166652/18680829. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166653/18683223. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166654/18683541. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(a b))) 3. ==[ beta ]==> ((b c)(^y.(a b))) 4. ==[ alpha ]==> ((b c)(^x.(a b))) REDUCED to normal form. ------ 166655/18683568. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((^y.y)(x x)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^x.(x x))) REDUCED to normal form. ------ 166656/18683775. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^z.(^x1.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 166657/18684384. ------ 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.(^x2.x2)))) 3. ==[ eta ]==> ((^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. ------ 166658/18684666. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 166659/18684828. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^c.a))) 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. ------ 166660/18684963. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 166661/18685107. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 166662/18685203. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 166663/18685440. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.d)) REDUCED to normal form. ------ 166664/18685626. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)(^z.a))(((a a)(^z.a))(^y.y))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.a))(^z.z))) REDUCED to normal form. ------ 166665/18685638. ------ 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) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 166666/18686025. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(z z))) 3. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 166667/18686043. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 166668/18686052. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 166669/18686064. ------ 1. ==[ start ]==> ((a a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 166670/18686073. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.x))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 166671/18686091. ------ 1. ==[ start ]==> ((a (a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> ((a (a a))((^y.y) b)) 4. ==[ alpha ]==> ((a (a a))((^x.x) b)) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 166672/18686118. ------ 1. ==[ start ]==> ((a b)((b (^a.a)) c)) 2. ==[ alpha ]==> ((a b)((b (^x.x)) c)) REDUCED to normal form. ------ 166673/18686289. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 166674/18686397. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 166675/18686433. ------ 1. ==[ start ]==> (((a (^a.a)) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(c (b (^y.y)))) REDUCED to normal form. ------ 166676/18686460. ------ 1. ==[ start ]==> ((((^a.a) a) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)(b ((^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. ------ 166677/18686478. ------ 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. ------ 166678/18686487. ------ 1. ==[ start ]==> (((a a)(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(a (a (a (^y.y))))) REDUCED to normal form. ------ 166679/18686514. ------ 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)(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. ------ 166680/18686541. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 166681/18686649. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((b a)((a a) a))) 3. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 166682/18686730. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a b)((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. ------ 166683/18686757. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a) a)(b a))) REDUCED to normal form. ------ 166684/18686784. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 166685/18686811. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a (a a)) b)) REDUCED to normal form. ------ 166686/18686838. ------ 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) 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. ------ 166687/18686865. ------ 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. ------ 166688/18686928. ------ 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)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(^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. ------ 166689/18686955. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 166690/18686982. ------ 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. ------ 166691/18687009. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 166692/18687018. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 166693/18687045. ------ 1. ==[ start ]==> (((^a.(^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)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 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. ------ 166694/18687153. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 166695/18687234. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((^x1.x1) b)((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)((^x1.x1) b))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b ((^x1.x1) b))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.z) b))) 9. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b b)) REDUCED to normal form. ------ 166696/18687333. ------ 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. ------ 166697/18687360. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z)) b)) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z)) b)) 4. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y)) b)) 5. ==[ beta ]==> ((a a)((b (^y.y)) b)) 6. ==[ alpha ]==> ((a a)((b (^x.x)) b)) REDUCED to normal form. ------ 166698/18687531. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (a ((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 166699/18687612. ------ 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. ------ 166700/18687639. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166701/18687702. ------ 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. ------ 166702/18687729. ------ 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.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a ((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166703/18687756. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b (^y.y))(a a))) REDUCED to normal form. ------ 166704/18687945. ------ 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 ((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. ------ 166705/18688107. ------ 1. ==[ start ]==> ((((a a) a) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a a)(b (^x.x)))) REDUCED to normal form. ------ 166706/18688233. ------ 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. ------ 166707/18688314. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 166708/18688341. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 166709/18688359. ------ 1. ==[ start ]==> (((a a)(a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 166710/18688413. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 166711/18688440. ------ 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. ------ 166712/18688521. ------ 1. ==[ start ]==> (((a b)(a a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 166713/18688548. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a (a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 166714/18688557. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166715/18688584. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 166716/18688719. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 166717/18688800. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 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. ------ 166718/18688863. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b ((a a)(a a)))) REDUCED to normal form. ------ 166719/18688890. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (b (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(a (b (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))(a (b (^y.y)))) 7. ==[ beta ]==> ((a (b (^y.y)))(a (b (^y.y)))) 8. ==[ alpha ]==> ((a (b (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 166720/18688917. ------ 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. ------ 166721/18688944. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)(a (^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. ------ 166722/18688971. ------ 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. ------ 166723/18689160. ------ 1. ==[ start ]==> (((^a.b) c)((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b) c)((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 166724/18689394. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 166725/18689502. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 166726/18689556. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 166727/18689637. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.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 a)) REDUCED to normal form. ------ 166728/18689979. ------ 1. ==[ start ]==> ((a (b a))((^c.(a a)) a)) 2. ==[ alpha ]==> ((a (b a))((^x.(a a)) a)) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 166729/18690213. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 166730/18690258. ------ 1. ==[ start ]==> (((^a.a)(b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))(c (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(c (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 166731/18690285. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((^y.y)(b (^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(b (^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166732/18690339. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)(a a))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(a a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(a a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 166733/18690420. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a 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. ------ 166734/18690528. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 166735/18690546. ------ 1. ==[ start ]==> (((a a)(b a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 166736/18690600. ------ 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.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(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 (a a))((a (^y.y))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 166737/18690627. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((a a)(^x.x))) REDUCED to normal form. ------ 166738/18690654. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) b) a)) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) b) a)) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^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. ------ 166739/18690681. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 166740/18690708. ------ 1. ==[ start ]==> (((a b)(a (a a)))((b a) c)) REDUCED to normal form. ------ 166741/18691104. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)((^z.z)(^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. ------ 166742/18691131. ------ 1. ==[ start ]==> (((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) a))) REDUCED to normal form. ------ 166743/18691212. ------ 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. ------ 166744/18691239. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(b a))) 5. ==[ beta ]==> ((^y.b)((a (^z.z))(b a))) 6. ==[ alpha ]==> ((^x.b)((a (^y.y))(b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 166745/18691284. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> (b (a (^x1.x1))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 166746/18691392. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a 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. ------ 166747/18691419. ------ 1. ==[ start ]==> ((a (^b.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 166748/18691464. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a (^x.x))(b a))(^z.b)) 6. ==[ alpha ]==> (((a (^x.x))(b a))(^y.b)) REDUCED to normal form. ------ 166749/18691491. ------ 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. ------ 166750/18691572. ------ 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. ------ 166751/18691599. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 166752/18691626. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((b a) b)) 3. ==[ beta ]==> (((a a)(a (a a)))((b a) b)) REDUCED to normal form. ------ 166753/18691743. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 166754/18691770. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.b))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(^y2.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. ------ 166755/18692022. ------ 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)(^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. ------ 166756/18692049. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^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. ------ 166757/18692076. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 166758/18692103. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a ((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a ((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (a a))) REDUCED to normal form. ------ 166759/18692229. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a 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)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 166760/18692337. ------ 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.(^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. ------ 166761/18692409. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^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)))) REDUCED to normal form. ------ 166762/18692463. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((b a) a)) 3. ==[ beta ]==> ((a (b a))((b a) a)) REDUCED to normal form. ------ 166763/18692490. ------ 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)(^y.y)) b)) REDUCED to normal form. ------ 166764/18693012. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166765/18693120. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 166766/18693174. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(a b))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(a b))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(a b))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 166767/18693255. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 166768/18693363. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.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. ------ 166769/18693489. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x)) 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. ------ 166770/18693516. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a)) b)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a)) b)) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 166771/18693543. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b) c)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b) c)) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 166772/18693732. ------ 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. ------ 166773/18693759. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 166774/18693786. ------ 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. ------ 166775/18693813. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^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. ------ 166776/18693903. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166777/18693984. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 166778/18694092. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^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. ------ 166779/18694128. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b (a b))) 3. ==[ beta ]==> ((b c)(b (a b))) REDUCED to normal form. ------ 166780/18694155. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(a ((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a (a a))) REDUCED to normal form. ------ 166781/18694263. ------ 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. ------ 166782/18694290. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 166783/18694362. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> (b (a (^z.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 166784/18694470. ------ 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. ------ 166785/18694596. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a) b)) REDUCED to normal form. ------ 166786/18694758. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b) a)) 3. ==[ beta ]==> (((a b)(a a))((^y.b) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.b) a)) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 166787/18694785. ------ 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)) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 166788/18694812. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z)) c)) 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. ------ 166789/18694974. ------ 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)))) 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. ------ 166790/18695064. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 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. ------ 166791/18695145. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(^a.(^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. ------ 166792/18695253. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166793/18695370. ------ 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. ------ 166794/18695388. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)(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. ------ 166795/18695415. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.a))) 3. ==[ beta ]==> ((^y.y)(a (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(a (^y.a))) 5. ==[ beta ]==> (a (^y.a)) 6. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 166796/18695469. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(a (^z.z)))) 7. ==[ beta ]==> ((b b)((^y.(y y))(a (^z.z)))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(a (^y.y)))) 9. ==[ beta ]==> ((b b)((a (^y.y))(a (^y.y)))) 10. ==[ alpha ]==> ((b b)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 166797/18695550. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1)(^y1.y1)))) 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. ------ 166798/18695658. ------ 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))(^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. ------ 166799/18695667. ------ 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. ------ 166800/18695694. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 166801/18695721. ------ 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. ------ 166802/18695775. ------ 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.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. ------ 166803/18695793. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.(z z)))) REDUCED to normal form. ------ 166804/18695838. ------ 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. ------ 166805/18695865. ------ 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.(^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. ------ 166806/18695892. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(^b.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. ------ 166807/18695919. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 166808/18695946. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a)) a)) REDUCED to normal form. ------ 166809/18695973. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a) b)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 166810/18696081. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 166811/18696108. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^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. ------ 166812/18696189. ------ 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.(^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. ------ 166813/18696207. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b c)) 3. ==[ beta ]==> ((a (^y.y))(b c)) 4. ==[ alpha ]==> ((a (^x.x))(b c)) REDUCED to normal form. ------ 166814/18696216. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.a))) REDUCED to normal form. ------ 166815/18696225. ------ 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. ------ 166816/18696612. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166817/18696630. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (^x1.x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a (^x1.x1))) 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. ------ 166818/18696639. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a a)) REDUCED to normal form. ------ 166819/18700566. ------ 1. ==[ start ]==> ((^a.(b a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((y y)(y y)))) 3. ==[ eta ]==> (b (^y.((y y)(y y)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 166820/18703320. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(b y))) 3. ==[ eta ]==> ((^x.((x x)(x x))) b) 4. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 166821/18707229. ------ 1. ==[ start ]==> (((a (a (^a.a))) a) b) 2. ==[ alpha ]==> (((a (a (^x.x))) a) b) REDUCED to normal form. ------ 166822/18707253. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z))) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166823/18707670. ------ 1. ==[ start ]==> (((a a)(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 166824/18707838. ------ 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. ------ 166825/18709134. ------ 1. ==[ start ]==> ((^a.(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((^y.y)(a a))) b) 4. ==[ alpha ]==> (((a b)((^x.x)(a a))) b) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 166826/18709521. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (^y.(((a b)(^z.(a a)))((a b)(^z.(a a))))) 4. ==[ alpha ]==> (^x.(((a b)(^y.(a a)))((a b)(^z.(a a))))) REDUCED to normal form. ------ 166827/18709695. ------ 1. ==[ start ]==> (((^a.b) b)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(y (^z.z)))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 166828/18710403. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a (^z.z))((^x1.x1) b))((a (^z.z))((^x1.x1) b)))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.x))((^y.y) b))((a (^z.z))((^x1.x1) b)))(^y1.y1)) 5. ==[ beta ]==> ((((a (^x.x)) b)((a (^z.z))((^x1.x1) b)))(^y1.y1)) 6. ==[ alpha ]==> ((((a (^x.x)) b)((a (^y.y))((^z.z) b)))(^x1.x1)) 7. ==[ beta ]==> ((((a (^x.x)) b)((a (^y.y)) b))(^x1.x1)) 8. ==[ alpha ]==> ((((a (^x.x)) b)((a (^y.y)) b))(^z.z)) REDUCED to normal form. ------ 166829/18710802. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 166830/18711159. ------ 1. ==[ start ]==> ((^a.(b a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(a ((a a)(a a)))) 3. ==[ eta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 166831/18711162. ------ 1. ==[ start ]==> ((a (b a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 166832/18711504. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 166833/18711708. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 166834/18712476. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 166835/18712599. ------ 1. ==[ start ]==> ((^a.(^b.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166836/18713367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^a.(^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. ------ 166837/18713913. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(a (b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(a (b a))) 3. ==[ beta ]==> (((a (b a))(a (b a)))((a (b a))(a (b a)))) REDUCED to normal form. ------ 166838/18713916. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(b x))) 3. ==[ eta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 166839/18714420. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 166840/18714672. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 166841/18715338. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 166842/18715554. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 166843/18715941. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(y b))) 3. ==[ beta ]==> (((a b)(a a))(^y.(y b))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(x b))) REDUCED to normal form. ------ 166844/18716733. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a 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. ------ 166845/18716742. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 166846/18716877. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 166847/18717396. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b c)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b c)) 3. ==[ beta ]==> ((b c)((b c)(^y.y))) 4. ==[ alpha ]==> ((b c)((b c)(^x.x))) REDUCED to normal form. ------ 166848/18717795. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 166849/18717813. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 166850/18717822. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.z))) REDUCED to normal form. ------ 166851/18717836. ------ 1. ==[ start ]==> (^a.(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(x (x (^z.z))))) REDUCED to normal form. ------ 166852/18717837. ------ 1. ==[ start ]==> (a (^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (a (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 166853/18717852. ------ 1. ==[ start ]==> ((a (^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 166854/18717861. ------ 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))) 5. ==[ beta ]==> (a ((^z.z)(^y.y))) 6. ==[ alpha ]==> (a ((^x.x)(^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 166855/18717879. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^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. ------ 166856/18717906. ------ 1. ==[ start ]==> (((^a.a)(a a))((b (^a.a)) 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)) REDUCED to normal form. ------ 166857/18717942. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)((^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. ------ 166858/18717969. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 166859/18717996. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 166860/18718077. ------ 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 (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 166861/18718131. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 166862/18718266. ------ 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))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 166863/18718284. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 166864/18718356. ------ 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) 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. ------ 166865/18718383. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 166866/18718410. ------ 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. ------ 166867/18718437. ------ 1. ==[ start ]==> ((a (a (a a)))((b a)((a a) a))) REDUCED to normal form. ------ 166868/18718680. ------ 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. ------ 166869/18718797. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166870/18718824. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 166871/18718878. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 166872/18718887. ------ 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. ------ 166873/18718914. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (a ((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 166874/18718932. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.(^y1.y1)))) 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. ------ 166875/18718941. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 166876/18718995. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 166877/18719013. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (a a))(^b.b))) 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. ------ 166878/18719022. ------ 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. ------ 166879/18719049. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.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. ------ 166880/18719346. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 166881/18719427. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^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. ------ 166882/18719454. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 166883/18719571. ------ 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. ------ 166884/18719598. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.z) a))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 166885/18719625. ------ 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. ------ 166886/18719652. ------ 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. ------ 166887/18719679. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 166888/18719706. ------ 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))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)(a b))) REDUCED to normal form. ------ 166889/18719733. ------ 1. ==[ start ]==> ((a (a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((a (a b))((a b)(a a))) REDUCED to normal form. ------ 166890/18719931. ------ 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. ------ 166891/18719958. ------ 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.(^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. ------ 166892/18719994. ------ 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) 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. ------ 166893/18720012. ------ 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. ------ 166894/18720021. ------ 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. ------ 166895/18720093. ------ 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 (((^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. ------ 166896/18720102. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 166897/18720120. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 166898/18720291. ------ 1. ==[ start ]==> (((^a.b) b)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 166899/18720336. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a)) b)) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a)) b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166900/18720363. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 166901/18720507. ------ 1. ==[ start ]==> (((a b) b)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 166902/18720588. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 166903/18720642. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a))(^c.(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. ------ 166904/18720714. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 166905/18720786. ------ 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)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(a (a a)))) REDUCED to normal form. ------ 166906/18720813. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 166907/18720840. ------ 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. ------ 166908/18720867. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 166909/18720894. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a 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. ------ 166910/18720921. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y)(^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)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a) a)((^x.x)((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. ------ 166911/18720948. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (a a))(b a))) REDUCED to normal form. ------ 166912/18720975. ------ 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))))) 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. ------ 166913/18721002. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 166914/18721173. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 166915/18721182. ------ 1. ==[ start ]==> (((a b) c)((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 166916/18721209. ------ 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. ------ 166917/18721236. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 166918/18721254. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 166919/18721290. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 166920/18721317. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(z z))(b a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(b a))) 5. ==[ beta ]==> ((a (^x.b))((b a)(b a))) REDUCED to normal form. ------ 166921/18721335. ------ 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)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 166922/18721371. ------ 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.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166923/18721398. ------ 1. ==[ start ]==> ((((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)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 166924/18721416. ------ 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 (((a a)(a a)) a)) REDUCED to normal form. ------ 166925/18721425. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 166926/18721452. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b)(^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)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 166927/18721479. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 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. ------ 166928/18721731. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b ((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b b)) REDUCED to normal form. ------ 166929/18721758. ------ 1. ==[ start ]==> ((a (b a))(a ((a a)(a a)))) REDUCED to normal form. ------ 166930/18722100. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 166931/18722118. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b)(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b)(^y.y))) 5. ==[ beta ]==> (((a b)(a b))(b (^y.y))) 6. ==[ alpha ]==> (((a b)(a b))(b (^x.x))) REDUCED to normal form. ------ 166932/18722127. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 166933/18722199. ------ 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 z)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 166934/18722208. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 166935/18722235. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 166936/18722262. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^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. ------ 166937/18722307. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 166938/18722586. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 166939/18722766. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> (b ((^x1.x1) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 166940/18723018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(c (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(c (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(c (^z.a))) 5. ==[ beta ]==> ((^y.b)(c (^z.a))) 6. ==[ alpha ]==> ((^x.b)(c (^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 166941/18723072. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 166942/18723099. ------ 1. ==[ start ]==> ((((^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 a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 166943/18723171. ------ 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)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166944/18723180. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 166945/18723198. ------ 1. ==[ start ]==> ((a (^b.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 166946/18723477. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 166947/18723684. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 166948/18723963. ------ 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.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 166949/18724008. ------ 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.(^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. ------ 166950/18724017. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 166951/18724044. ------ 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) 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. ------ 166952/18724071. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 166953/18724125. ------ 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.(^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. ------ 166954/18724152. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(z z))(a b))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(a b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(a b))) 5. ==[ beta ]==> ((b (^x.x))((a b)(a b))) REDUCED to normal form. ------ 166955/18724485. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(b ((a a)(^y.y)))) 3. ==[ beta ]==> ((b (a a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b (a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 166956/18724512. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(a (b a))) REDUCED to normal form. ------ 166957/18724548. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 166958/18724791. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((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. ------ 166959/18724827. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 166960/18724854. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 166961/18724872. ------ 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. ------ 166962/18724899. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^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. ------ 166963/18724908. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^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. ------ 166964/18724935. ------ 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 y1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 166965/18724953. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> (((b a)(b a))(a (^y.b))) 6. ==[ alpha ]==> (((b a)(b a))(a (^x.b))) REDUCED to normal form. ------ 166966/18725016. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 166967/18725034. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a)(^y.y)) a)) 3. ==[ beta ]==> (b (((a a)(^y.y)) a)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 166968/18725043. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 166969/18725097. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 166970/18725151. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(^a.a))(^b.(^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. ------ 166971/18725178. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.a)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.a))) 7. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 166972/18725205. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 166973/18725241. ------ 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)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 166974/18725268. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a ((a a)(^y.y)))) REDUCED to normal form. ------ 166975/18725295. ------ 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)(a a))(a a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 166976/18725322. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)(a (^x.x)))) REDUCED to normal form. ------ 166977/18725349. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((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. ------ 166978/18725376. ------ 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)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^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))((^y.y)(a (a a)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(a (a a)))) 7. ==[ beta ]==> ((((a a) a)(a a))(a (a a))) REDUCED to normal form. ------ 166979/18725403. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (a a))((^x.x)(^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. ------ 166980/18725430. ------ 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. ------ 166981/18725457. ------ 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 (^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(a b))) REDUCED to normal form. ------ 166982/18725682. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 166983/18725763. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 166984/18725907. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 166985/18725934. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(^b.(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. ------ 166986/18725979. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.b) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.b) b)) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 166987/18726150. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 166988/18726177. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(a a))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 166989/18726249. ------ 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. ------ 166990/18726258. ------ 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. ------ 166991/18726285. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 166992/18726312. ------ 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 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. ------ 166993/18726483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)(c ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b a)(c ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((b a)(c (^y.y))) 8. ==[ alpha ]==> ((b a)(c (^x.x))) REDUCED to normal form. ------ 166994/18726510. ------ 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. ------ 166995/18726537. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a (a b))) 3. ==[ beta ]==> (((a b)(a a))(a (a b))) REDUCED to normal form. ------ 166996/18726564. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)(a a))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)(a a))) REDUCED to normal form. ------ 166997/18726591. ------ 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 (^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)))) 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. ------ 166998/18726645. ------ 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. ------ 166999/18726672. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((a (^y.y))((^z.z)(^x1.x1)))) 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. ------ 167000/18726699. ------ 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))) REDUCED to normal form. ------ 167001/18726843. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 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. ------ 167002/18726924. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 167003/18727248. ------ 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. ------ 167004/18727257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 167005/18727284. ------ 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)((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167006/18727329. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((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. ------ 167007/18727338. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 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. ------ 167008/18727365. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 167009/18727392. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 167010/18727446. ------ 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))(^x2.(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. ------ 167011/18727473. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 167012/18727590. ------ 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. ------ 167013/18727671. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c c)) 3. ==[ beta ]==> (((a (a a)) b)(c c)) REDUCED to normal form. ------ 167014/18727806. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(b a)) REDUCED to normal form. ------ 167015/18727860. ------ 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. ------ 167016/18727887. ------ 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. ------ 167017/18727914. ------ 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)((^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. ------ 167018/18727986. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^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. ------ 167019/18727995. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b c)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b c)) REDUCED to normal form. ------ 167020/18728004. ------ 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 ]==> ((^y.(y (^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.a))) 5. ==[ beta ]==> (((a a)(^z.a))(^y.y)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 167021/18728391. ------ 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))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 167022/18728409. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^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. ------ 167023/18728418. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.y))) REDUCED to normal form. ------ 167024/18728435. ------ 1. ==[ start ]==> (^a.((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.((^y.y)(x (x (^z.z))))) 3. ==[ beta ]==> (^x.(x (x (^z.z)))) 4. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 167025/18728436. ------ 1. ==[ start ]==> (a ((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (a ((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> (a (a (a (^y.y)))) 4. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 167026/18728439. ------ 1. ==[ start ]==> ((^a.a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (^y.(a (a (^z.z)))) 4. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 167027/18732354. ------ 1. ==[ start ]==> ((^a.(b a))(^b.(^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. ------ 167028/18739035. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a)))) a) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y)))) a) 3. ==[ beta ]==> ((a (a (^y.y))) a) 4. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 167029/18739041. ------ 1. ==[ start ]==> ((^a.a)((^a.a)(a (a (^a.a))))) 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. ------ 167030/18739044. ------ 1. ==[ start ]==> ((a a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 167031/18739068. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((^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))) 5. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 (^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 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 ]==> ((^z.z)(^y.y)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167032/18739176. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^x1.(^y1.y1)))(^y.y)) 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. ------ 167033/18739365. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.y1))) 3. ==[ eta ]==> ((^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. ------ 167034/18739485. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 167035/18739536. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 167036/18739860. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167037/18739908. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^a.(^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. ------ 167038/18740313. ------ 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. ------ 167039/18740418. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((^y.y)(^z.(z z)))((^y.y)(^z.(z z))))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1))))((^y1.y1)(^z1.(z1 z1)))) 5. ==[ beta ]==> (((^y.(y y))((^z.z)(^x1.(x1 x1))))((^y1.y1)(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.(z z))))((^x1.x1)(^y1.(y1 y1)))) 7. ==[ beta ]==> ((((^y.y)(^z.(z z)))((^y.y)(^z.(z z))))((^x1.x1)(^y1.(y1 y1)))) 8. ==[ alpha ]==> ((((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1))))((^y1.y1)(^z1.(z1 z1)))) IRREDUCIBLE: cycle. ------ 167040/18740751. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z))(a a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 167041/18741105. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 167042/18741492. ------ 1. ==[ start ]==> (((^a.b) b)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 167043/18741501. ------ 1. ==[ start ]==> (((a b)(a a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 167044/18742239. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 167045/18742956. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(^z.(a a)))) 3. ==[ eta ]==> (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. ------ 167046/18742959. ------ 1. ==[ start ]==> ((a (b a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 167047/18743634. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(^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. ------ 167048/18743793. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^x1.b)(^y1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.x1))) 5. ==[ beta ]==> (b (^z.(^x1.x1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 167049/18743967. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^a.((^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. ------ 167050/18744264. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 167051/18744579. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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))))) REDUCED to normal form. ------ 167052/18744711. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 167053/18744885. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^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. ------ 167054/18745443. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(y a))) 3. ==[ beta ]==> ((a (b a))(^y.(y a))) 4. ==[ alpha ]==> ((a (b a))(^x.(x a))) REDUCED to normal form. ------ 167055/18746217. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 167056/18746469. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^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. ------ 167057/18746790. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 167058/18747342. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(a b))) 3. ==[ beta ]==> (b (^z.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 167059/18747738. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.y))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.y))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.x))) REDUCED to normal form. ------ 167060/18748395. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167061/18748539. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 167062/18748770. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 167063/18748818. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 167064/18748926. ------ 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. ------ 167065/18749193. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^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. ------ 167066/18749592. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.a)) 3. ==[ beta ]==> (((^y.y) b)(^z.a)) 4. ==[ alpha ]==> (((^x.x) b)(^y.a)) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 167067/18749610. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(x1 x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 167068/18749619. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.a)) REDUCED to normal form. ------ 167069/18749637. ------ 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. ------ 167070/18749649. ------ 1. ==[ start ]==> ((a a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)(a (a (^y.y)))) 4. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 167071/18749667. ------ 1. ==[ start ]==> (((^a.a) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y))) a)) 3. ==[ beta ]==> (a ((a (a (^y.y))) a)) 4. ==[ alpha ]==> (a ((a (a (^x.x))) a)) REDUCED to normal form. ------ 167072/18749676. ------ 1. ==[ start ]==> ((a (a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a (a a))((^z.z)(^y.y))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 167073/18749694. ------ 1. ==[ start ]==> (((a a) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a a) a)((^y.y) b)) 4. ==[ alpha ]==> (((a a) a)((^x.x) b)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 167074/18749721. ------ 1. ==[ start ]==> (((a a)(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 167075/18749784. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 167076/18749973. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 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. ------ 167077/18750063. ------ 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. ------ 167078/18750090. ------ 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)(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. ------ 167079/18750099. ------ 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 (^x.x))(^y.(^z.z)))(a (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 167080/18750144. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 167081/18750252. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.(y y))((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.(x x))((b a)((a a) a))) 5. ==[ beta ]==> (((b a)((a a) a))((b a)((a a) a))) REDUCED to normal form. ------ 167082/18750279. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((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. ------ 167083/18750333. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)((a a)(^z.z)))) 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. ------ 167084/18750360. ------ 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. ------ 167085/18750387. ------ 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)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 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. ------ 167086/18750441. ------ 1. ==[ start ]==> (((^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)))) 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. ------ 167087/18750468. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 167088/18750513. ------ 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)) a)(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 167089/18750558. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 167090/18750693. ------ 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. ------ 167091/18750720. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (a (((^y.y)(a a))(^z.(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. ------ 167092/18750747. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 167093/18750801. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.a))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 167094/18750828. ------ 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. ------ 167095/18750891. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 167096/18750918. ------ 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. ------ 167097/18751026. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(y y))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(x x))) REDUCED to normal form. ------ 167098/18751359. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y))(a a))) REDUCED to normal form. ------ 167099/18751548. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.b)((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.b)((a b)((^y.y)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 167100/18751629. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(a (^z.(^x1.x1))))) IRREDUCIBLE: cycle. ------ 167101/18751710. ------ 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 a)(b (^z.z)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 167102/18751746. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 167103/18751800. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 167104/18751827. ------ 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. ------ 167105/18751854. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((b a)(^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 167106/18751908. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.b))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 167107/18751944. ------ 1. ==[ start ]==> (((a a)(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 167108/18751998. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 167109/18752025. ------ 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. ------ 167110/18752052. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)((^z.z) b))) 7. ==[ beta ]==> (a ((^y.a)((^z.z) b))) 8. ==[ alpha ]==> (a ((^x.a)((^y.y) b))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167111/18752079. ------ 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. ------ 167112/18752106. ------ 1. ==[ start ]==> (((a b)(a a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)(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. ------ 167113/18752520. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 167114/18752529. ------ 1. ==[ start ]==> (((a b)(^a.(^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 a)) REDUCED to normal form. ------ 167115/18752556. ------ 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. ------ 167116/18752844. ------ 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)))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 167117/18752988. ------ 1. ==[ start ]==> (((a b) c)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 167118/18753015. ------ 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. ------ 167119/18753042. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(^y.b))) REDUCED to normal form. ------ 167120/18753096. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 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. ------ 167121/18753177. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.a))(^b.b))) 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. ------ 167122/18753231. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 167123/18753258. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) b) b)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b) b)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 167124/18753375. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 167125/18753402. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.b)(^y.b))) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 167126/18753456. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(^a.a))(^c.(^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. ------ 167127/18753510. ------ 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)(^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. ------ 167128/18753537. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.a))(^b.b))) 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. ------ 167129/18753564. ------ 1. ==[ start ]==> ((a (b a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(a a)))) 3. ==[ beta ]==> ((a (b a))(^y.(a a))) 4. ==[ alpha ]==> ((a (b a))(^x.(a a))) REDUCED to normal form. ------ 167130/18753654. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a)((^z.z) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a)((^z.z) a))) 5. ==[ beta ]==> (b ((b a)((^z.z) a))) 6. ==[ alpha ]==> (b ((b a)((^x.x) a))) 7. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 167131/18753735. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 167132/18753843. ------ 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))) 5. ==[ beta ]==> ((b a)(a (b a))) REDUCED to normal form. ------ 167133/18753870. ------ 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.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(a (^y1.(^z1.z1))))) 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. ------ 167134/18753933. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.b))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(b (^y.y))) REDUCED to normal form. ------ 167135/18753987. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 167136/18754014. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 167137/18754041. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(a a))(^b.(^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. ------ 167138/18754068. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.a))) REDUCED to normal form. ------ 167139/18754131. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 167140/18754158. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 167141/18754185. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.a)(b a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.a)(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(b a))) 5. ==[ beta ]==> ((a (a a))((^y.a)(b a))) 6. ==[ alpha ]==> ((a (a a))((^x.a)(b a))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 167142/18754212. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(a (^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. ------ 167143/18754239. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^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. ------ 167144/18754266. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 167145/18754293. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 167146/18754401. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 167147/18754572. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((^x1.x1) b))) 3. ==[ beta ]==> (b (a ((^x1.x1) b))) 4. ==[ alpha ]==> (b (a ((^x.x) b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 167148/18754680. ------ 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))(((^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. ------ 167149/18754707. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((^z.z)(^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. ------ 167150/18754734. ------ 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))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 167151/18754788. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(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)(a a))((a (a a))((^y.y)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((a (a a))((^x.x)(a a)))) 9. ==[ beta ]==> (((a a)(a a))((a (a a))(a a))) REDUCED to normal form. ------ 167152/18754869. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a a)(a (^a.(^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. ------ 167153/18754905. ------ 1. ==[ start ]==> ((((^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.y1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 167154/18754932. ------ 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. ------ 167155/18754986. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 167156/18755022. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 167157/18755049. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 167158/18755076. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 167159/18755103. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (((a (a a))(a a))((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (((a (a a))(a a))((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (((a (a a))(a a))((a a)(a a))) REDUCED to normal form. ------ 167160/18755130. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.a)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 167161/18755157. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(b 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. ------ 167162/18755184. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 167163/18755211. ------ 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.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))(^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. ------ 167164/18755292. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 167165/18755319. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 167166/18755490. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 167167/18755598. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((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. ------ 167168/18755652. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)(((^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 ((^y.y)((a a) a))) 8. ==[ alpha ]==> (b ((^x.x)((a a) a))) 9. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 167169/18755679. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((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. ------ 167170/18755733. ------ 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 (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 167171/18755796. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a)(^y.y))) REDUCED to normal form. ------ 167172/18755823. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 167173/18755850. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 167174/18755877. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(^z.(z z)))) REDUCED to normal form. ------ 167175/18755958. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (a a))(^z.b))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(^z.b))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.b))) REDUCED to normal form. ------ 167176/18755994. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 167177/18756021. ------ 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.(^y1.y1))((a a)(^z1.z1)))) 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. ------ 167178/18756048. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.y)(b a))) 3. ==[ beta ]==> ((a (b a))((^y.y)(b a))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(b a))) 5. ==[ beta ]==> ((a (b a))(b a)) REDUCED to normal form. ------ 167179/18756129. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(a a))(^b.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. ------ 167180/18756156. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 167181/18756210. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))(^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. ------ 167182/18756264. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 167183/18756291. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 167184/18756354. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((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. ------ 167185/18756489. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))((a a) a))) 3. ==[ beta ]==> (b ((a (a a))((a a) a))) REDUCED to normal form. ------ 167186/18756633. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 167187/18756660. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a b)(^x.a))) REDUCED to normal form. ------ 167188/18756714. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(^a.a))(^b.(^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. ------ 167189/18756822. ------ 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. ------ 167190/18756849. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 167191/18756903. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b) c)) REDUCED to normal form. ------ 167192/18757047. ------ 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.(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. ------ 167193/18757074. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.z)(^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. ------ 167194/18757344. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(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 a)) REDUCED to normal form. ------ 167195/18757371. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 167196/18757398. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 167197/18757785. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)(a a))) 3. ==[ beta ]==> ((b (^y.y))((a b)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(a a))) REDUCED to normal form. ------ 167198/18757812. ------ 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. ------ 167199/18757866. ------ 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. ------ 167200/18757947. ------ 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 b))) REDUCED to normal form. ------ 167201/18757983. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.b))((a b)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))((a b)(^y.y))) REDUCED to normal form. ------ 167202/18758064. ------ 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. ------ 167203/18758091. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 167204/18758181. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 167205/18758235. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 167206/18758262. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 167207/18758289. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 167208/18758343. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(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))) 5. ==[ beta ]==> (((a b)(a a))(^y.b)) 6. ==[ alpha ]==> (((a b)(a a))(^x.b)) REDUCED to normal form. ------ 167209/18758478. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c (^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(c (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(c (^x.(^y.y)))) REDUCED to normal form. ------ 167210/18758505. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 167211/18758838. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 167212/18758973. ------ 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. ------ 167213/18759000. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 167214/18759063. ------ 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. ------ 167215/18759090. ------ 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))))(((^z1.z1) a)(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167216/18759144. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 167217/18759171. ------ 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)(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 167218/18759198. ------ 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. ------ 167219/18759306. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z)) 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. ------ 167220/18759360. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 167221/18759378. ------ 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 (^y.y))))((a (^z.z)) a)) REDUCED to normal form. ------ 167222/18759396. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 167223/18759423. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 167224/18759450. ------ 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 y))(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(a a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 167225/18759477. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 167226/18759504. ------ 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))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 167227/18759531. ------ 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. ------ 167228/18759558. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(^z.z))) 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. ------ 167229/18759585. ------ 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.(^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. ------ 167230/18759612. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^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. ------ 167231/18759693. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (^a.(^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. ------ 167232/18759720. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (^b.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. ------ 167233/18759774. ------ 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))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 167234/18759792. ------ 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 (^y.y))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 167235/18759801. ------ 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)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 167236/18759810. ------ 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 ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 167237/18760197. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 167238/18760215. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 167239/18760224. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 167240/18760242. ------ 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. ------ 167241/18760250. ------ 1. ==[ start ]==> (^a.((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.((x x)(^y.(y (^z.z))))) REDUCED to normal form. ------ 167242/18760251. ------ 1. ==[ start ]==> (a ((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (a ((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 167243/18760263. ------ 1. ==[ start ]==> ((^a.(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167244/18770850. ------ 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. ------ 167245/18770859. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a)))) a) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 167246/18770865. ------ 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. ------ 167247/18770874. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167248/18770877. ------ 1. ==[ start ]==> ((a (^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 167249/18770892. ------ 1. ==[ start ]==> ((^a.(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y))) a)) 3. ==[ beta ]==> (((a (a (^y.y))) a)((a (a (^y.y))) a)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a (^y.y))) a)) REDUCED to normal form. ------ 167250/18770919. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 167251/18771117. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(a a))(^c.(^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 a)) REDUCED to normal form. ------ 167252/18771309. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 167253/18771318. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) REDUCED to normal form. ------ 167254/18771684. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167255/18771810. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(a a))(^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. ------ 167256/18772560. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 167257/18772938. ------ 1. ==[ start ]==> (((a b) a)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 167258/18773142. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(a b))) 3. ==[ beta ]==> (^y.(((^z.(a a))(a b))((^z.(a a))(a b)))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(a b))((^z.(a a))(a b)))) 5. ==[ beta ]==> (^x.((a a)((^z.(a a))(a b)))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(a b)))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 167259/18773325. ------ 1. ==[ start ]==> (((a b)(a a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 167260/18773349. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b (^z.z)) a)) 3. ==[ beta ]==> ((^y.y)(((b (^z.z)) a)((b (^z.z)) a))) 4. ==[ alpha ]==> ((^x.x)(((b (^y.y)) a)((b (^z.z)) a))) 5. ==[ beta ]==> (((b (^y.y)) a)((b (^z.z)) a)) 6. ==[ alpha ]==> (((b (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 167261/18773721. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 167262/18774441. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^b.((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. ------ 167263/18775125. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(^y.b)) REDUCED to normal form. ------ 167264/18775143. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 167265/18775791. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (b (^x1.(^y1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 167266/18776097. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 167267/18776220. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167268/18776403. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 167269/18776709. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^b.(^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. ------ 167270/18776988. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(b a))) 5. ==[ beta ]==> ((^y.(a a))(^z.(b a))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167271/18777267. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.a))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.a))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.a))) REDUCED to normal form. ------ 167272/18778059. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 167273/18778614. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a)(^b.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. ------ 167274/18779175. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(a b))) REDUCED to normal form. ------ 167275/18779775. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a)(^x1.x1))) 3. ==[ eta ]==> ((^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. ------ 167276/18780363. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.e)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.e)) REDUCED to normal form. ------ 167277/18780525. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 167278/18780750. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 167279/18781017. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(^a.(^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. ------ 167280/18781416. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.b)) 3. ==[ beta ]==> (((^y.y) b)(^z.b)) 4. ==[ alpha ]==> (((^x.x) b)(^y.b)) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 167281/18781434. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 167282/18781443. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(y y))) REDUCED to normal form. ------ 167283/18781461. ------ 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))) REDUCED to normal form. ------ 167284/18781470. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 167285/18781482. ------ 1. ==[ start ]==> ((a a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 167286/18781491. ------ 1. ==[ start ]==> ((a (^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 167287/18781509. ------ 1. ==[ start ]==> ((a (a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (a a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 167288/18781518. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 167289/18781536. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> ((a b)((^y.y) b)) 4. ==[ alpha ]==> ((a b)((^x.x) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 167290/18781626. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 167291/18781734. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 167292/18781815. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 167293/18781905. ------ 1. ==[ start ]==> (((a a)(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.a))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 167294/18781923. ------ 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 ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 167295/18781932. ------ 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))))) REDUCED to normal form. ------ 167296/18781959. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^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)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 167297/18782067. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^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. ------ 167298/18782148. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(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. ------ 167299/18782175. ------ 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. ------ 167300/18782202. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(b a))) REDUCED to normal form. ------ 167301/18782229. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(a (^x1.(^y1.y1))))) 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. ------ 167302/18782256. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 167303/18782283. ------ 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. ------ 167304/18782301. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 167305/18782373. ------ 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)(^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. ------ 167306/18782400. ------ 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. ------ 167307/18782427. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 167308/18782436. ------ 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) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167309/18782463. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(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. ------ 167310/18782571. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167311/18782598. ------ 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. ------ 167312/18782652. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 167313/18782778. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((a ((^x.x) 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) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 167314/18782805. ------ 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. ------ 167315/18782895. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 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. ------ 167316/18782949. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 167317/18783057. ------ 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))(^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. ------ 167318/18783111. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.a)(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 167319/18783120. ------ 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. ------ 167320/18783147. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b (b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (b (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167321/18783174. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(a ((^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. ------ 167322/18783363. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 167323/18783525. ------ 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)))) REDUCED to normal form. ------ 167324/18783552. ------ 1. ==[ start ]==> (((a b) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((a a)(b (^x.x)))) REDUCED to normal form. ------ 167325/18783651. ------ 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. ------ 167326/18783732. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 167327/18783759. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(a b))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 167328/18783777. ------ 1. ==[ start ]==> (((a a)(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a b)(^x.(a a)))) REDUCED to normal form. ------ 167329/18783858. ------ 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.(^y.(^z.z))))) REDUCED to normal form. ------ 167330/18783885. ------ 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) 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))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 167331/18783966. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b (^y.y)) a)) 3. ==[ beta ]==> ((a (a a))((b (^y.y)) a)) 4. ==[ alpha ]==> ((a (a a))((b (^x.x)) a)) REDUCED to normal form. ------ 167332/18784002. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 167333/18784056. ------ 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)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167334/18784137. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 167335/18784272. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 11. ==[ beta ]==> ((^y.a)(^z.z)) 12. ==[ alpha ]==> ((^x.a)(^y.y)) 13. ==[ beta ]==> a REDUCED to normal form. ------ 167336/18784281. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c ((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(c b)) REDUCED to normal form. ------ 167337/18784308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b ((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))(b ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))(b ((a a)(a a)))) 7. ==[ beta ]==> ((b ((a a)(a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 167338/18784335. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (b (^y.y)))) REDUCED to normal form. ------ 167339/18784362. ------ 1. ==[ start ]==> (((a b)(^a.(^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. ------ 167340/18784389. ------ 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. ------ 167341/18784578. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 167342/18784677. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(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. ------ 167343/18784893. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a b))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 167344/18784974. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(y y))(b a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))(b a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((b a)(b a))) REDUCED to normal form. ------ 167345/18785055. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 167346/18785631. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 167347/18785739. ------ 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. ------ 167348/18785757. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(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. ------ 167349/18785964. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(^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)))) 5. ==[ beta ]==> (((a a)(b a))(^y.(a a))) 6. ==[ alpha ]==> (((a a)(b a))(^x.(a a))) REDUCED to normal form. ------ 167350/18786045. ------ 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.(^z.(^x1.x1))))) REDUCED to normal form. ------ 167351/18786072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a)(^b.b))) 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. ------ 167352/18786099. ------ 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)(^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. ------ 167353/18786126. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 167354/18786153. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((b a) c)) 3. ==[ beta ]==> (((a a)((^y.y) a))((b a) c)) 4. ==[ alpha ]==> (((a a)((^x.x) a))((b a) c)) 5. ==[ beta ]==> (((a a) a)((b a) c)) REDUCED to normal form. ------ 167355/18786243. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167356/18786324. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^z.(z z))(^x1.(^y1.y1)))) 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. ------ 167357/18786405. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 167358/18786522. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a (a a)))) REDUCED to normal form. ------ 167359/18786549. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a b)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a b)(^x1.x1))) REDUCED to normal form. ------ 167360/18786630. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a (a a))(a a))) REDUCED to normal form. ------ 167361/18786657. ------ 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) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y) a)((a a)(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 167362/18786702. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 167363/18786711. ------ 1. ==[ start ]==> (((a b)(^b.(^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. ------ 167364/18786837. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 167365/18786855. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 167366/18786882. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 167367/18786909. ------ 1. ==[ start ]==> ((((^a.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))(^y1.b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.b))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.b)) 8. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 167368/18786936. ------ 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.(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. ------ 167369/18786963. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^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. ------ 167370/18787017. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 167371/18787044. ------ 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)) REDUCED to normal form. ------ 167372/18787071. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((b a) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a) b)) REDUCED to normal form. ------ 167373/18787161. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.b)(^b.(^a.a)))) 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. ------ 167374/18787323. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 167375/18787440. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a b)(a (a a)))) REDUCED to normal form. ------ 167376/18787467. ------ 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. ------ 167377/18787494. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^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))((^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. ------ 167378/18787521. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (a a))(a b))) REDUCED to normal form. ------ 167379/18787602. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(b a))) 5. ==[ beta ]==> ((^y.(a a))((a a)(b a))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167380/18787827. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) b)(a (^y.(a a)))) 6. ==[ alpha ]==> (((a a) b)(a (^x.(a a)))) REDUCED to normal form. ------ 167381/18787908. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((b a) a)) REDUCED to normal form. ------ 167382/18787935. ------ 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)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z)) b)) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z)) b)) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y)) b)) 7. ==[ beta ]==> ((a a)(((a a)(^y.y)) b)) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 167383/18787962. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(a b))((a a) c)) REDUCED to normal form. ------ 167384/18788511. ------ 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) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 167385/18788538. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 167386/18788592. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> (((b a)(b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 167387/18788673. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 167388/18788961. ------ 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 a)) REDUCED to normal form. ------ 167389/18788988. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b) c)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b) c)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b) c)) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b) c)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b) c)) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 167390/18789177. ------ 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. ------ 167391/18789204. ------ 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. ------ 167392/18789231. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 167393/18789321. ------ 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 a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167394/18789402. ------ 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))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 167395/18789510. ------ 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.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167396/18789546. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c ((a a) a))) 3. ==[ beta ]==> ((b c)(c ((a a) a))) REDUCED to normal form. ------ 167397/18789573. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (a b))) REDUCED to normal form. ------ 167398/18789681. ------ 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) 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. ------ 167399/18789708. ------ 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 (a a)))) REDUCED to normal form. ------ 167400/18789780. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b (^z.b))) 3. ==[ beta ]==> (b (b (^z.b))) 4. ==[ alpha ]==> (b (b (^x.b))) REDUCED to normal form. ------ 167401/18789789. ------ 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. ------ 167402/18789888. ------ 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) 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. ------ 167403/18790014. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b) a)) REDUCED to normal form. ------ 167404/18790041. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a) a) b)) REDUCED to normal form. ------ 167405/18790068. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z)) c)) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y)) c)) 7. ==[ beta ]==> ((a b)((^y.y) c)) 8. ==[ alpha ]==> ((a b)((^x.x) c)) 9. ==[ beta ]==> ((a b) c) REDUCED to normal form. ------ 167406/18790203. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 167407/18790392. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 167408/18790482. ------ 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. ------ 167409/18790563. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 167410/18790671. ------ 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.(^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. ------ 167411/18790788. ------ 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 (a ((^y.y) a))) 8. ==[ alpha ]==> (a (a ((^x.x) a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 167412/18790833. ------ 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)(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 167413/18790887. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(a a))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(a a))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 167414/18790968. ------ 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. ------ 167415/18791076. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.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. ------ 167416/18791085. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c ((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c a)) REDUCED to normal form. ------ 167417/18791112. ------ 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. ------ 167418/18791139. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.y))) REDUCED to normal form. ------ 167419/18791193. ------ 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)(^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. ------ 167420/18791283. ------ 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. ------ 167421/18791310. ------ 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.(^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. ------ 167422/18791337. ------ 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 (^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 167423/18791364. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 167424/18791391. ------ 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. ------ 167425/18791418. ------ 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) 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)) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a) b)) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a) b)) 7. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 167426/18791445. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y)) c)) REDUCED to normal form. ------ 167427/18791499. ------ 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)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 167428/18791526. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.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. ------ 167429/18791607. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.x1))) 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))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 167430/18791634. ------ 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)))) REDUCED to normal form. ------ 167431/18791643. ------ 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 ]==> ((^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. ------ 167432/18792030. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 167433/18792048. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^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. ------ 167434/18792057. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (a a))) REDUCED to normal form. ------ 167435/18792075. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 167436/18792084. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 167437/18802701. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a)))) b) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y)))) b) REDUCED to normal form. ------ 167438/18802725. ------ 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. ------ 167439/18802737. ------ 1. ==[ start ]==> (((^a.a) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (a (^y.(a (a (^z.z))))) 4. ==[ alpha ]==> (a (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 167440/18802806. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 167441/18803169. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) REDUCED to normal form. ------ 167442/18803310. ------ 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. ------ 167443/18804606. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((((^y.y)(a a))(a b)) b) 4. ==[ alpha ]==> ((((^x.x)(a a))(a b)) b) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 167444/18804993. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))(^x1.b))(((^z.z)(a a))(^x1.b)))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))(^z.b))(((^x1.x1)(a a))(^y1.b)))) 5. ==[ beta ]==> (^x.(((a a)(^z.b))(((^x1.x1)(a a))(^y1.b)))) 6. ==[ alpha ]==> (^x.(((a a)(^y.b))(((^z.z)(a a))(^x1.b)))) 7. ==[ beta ]==> (^x.(((a a)(^y.b))((a a)(^x1.b)))) 8. ==[ alpha ]==> (^x.(((a a)(^y.b))((a a)(^z.b)))) REDUCED to normal form. ------ 167445/18805875. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((((^z.z) a)(a (^x1.(^y1.y1))))(((^z.z) a)(a (^x1.(^y1.y1)))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1)))))(^x2.x2)) 5. ==[ beta ]==> (((a (a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1)))))(^x2.x2)) 6. ==[ alpha ]==> (((a (a (^x.(^y.y))))(((^z.z) a)(a (^x1.(^y1.y1)))))(^z1.z1)) 7. ==[ beta ]==> (((a (a (^x.(^y.y))))(a (a (^x1.(^y1.y1)))))(^z1.z1)) 8. ==[ alpha ]==> (((a (a (^x.(^y.y))))(a (a (^z.(^x1.x1)))))(^y1.y1)) REDUCED to normal form. ------ 167446/18806292. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 167447/18806301. ------ 1. ==[ start ]==> (((a b)(^b.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 167448/18806631. ------ 1. ==[ start ]==> ((^a.(b a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))(b ((^y.y) b))) 3. ==[ eta ]==> (b (b ((^y.y) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 167449/18807003. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(y y)))) REDUCED to normal form. ------ 167450/18807180. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a) a)(^y1.b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 167451/18807975. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 167452/18808071. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167453/18808866. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 167454/18809385. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((b ((a a)(^y.y)))(b ((a a)(^y.y))))((b ((a a)(^y.y)))(b ((a a)(^y.y))))) 4. ==[ alpha ]==> (((b ((a a)(^x.x)))(b ((a a)(^y.y))))((b ((a a)(^z.z)))(b ((a a)(^x1.x1))))) REDUCED to normal form. ------ 167455/18809910. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 167456/18809919. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 167457/18810171. ------ 1. ==[ start ]==> ((((^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.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 167458/18811053. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(y y)))) REDUCED to normal form. ------ 167459/18811440. ------ 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. ------ 167460/18812241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 167461/18812376. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 167462/18812445. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a) c)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 167463/18812493. ------ 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. ------ 167464/18812736. ------ 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. ------ 167465/18813267. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(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))) REDUCED to normal form. ------ 167466/18813294. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.z))) REDUCED to normal form. ------ 167467/18813312. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.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)) REDUCED to normal form. ------ 167468/18813321. ------ 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. ------ 167469/18813351. ------ 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. ------ 167470/18813360. ------ 1. ==[ start ]==> (((^a.a) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (a ((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> (a ((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (^y.y)))) 6. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 167471/18813378. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 167472/18813387. ------ 1. ==[ start ]==> (((a a) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a a) a)((^z.z)(^y.y))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 167473/18813405. ------ 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. ------ 167474/18813432. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 167475/18813495. ------ 1. ==[ start ]==> (((a a) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 167476/18813711. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 167477/18813792. ------ 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)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) REDUCED to normal form. ------ 167478/18813855. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 167479/18813882. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 167480/18813909. ------ 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. ------ 167481/18813936. ------ 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. ------ 167482/18814179. ------ 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. ------ 167483/18814206. ------ 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.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. ------ 167484/18814296. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167485/18814323. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(y1 y1)))) 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. ------ 167486/18814377. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.a))) 5. ==[ beta ]==> ((^y.y)((b a)(^y1.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. ------ 167487/18814431. ------ 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)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 167488/18814440. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 167489/18814458. ------ 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. ------ 167490/18814467. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 167491/18814494. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(b a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(b a))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 167492/18814512. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 167493/18814521. ------ 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. ------ 167494/18814548. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 9. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 10. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 11. ==[ beta ]==> (b ((^y.y) b)) 12. ==[ alpha ]==> (b ((^x.x) b)) 13. ==[ beta ]==> (b b) REDUCED to normal form. ------ 167495/18814845. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 167496/18814872. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 167497/18814926. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 167498/18814953. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a a))(^b.b))) 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))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^z.z))) 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. ------ 167499/18814980. ------ 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. ------ 167500/18815070. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x))(a a))) REDUCED to normal form. ------ 167501/18815097. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 167502/18815124. ------ 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. ------ 167503/18815151. ------ 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. ------ 167504/18815178. ------ 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 a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 167505/18815205. ------ 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))) REDUCED to normal form. ------ 167506/18815232. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> ((a (a b))((a a)(a b))) REDUCED to normal form. ------ 167507/18815385. ------ 1. ==[ start ]==> ((((a a) a) b)(c (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(c (^x.(a a)))) REDUCED to normal form. ------ 167508/18815457. ------ 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)((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. ------ 167509/18815493. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 167510/18815511. ------ 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. ------ 167511/18815520. ------ 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) 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. ------ 167512/18815547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 167513/18815592. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 167514/18815601. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 167515/18815619. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 167516/18815790. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) 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)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 167517/18815835. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b (^z.z)) a)) 3. ==[ beta ]==> ((^y.(a a))((b (^z.z)) a)) 4. ==[ alpha ]==> ((^x.(a a))((b (^y.y)) a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167518/18815862. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 167519/18816006. ------ 1. ==[ start ]==> (((a b) b)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 167520/18816033. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 167521/18816060. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 167522/18816141. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 167523/18816285. ------ 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)(a a))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 167524/18816312. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b a)(a (a a)))) REDUCED to normal form. ------ 167525/18816339. ------ 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. ------ 167526/18816366. ------ 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 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. ------ 167527/18816393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a b)(a b))) 5. ==[ beta ]==> ((a (a a))((a b)(a b))) REDUCED to normal form. ------ 167528/18816420. ------ 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)))) 5. ==[ beta ]==> ((((a a) a) a)(((a a) a)(a a))) REDUCED to normal form. ------ 167529/18816447. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 167530/18816474. ------ 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. ------ 167531/18816501. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 167532/18816672. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 167533/18816681. ------ 1. ==[ start ]==> (((a b) c)((^d.a)(a (a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(a (a a)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 167534/18816708. ------ 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. ------ 167535/18816735. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 167536/18816753. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.b))) REDUCED to normal form. ------ 167537/18816780. ------ 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 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. ------ 167538/18816789. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 167539/18816816. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 167540/18816870. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.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. ------ 167541/18816897. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 167542/18816915. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 167543/18816924. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 167544/18816978. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b)(^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. ------ 167545/18817257. ------ 1. ==[ start ]==> ((a (b a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))(b ((^x.x) b))) 3. ==[ beta ]==> ((a (b a))(b b)) REDUCED to normal form. ------ 167546/18817347. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1))) c)) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) c)) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 167547/18817599. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b (^z.z))) 3. ==[ beta ]==> ((a (^y.(a a)))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.y))) REDUCED to normal form. ------ 167548/18817626. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 167549/18817680. ------ 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 (^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. ------ 167550/18817698. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a)(^y.a))) 3. ==[ beta ]==> (b ((b a)(^y.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 167551/18817734. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 167552/18817761. ------ 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.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 167553/18817806. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.b))) REDUCED to normal form. ------ 167554/18818085. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(a a))(^b.(^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. ------ 167555/18818571. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 167556/18818598. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(a (^z.z))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 167557/18818625. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(a a))) 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. ------ 167558/18818670. ------ 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 a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167559/18818697. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.x))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 167560/18818976. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 167561/18819489. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 167562/18819507. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a)(^y.y))) 3. ==[ beta ]==> (b ((b a)(^y.y))) 4. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 167563/18819516. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(a a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 167564/18819543. ------ 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))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(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. ------ 167565/18819570. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 167566/18819615. ------ 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.(^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. ------ 167567/18819651. ------ 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. ------ 167568/18819984. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((b (a a))(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b (a a))(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((b (a a))(c (a a))) REDUCED to normal form. ------ 167569/18820011. ------ 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. ------ 167570/18820326. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 167571/18820353. ------ 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 a)) REDUCED to normal form. ------ 167572/18820371. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b)(^b.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. ------ 167573/18820398. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((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. ------ 167574/18820407. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.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. ------ 167575/18820434. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 167576/18820452. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (a a))(^y.a))) 3. ==[ beta ]==> (((b a)(b a))((a (a a))(^y.a))) 4. ==[ alpha ]==> (((b a)(b a))((a (a a))(^x.a))) REDUCED to normal form. ------ 167577/18820515. ------ 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)(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. ------ 167578/18820533. ------ 1. ==[ start ]==> (((^a.b)(a b))((a a)(^c.(^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. ------ 167579/18820542. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 167580/18820596. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 167581/18820650. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 167582/18820677. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(^a.a))(^b.(^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. ------ 167583/18820767. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b ((^y.y)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(b (a a))) REDUCED to normal form. ------ 167584/18820794. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 167585/18820821. ------ 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. ------ 167586/18820848. ------ 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)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(a (^y.y)))) REDUCED to normal form. ------ 167587/18820875. ------ 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. ------ 167588/18820902. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a b)(a b))(a (a a))) REDUCED to normal form. ------ 167589/18820929. ------ 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)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (a a))((^x.x)(^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. ------ 167590/18820956. ------ 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 a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a ((a a) a))) REDUCED to normal form. ------ 167591/18821010. ------ 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)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a a))) REDUCED to normal form. ------ 167592/18821262. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 167593/18821406. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.a))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.a))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 167594/18821433. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^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. ------ 167595/18821478. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^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 a)) REDUCED to normal form. ------ 167596/18821505. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b) b)) 3. ==[ beta ]==> ((^y.y)((^z.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. ------ 167597/18821649. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b (^y.b))) REDUCED to normal form. ------ 167598/18821676. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 167599/18821748. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^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. ------ 167600/18821757. ------ 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) 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. ------ 167601/18821784. ------ 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. ------ 167602/18821811. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 167603/18822036. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b ((a a) a))) 3. ==[ beta ]==> (((a b)(a a))(b ((a a) a))) REDUCED to normal form. ------ 167604/18822063. ------ 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. ------ 167605/18822090. ------ 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. ------ 167606/18822144. ------ 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. ------ 167607/18822171. ------ 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. ------ 167608/18822198. ------ 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 (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 167609/18822342. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 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. ------ 167610/18822423. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a) a)) 3. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 167611/18822747. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x) b)((^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 b)(((^y.y)(^z.z))(^x1.x1))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.z))) 9. ==[ beta ]==> ((b b)((^y.y)(^z.z))) 10. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 11. ==[ beta ]==> ((b b)(^y.y)) 12. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 167612/18822756. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 167613/18822783. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167614/18822828. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 167615/18822837. ------ 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. ------ 167616/18822864. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 167617/18822891. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^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. ------ 167618/18822945. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 167619/18822972. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 167620/18822999. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 167621/18823071. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a) c)) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 167622/18823089. ------ 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) 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. ------ 167623/18823116. ------ 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. ------ 167624/18823305. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (a (^y.y)))) REDUCED to normal form. ------ 167625/18823359. ------ 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. ------ 167626/18823386. ------ 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. ------ 167627/18823413. ------ 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 (^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. ------ 167628/18823485. ------ 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))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 167629/18823503. ------ 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 ]==> ((^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. ------ 167630/18823890. ------ 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. ------ 167631/18823908. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((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. ------ 167632/18823917. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 167633/18823935. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^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. ------ 167634/18823944. ------ 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. ------ 167635/18823961. ------ 1. ==[ start ]==> (^a.((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(^y1.y1)) x))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167636/18823962. ------ 1. ==[ start ]==> (a ((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (a ((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 167637/18823992. ------ 1. ==[ start ]==> ((^a.(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.(a (a (^z.z))))(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.(a (a (^y.y))))(^z.(a (a (^x1.x1))))) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 167638/18825675. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((^x.(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.b) 6. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 167639/18826449. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^z.(z (^x1.x1))))) 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 ]==> ((^z.(z (^x1.x1)))(^y.y)) 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. ------ 167640/18832875. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.b))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167641/18834588. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a)) a) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a)) a) 3. ==[ beta ]==> ((^y.y) a) 4. ==[ alpha ]==> ((^x.x) a) 5. ==[ beta ]==> a REDUCED to normal form. ------ 167642/18834594. ------ 1. ==[ start ]==> ((^a.a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^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. ------ 167643/18834621. ------ 1. ==[ start ]==> ((^a.(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((^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))))) 5. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (a (^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. ------ 167644/18834624. ------ 1. ==[ start ]==> ((a (a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 167645/18834648. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 167646/18835089. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 167647/18835413. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167648/18835488. ------ 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))))) REDUCED to normal form. ------ 167649/18835893. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a a)(^x.((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)(^x.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 167650/18836304. ------ 1. ==[ start ]==> ((^a.(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 167651/18836307. ------ 1. ==[ start ]==> ((a (^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((a (^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 167652/18836685. ------ 1. ==[ start ]==> (((^a.a)(a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((a b)(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((a b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 167653/18837078. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(b (^x1.x1)))((^z.z)(b (^x1.x1))))) 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 (^x.x))(b (^z.z))) 10. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 167654/18837081. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 167655/18837468. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(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. ------ 167656/18838179. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 167657/18838509. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.x1))) 3. ==[ eta ]==> (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. ------ 167658/18838872. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(a b))(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y) b))) 5. ==[ beta ]==> (((a b)(a b))(^x.b)) REDUCED to normal form. ------ 167659/18839214. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a) a)((^x.x)(^y.y)))(^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. ------ 167660/18839346. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(a a))(^b.(^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 a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 167661/18840159. ------ 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.(^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))))) REDUCED to normal form. ------ 167662/18840264. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 167663/18840438. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^d.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(b a))) 3. ==[ beta ]==> (b (^z.(b a))) 4. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 167664/18841023. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(y a))) REDUCED to normal form. ------ 167665/18841302. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(b x1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.z)) b) 4. ==[ beta ]==> ((^y.y) b) 5. ==[ alpha ]==> ((^x.x) b) 6. ==[ beta ]==> b REDUCED to normal form. ------ 167666/18841545. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^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. ------ 167667/18841797. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 167668/18842049. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 167669/18842292. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^a.(^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. ------ 167670/18842343. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 167671/18842733. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 167672/18843129. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a y))) 3. ==[ eta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 167673/18843318. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 167674/18843504. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a (^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a (^x1.b))) 3. ==[ eta ]==> ((^y.(^z.z))(a (^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167675/18843507. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((a ((^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. ------ 167676/18844119. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 167677/18844323. ------ 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))) REDUCED to normal form. ------ 167678/18844398. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.(^b.(^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. ------ 167679/18844506. ------ 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. ------ 167680/18844614. ------ 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 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 167681/18844722. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 167682/18844746. ------ 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 (((^y.a)(a a))(^z.z))) 6. ==[ alpha ]==> (a (((^x.a)(a a))(^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 167683/18845145. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 167684/18845163. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.b)) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.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. ------ 167685/18845190. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^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. ------ 167686/18845199. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 167687/18845217. ------ 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)(^y1.y1)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167688/18845229. ------ 1. ==[ start ]==> ((a a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 167689/18845247. ------ 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. ------ 167690/18845256. ------ 1. ==[ start ]==> ((a (a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.x)(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. ------ 167691/18845274. ------ 1. ==[ start ]==> (((a a) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a) a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 167692/18845283. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a b)((^z.z)(^y.y))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 167693/18845301. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 167694/18845328. ------ 1. ==[ start ]==> (((^a.a) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x) b)((b (^y.y)) c)) 3. ==[ beta ]==> (b ((b (^y.y)) c)) 4. ==[ alpha ]==> (b ((b (^x.x)) c)) REDUCED to normal form. ------ 167695/18845499. ------ 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. ------ 167696/18845670. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 167697/18845706. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^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. ------ 167698/18845724. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 167699/18845832. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^x2.x2))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.z1))) REDUCED to normal form. ------ 167700/18845859. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 167701/18845913. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(a a))((^x1.x1)(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. ------ 167702/18845940. ------ 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. ------ 167703/18845967. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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. ------ 167704/18846021. ------ 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))((^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. ------ 167705/18846048. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 167706/18846120. ------ 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))))) REDUCED to normal form. ------ 167707/18846138. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) 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)(^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. ------ 167708/18846273. ------ 1. ==[ start ]==> (((a (a a)) b)((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a)) b)((b a)(^x.a))) REDUCED to normal form. ------ 167709/18846300. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (a (((a a)(^y.y))(^z.b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 167710/18846327. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 167711/18846354. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 167712/18846408. ------ 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. ------ 167713/18846435. ------ 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. ------ 167714/18846471. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 167715/18846498. ------ 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. ------ 167716/18846525. ------ 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 a)((^y.y)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a a)((^x.x)((^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. ------ 167717/18846939. ------ 1. ==[ start ]==> ((a (^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.b))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.y))) REDUCED to normal form. ------ 167718/18847128. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(a b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 167719/18847209. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(b a))) IRREDUCIBLE: cycle. ------ 167720/18847290. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 167721/18847317. ------ 1. ==[ start ]==> (((^a.a)(a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((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. ------ 167722/18847380. ------ 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))(^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. ------ 167723/18847407. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(b (^z.a))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b (^y.a))) REDUCED to normal form. ------ 167724/18847434. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 167725/18847461. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 167726/18847488. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 167727/18847524. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(a b))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 167728/18847551. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) b) REDUCED to normal form. ------ 167729/18847605. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(b 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. ------ 167730/18847632. ------ 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.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a ((^y.(y y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (a ((^x.(x x))(a (^y.(^z.z))))) 9. ==[ beta ]==> (a ((a (^y.(^z.z)))(a (^y.(^z.z))))) 10. ==[ alpha ]==> (a ((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 167731/18847659. ------ 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. ------ 167732/18847677. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((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. ------ 167733/18847686. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 167734/18847713. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(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)))) 5. ==[ beta ]==> ((a (a a))(b (^y.y))) 6. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 167735/18848100. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 167736/18848424. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((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. ------ 167737/18848568. ------ 1. ==[ start ]==> (((a b) c)((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) c)((b a)(^x.(x x)))) REDUCED to normal form. ------ 167738/18848595. ------ 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. ------ 167739/18848676. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 167740/18848703. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 167741/18848757. ------ 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)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167742/18848784. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 167743/18848811. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 167744/18848838. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 167745/18848865. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b b)) REDUCED to normal form. ------ 167746/18848901. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^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. ------ 167747/18848955. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 167748/18848982. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(a a))(^c.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. ------ 167749/18849009. ------ 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)(^z1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(^z1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((^y.y)((^z.b)(^x1.b))) 8. ==[ alpha ]==> ((^x.x)((^y.b)(^z.b))) 9. ==[ beta ]==> ((^y.b)(^z.b)) 10. ==[ alpha ]==> ((^x.b)(^y.b)) 11. ==[ beta ]==> b REDUCED to normal form. ------ 167750/18849063. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 167751/18849117. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 167752/18849144. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 167753/18849234. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 167754/18849315. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1)(^y1.y1)))) 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. ------ 167755/18849423. ------ 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. ------ 167756/18849450. ------ 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) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 167757/18849504. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(a b))((a a)((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a b))((a a)((^x.x) b))) 5. ==[ beta ]==> (((a b)(a b))((a a) b)) REDUCED to normal form. ------ 167758/18849567. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 167759/18849594. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 167760/18849621. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 167761/18849648. ------ 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)))(((^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. ------ 167762/18849711. ------ 1. ==[ start ]==> (((a a)(b a))((^c.a)(a b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(a b))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 167763/18849738. ------ 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))((^y1.y1)(a 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. ------ 167764/18849765. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.(y y))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> ((a (a a))(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 167765/18849792. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.a)(b a))) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 167766/18849819. ------ 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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 167767/18849846. ------ 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)(^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. ------ 167768/18849873. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 167769/18849900. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 167770/18849981. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(a a))(^b.(^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. ------ 167771/18850152. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(b (a (^a.(^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. ------ 167772/18850260. ------ 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) 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. ------ 167773/18850287. ------ 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)(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. ------ 167774/18850314. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 167775/18850368. ------ 1. ==[ start ]==> (((^a.(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))(a b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(a b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(a b))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(a b))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(a b))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)(a b))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)(a b))) 11. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 167776/18850449. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (b ((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 167777/18850512. ------ 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))) REDUCED to normal form. ------ 167778/18850566. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1))(^y1.a))) REDUCED to normal form. ------ 167779/18850602. ------ 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 a)) REDUCED to normal form. ------ 167780/18850629. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 167781/18850683. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 167782/18850710. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)((^y.(y y))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)(((^y.y)(a a))((^y.y)(a a)))) 8. ==[ alpha ]==> ((a b)(((^x.x)(a a))((^y.y)(a a)))) 9. ==[ beta ]==> ((a b)((a a)((^y.y)(a a)))) 10. ==[ alpha ]==> ((a b)((a a)((^x.x)(a a)))) 11. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 167783/18850737. ------ 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) REDUCED to normal form. ------ 167784/18850764. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 167785/18850791. ------ 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.(^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. ------ 167786/18850818. ------ 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.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(^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. ------ 167787/18850863. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167788/18850899. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 167789/18851070. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(b (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 167790/18851178. ------ 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) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(a a))((^x2.x2) 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. ------ 167791/18851232. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((a a) a)((^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. ------ 167792/18851259. ------ 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)(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))((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. ------ 167793/18851313. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a ((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a ((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (a a))) REDUCED to normal form. ------ 167794/18851403. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(^y.y))) REDUCED to normal form. ------ 167795/18851430. ------ 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.(^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. ------ 167796/18851457. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^z.a))) REDUCED to normal form. ------ 167797/18851511. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 167798/18851538. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(^a.a))(^c.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 (^x.x))((^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. ------ 167799/18851574. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(a b))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(a b))) 5. ==[ beta ]==> (((a a) b)((a b)(a b))) REDUCED to normal form. ------ 167800/18851601. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 167801/18851628. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 167802/18851655. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)(b a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 167803/18851709. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.(^a.a))(^a.(^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. ------ 167804/18851736. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(a a))(^b.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. ------ 167805/18851763. ------ 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)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 167806/18851844. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^y1.b)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(^y1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 167807/18851871. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 167808/18851934. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 167809/18852069. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 167810/18852177. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 167811/18852213. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 167812/18852240. ------ 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)))) 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. ------ 167813/18852294. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 167814/18852321. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 167815/18852402. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 167816/18852429. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 167817/18852483. ------ 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. ------ 167818/18852627. ------ 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. ------ 167819/18852654. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 167820/18852897. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b (^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.(a a)))) REDUCED to normal form. ------ 167821/18852924. ------ 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)))) REDUCED to normal form. ------ 167822/18852951. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 167823/18852978. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 167824/18853365. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(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 (^x.x))(a (a a))) REDUCED to normal form. ------ 167825/18853392. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((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. ------ 167826/18853428. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 167827/18853446. ------ 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) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)((^x2.x2) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1) a)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1) a)) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 167828/18853527. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((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. ------ 167829/18853644. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.a)) REDUCED to normal form. ------ 167830/18853671. ------ 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 z)))) 3. ==[ beta ]==> ((b (^y.a))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.a))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 167831/18853698. ------ 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) 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. ------ 167832/18853761. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(a b))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a b)) REDUCED to normal form. ------ 167833/18853788. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 167834/18853815. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 167835/18853842. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^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. ------ 167836/18853869. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> ((b a)((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 167837/18853896. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.a)(^b.(^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. ------ 167838/18853923. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(^a.a))(^c.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))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 167839/18853950. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 167840/18854139. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a (^a.b))) 2. ==[ alpha ]==> ((a ((^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. ------ 167841/18854418. ------ 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. ------ 167842/18854553. ------ 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) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 167843/18854580. ------ 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. ------ 167844/18854643. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 167845/18854670. ------ 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. ------ 167846/18854715. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c d)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c d)) 3. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 167847/18854724. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 167848/18854751. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 167849/18854778. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 167850/18854832. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a c)) REDUCED to normal form. ------ 167851/18854940. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 167852/18854958. ------ 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 (^x.(x (^y.y))))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 167853/18855003. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 167854/18855030. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a (^b.(^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. ------ 167855/18855057. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(a a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(a a))) 5. ==[ beta ]==> (((a (a a)) b)((a a)(a a))) REDUCED to normal form. ------ 167856/18855084. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 167857/18855111. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 167858/18855138. ------ 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. ------ 167859/18855165. ------ 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 z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.y))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^y.y))) 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. ------ 167860/18855192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(^a.(^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. ------ 167861/18855246. ------ 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 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(y1 y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(x1 x1))) REDUCED to normal form. ------ 167862/18855354. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 167863/18855372. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((^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. ------ 167864/18855381. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.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. ------ 167865/18855777. ------ 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. ------ 167866/18855795. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a b)) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 167867/18855804. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a) a)) REDUCED to normal form. ------ 167868/18855822. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 167869/18855831. ------ 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. ------ 167870/18855849. ------ 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)(a a)) 4. ==[ alpha ]==> ((^x.x)(a a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167871/18866484. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a)) b) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a)) b) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 167872/18866508. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167873/18866526. ------ 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. ------ 167874/18866538. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^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. ------ 167875/18866553. ------ 1. ==[ start ]==> ((^a.b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.b)((a (a (^y.y))) a)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 167876/18866751. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(^a.a))(^b.(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. ------ 167877/18866979. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^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. ------ 167878/18867444. ------ 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)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167879/18868599. ------ 1. ==[ start ]==> (((a a)(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 167880/18868776. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))((a a) a))((^z.(^x1.x1))((a a) a)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a)))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.(^y1.y1))((a a) a)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))((a a) a)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))((a a) a))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))((a a) a))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167881/18868995. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(y (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167882/18869382. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 167883/18870786. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.((^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. ------ 167884/18870963. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.b)((a a) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 167885/18871854. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 167886/18872649. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^c.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(b a))) REDUCED to normal form. ------ 167887/18872667. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^a.(^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. ------ 167888/18874248. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 167889/18874422. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^b.((^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 (^x.(a a))) REDUCED to normal form. ------ 167890/18874638. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 167891/18874836. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(a b))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(a b))) REDUCED to normal form. ------ 167892/18875034. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 167893/18875583. ------ 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))) REDUCED to normal form. ------ 167894/18875907. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(^c.a))) 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. ------ 167895/18876411. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 167896/18876651. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(^a.a))) 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. ------ 167897/18877068. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 167898/18877077. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.b)) REDUCED to normal form. ------ 167899/18877095. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(^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))) REDUCED to normal form. ------ 167900/18877104. ------ 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. ------ 167901/18877122. ------ 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)(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167902/18877152. ------ 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 (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 167903/18877170. ------ 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. ------ 167904/18877179. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 167905/18877197. ------ 1. ==[ start ]==> ((a b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a b)((a (a (^x.x))) a)) REDUCED to normal form. ------ 167906/18877206. ------ 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. ------ 167907/18877251. ------ 1. ==[ start ]==> (((a a)(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(a a))((b (^x.x)) c)) REDUCED to normal form. ------ 167908/18877314. ------ 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)((^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. ------ 167909/18877395. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(^a.a))(^b.(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. ------ 167910/18877476. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 167911/18877503. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 167912/18877566. ------ 1. ==[ start ]==> (((a a)(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(c (b (^y.y)))) REDUCED to normal form. ------ 167913/18877593. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 167914/18877620. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(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. ------ 167915/18877728. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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)))) 5. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 167916/18877809. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 167917/18877836. ------ 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. ------ 167918/18877863. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 167919/18877890. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a) a)(b a))) REDUCED to normal form. ------ 167920/18877917. ------ 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))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^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. ------ 167921/18877944. ------ 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. ------ 167922/18878061. ------ 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. ------ 167923/18878088. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^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)))) REDUCED to normal form. ------ 167924/18878178. ------ 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.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167925/18878259. ------ 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. ------ 167926/18878466. ------ 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. ------ 167927/18878493. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b (^z.z)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y)) b)) 5. ==[ beta ]==> ((a a)((b (^y.y)) b)) 6. ==[ alpha ]==> ((a a)((b (^x.x)) b)) REDUCED to normal form. ------ 167928/18878556. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^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. ------ 167929/18878691. ------ 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. ------ 167930/18878772. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a a))(^b.b))) 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))) 9. ==[ beta ]==> ((a a)((^y.y)(^y.y))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 167931/18878835. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 167932/18879024. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 167933/18879186. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a)((^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. ------ 167934/18879204. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c (^z.(a a)))) 3. ==[ beta ]==> (b (c (^z.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 167935/18879213. ------ 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. ------ 167936/18879240. ------ 1. ==[ start ]==> (((a a)(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a a)(b (^y.y)))) REDUCED to normal form. ------ 167937/18879420. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 167938/18879438. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(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. ------ 167939/18879465. ------ 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. ------ 167940/18879546. ------ 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. ------ 167941/18879573. ------ 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. ------ 167942/18879600. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 167943/18879636. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167944/18879717. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.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. ------ 167945/18879798. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(^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. ------ 167946/18879852. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((a a)((^y.b)(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.(a a)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 167947/18879879. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 167948/18879933. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 11. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 12. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 13. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 14. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 15. ==[ beta ]==> (^y.(^z.z)) 16. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 167949/18879996. ------ 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. ------ 167950/18880023. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 167951/18880050. ------ 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. ------ 167952/18880086. ------ 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)(a a))((^y.y) c)) 4. ==[ alpha ]==> (((a a)(a a))((^x.x) c)) 5. ==[ beta ]==> (((a a)(a a)) c) REDUCED to normal form. ------ 167953/18880239. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 167954/18880338. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(c (^x1.x1))) 3. ==[ beta ]==> ((^y.y)(c (^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(c (^y.y))) 5. ==[ beta ]==> (c (^y.y)) 6. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 167955/18880473. ------ 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) 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. ------ 167956/18880554. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 167957/18880581. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 167958/18880635. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))((a a)(^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. ------ 167959/18880716. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 167960/18881292. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)(a b))) REDUCED to normal form. ------ 167961/18881400. ------ 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.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 167962/18881418. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b (^y.y))) 3. ==[ beta ]==> (((a b)(a b))(b (^y.y))) 4. ==[ alpha ]==> (((a b)(a b))(b (^x.x))) REDUCED to normal form. ------ 167963/18881427. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a) b)) REDUCED to normal form. ------ 167964/18881499. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 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. ------ 167965/18881607. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 167966/18881625. ------ 1. ==[ start ]==> (((a a)(b a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a a)(b a))(((a a) a)(^x.b))) REDUCED to normal form. ------ 167967/18881652. ------ 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)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 167968/18881733. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^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))))) REDUCED to normal form. ------ 167969/18881760. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 167970/18881787. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) b) a)) 3. ==[ beta ]==> (((a b)(a (a a)))(b a)) REDUCED to normal form. ------ 167971/18881814. ------ 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.(^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)) REDUCED to normal form. ------ 167972/18881841. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((b a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((b a) c)) REDUCED to normal form. ------ 167973/18881904. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(a a))(^b.(^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. ------ 167974/18881985. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 167975/18882066. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^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. ------ 167976/18882183. ------ 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)(^z.z)) a)) REDUCED to normal form. ------ 167977/18882210. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(a (a a)))) REDUCED to normal form. ------ 167978/18882291. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)(a b))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(a b))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(a b)) REDUCED to normal form. ------ 167979/18882318. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((a (a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.b)((a (a a))((^y.y)(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 167980/18882363. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c (^d.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c (^x1.a))) 3. ==[ beta ]==> (b (c (^x1.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 167981/18882372. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 167982/18882399. ------ 1. ==[ start ]==> ((((^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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 167983/18882498. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 167984/18882516. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(^z.(z z)))) REDUCED to normal form. ------ 167985/18882543. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 167986/18882597. ------ 1. ==[ start ]==> (((a (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))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.b))) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.b))) 7. ==[ beta ]==> (((a (a a))(a a))(^y.b)) 8. ==[ alpha ]==> (((a (a a))(a a))(^x.b)) REDUCED to normal form. ------ 167987/18882624. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a b)((a (a a))(^y.(a a)))) 6. ==[ alpha ]==> ((a b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 167988/18882705. ------ 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. ------ 167989/18882732. ------ 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)) REDUCED to normal form. ------ 167990/18882822. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(x1 x1)))) 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. ------ 167991/18882849. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.b)(^x2.(^y2.y2)))) 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. ------ 167992/18882984. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.a))(^d.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. ------ 167993/18883101. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a) a)) REDUCED to normal form. ------ 167994/18883128. ------ 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. ------ 167995/18883155. ------ 1. ==[ start ]==> (((a a)(^b.b))(((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. ------ 167996/18883182. ------ 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)(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.z1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a) a)) REDUCED to normal form. ------ 167997/18883263. ------ 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 (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((a (^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 167998/18883290. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)(b a))) REDUCED to normal form. ------ 167999/18883308. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(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. ------ 168000/18883416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 168001/18883488. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (a a))(^y.b))) 3. ==[ beta ]==> (((a a) b)((a (a a))(^y.b))) 4. ==[ alpha ]==> (((a a) b)((a (a a))(^x.b))) REDUCED to normal form. ------ 168002/18883515. ------ 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) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^x1.(a a)))) REDUCED to normal form. ------ 168003/18883542. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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)))) REDUCED to normal form. ------ 168004/18883596. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((b a) a)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((b a) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a) a)) 5. ==[ beta ]==> (((^y.y)(a a))((b a) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((b a) a)) 7. ==[ beta ]==> ((a a)((b a) a)) REDUCED to normal form. ------ 168005/18883623. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 168006/18883650. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(a a)) c)) 3. ==[ beta ]==> (((a b)((a a) a))((a a) c)) REDUCED to normal form. ------ 168007/18884091. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 168008/18884172. ------ 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 (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 168009/18884199. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1) 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. ------ 168010/18884253. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 168011/18884334. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 168012/18884442. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 168013/18884622. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.(^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. ------ 168014/18884649. ------ 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 a)) REDUCED to normal form. ------ 168015/18884676. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.b) c)) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b) c)) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b) c)) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 168016/18884703. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a) d)) 2. ==[ alpha ]==> (((a b)(a b))((^x.a) d)) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 168017/18884865. ------ 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. ------ 168018/18884892. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 168019/18884982. ------ 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 y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))((^y2.y2)(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))((^y2.y2)(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168020/18885063. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168021/18885171. ------ 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.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168022/18885207. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b c)(d ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b c)(d ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b c)(d (^y.y))) 6. ==[ alpha ]==> ((b c)(d (^x.x))) REDUCED to normal form. ------ 168023/18885234. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c ((a a) a))) REDUCED to normal form. ------ 168024/18885279. ------ 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 (^x.x))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 168025/18885342. ------ 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. ------ 168026/18885369. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1) a)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1) a)) 7. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 168027/18885441. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 168028/18885450. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 168029/18885477. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(a b))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(a b))) REDUCED to normal form. ------ 168030/18885675. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 168031/18885702. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b) a)) REDUCED to normal form. ------ 168032/18885729. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a) b)) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a) b)) 5. ==[ beta ]==> ((a b)(((a a) a) b)) REDUCED to normal form. ------ 168033/18885891. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 168034/18885945. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1)) c)) 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. ------ 168035/18886143. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))((^x1.x1) 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. ------ 168036/18886224. ------ 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. ------ 168037/18886332. ------ 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)(^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. ------ 168038/18886449. ------ 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. ------ 168039/18886494. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(y y)))) 5. ==[ beta ]==> (c (^y.(y y))) 6. ==[ alpha ]==> (c (^x.(x x))) REDUCED to normal form. ------ 168040/18886548. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a (^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a (^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (^y.a))) 7. ==[ beta ]==> ((b b)(a (^y.a))) 8. ==[ alpha ]==> ((b b)(a (^x.a))) REDUCED to normal form. ------ 168041/18886629. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 168042/18886638. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c d)) REDUCED to normal form. ------ 168043/18886737. ------ 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.(^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. ------ 168044/18886773. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(c ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(c a)) REDUCED to normal form. ------ 168045/18886800. ------ 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. ------ 168046/18886854. ------ 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. ------ 168047/18886890. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a) c)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 168048/18886971. ------ 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. ------ 168049/18886998. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^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. ------ 168050/18887025. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 168051/18887052. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 168052/18887079. ------ 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. ------ 168053/18887106. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a b)) REDUCED to normal form. ------ 168054/18887187. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y)) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y)) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x)) a)) 5. ==[ beta ]==> ((b (a (a a)))(a a)) REDUCED to normal form. ------ 168055/18887214. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a) b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a) b)) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 168056/18887295. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(^a.a))) 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. ------ 168057/18887304. ------ 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 (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 168058/18887691. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 168059/18887709. ------ 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. ------ 168060/18887718. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a b)) REDUCED to normal form. ------ 168061/18887736. ------ 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 (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 168062/18887745. ------ 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. ------ 168063/18887763. ------ 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)(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 168064/18898479. ------ 1. ==[ start ]==> (((a a) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 168065/18898521. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 168066/18898911. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(^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))))) REDUCED to normal form. ------ 168067/18898926. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168068/18899025. ------ 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. ------ 168069/18899343. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^a.(^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. ------ 168070/18900162. ------ 1. ==[ start ]==> (((a a)((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 168071/18900321. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a) a)) b) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 168072/18900708. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.((((a a)(^z.z))(^x1.a))(((a a)(^z.z))(^x1.a)))) 4. ==[ alpha ]==> (^x.((((a a)(^y.y))(^z.a))(((a a)(^x1.x1))(^y1.a)))) REDUCED to normal form. ------ 168073/18900927. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.(^d.(^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 a) REDUCED to normal form. ------ 168074/18901590. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (a a))(b a))) 3. ==[ beta ]==> ((((a (a a))(b a))((a (a a))(b a)))(^y.y)) 4. ==[ alpha ]==> ((((a (a a))(b a))((a (a a))(b a)))(^x.x)) REDUCED to normal form. ------ 168075/18902043. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^b.((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)))) REDUCED to normal form. ------ 168076/18902346. ------ 1. ==[ start ]==> ((^a.(b a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(c (a (^y.(^z.z))))) 3. ==[ eta ]==> (b (c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 168077/18902895. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a b)(^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 168078/18903717. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 168079/18903786. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168080/18904608. ------ 1. ==[ start ]==> (((a b)(^c.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 168081/18905913. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 168082/18906129. ------ 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)))(^y.(a a))) REDUCED to normal form. ------ 168083/18906354. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168084/18907182. ------ 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. ------ 168085/18907341. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)((a a) a))) 3. ==[ eta ]==> ((^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. ------ 168086/18907515. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (b (^x1.(^y1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 168087/18907848. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 168088/18907983. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 168089/18908160. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 168090/18908478. ------ 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. ------ 168091/18908577. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 168092/18908982. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^a.(^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. ------ 168093/18909009. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(a a))) REDUCED to normal form. ------ 168094/18909036. ------ 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. ------ 168095/18909054. ------ 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)(^y1.a)) 4. ==[ alpha ]==> ((^x.x)(^y.a)) 5. ==[ beta ]==> (^y.a) 6. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 168096/18909102. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) a)((^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 (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 168097/18909120. ------ 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. ------ 168098/18909129. ------ 1. ==[ start ]==> (((a a) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.x)(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. ------ 168099/18909147. ------ 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. ------ 168100/18909156. ------ 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))((^x1.x1)(^z.z))) 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. ------ 168101/18909174. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 168102/18909237. ------ 1. ==[ start ]==> (((a a) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 168103/18909264. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.b)(^b.(^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. ------ 168104/18909372. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(a a))(^c.(^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 a) REDUCED to normal form. ------ 168105/18909453. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 168106/18909561. ------ 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))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 168107/18909579. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((a (^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 168108/18909597. ------ 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) 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. ------ 168109/18909624. ------ 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))(a (^x1.x1)))) REDUCED to normal form. ------ 168110/18909651. ------ 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. ------ 168111/18909678. ------ 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. ------ 168112/18909921. ------ 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. ------ 168113/18909948. ------ 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)))) REDUCED to normal form. ------ 168114/18909975. ------ 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.(^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. ------ 168115/18909993. ------ 1. ==[ start ]==> (((^a.(a a)) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(a (^y.(y (^z.z))))) 3. ==[ beta ]==> ((b b)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((b b)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 168116/18910038. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168117/18910065. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.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. ------ 168118/18910119. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 168119/18910128. ------ 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. ------ 168120/18910173. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 168121/18910182. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(^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)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 168122/18910200. ------ 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. ------ 168123/18910209. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 168124/18910236. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 168125/18910290. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168126/18910587. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 168127/18910614. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 168128/18910668. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 168129/18910695. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 168130/18910722. ------ 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. ------ 168131/18910749. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168132/18910812. ------ 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. ------ 168133/18910839. ------ 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))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(a a))) REDUCED to normal form. ------ 168134/18910866. ------ 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. ------ 168135/18910893. ------ 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. ------ 168136/18910920. ------ 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 (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.(^y1.y1)))(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)))) REDUCED to normal form. ------ 168137/18910947. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a a))((b a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a a))((b a)(^x.x))) REDUCED to normal form. ------ 168138/18910974. ------ 1. ==[ start ]==> ((a (a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 168139/18911154. ------ 1. ==[ start ]==> (((a b) a)(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)(c (^x.(a a)))) REDUCED to normal form. ------ 168140/18911253. ------ 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. ------ 168141/18911289. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.a)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)((^z.z) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 168142/18911316. ------ 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 (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. ------ 168143/18911334. ------ 1. ==[ start ]==> (((^a.b)(a a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 168144/18911361. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 168145/18911532. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 168146/18911604. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 168147/18911658. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b) c)) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b) c)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 7. ==[ beta ]==> (((^y.y) b) c) 8. ==[ alpha ]==> (((^x.x) b) c) 9. ==[ beta ]==> (b c) REDUCED to normal form. ------ 168148/18911748. ------ 1. ==[ start ]==> (((a b) b)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 168149/18911775. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.b))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 168150/18911802. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 168151/18911829. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 168152/18911883. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 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. ------ 168153/18911910. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)(^z.z))) 7. ==[ beta ]==> (((^y.a)(^z.z))((^y.a)(^z.z))) 8. ==[ alpha ]==> (((^x.a)(^y.y))((^z.a)(^x1.x1))) 9. ==[ beta ]==> (a ((^z.a)(^x1.x1))) 10. ==[ alpha ]==> (a ((^x.a)(^y.y))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168154/18911937. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 168155/18912027. ------ 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)(a a))(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(a (^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. ------ 168156/18912054. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 168157/18912081. ------ 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. ------ 168158/18912108. ------ 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)))(((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. ------ 168159/18912135. ------ 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 a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(a a))((a a) a))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))((a a) a))) 7. ==[ beta ]==> ((a (a a))((a a)((a a) a))) REDUCED to normal form. ------ 168160/18912162. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a b)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a b)(a b))) 3. ==[ beta ]==> ((((a a) a) a)((a b)(a b))) REDUCED to normal form. ------ 168161/18912189. ------ 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.y)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 168162/18912216. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^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))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((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. ------ 168163/18912243. ------ 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. ------ 168164/18912414. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 168165/18912423. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 168166/18912522. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((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. ------ 168167/18912531. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 168168/18912558. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 168169/18912612. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168170/18912639. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 168171/18912657. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((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. ------ 168172/18912666. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 168173/18912693. ------ 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)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 168174/18912999. ------ 1. ==[ start ]==> ((a (b a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 168175/18913089. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z) b)) 5. ==[ beta ]==> (b ((^z.z) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 168176/18913341. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168177/18913368. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b (^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b (^y.y))) REDUCED to normal form. ------ 168178/18913422. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 168179/18913440. ------ 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)))(^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. ------ 168180/18913449. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 168181/18913548. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.a))) REDUCED to normal form. ------ 168182/18914313. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c (^d.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 168183/18914340. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168184/18914367. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a (^z.z))) REDUCED to normal form. ------ 168185/18914412. ------ 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. ------ 168186/18914439. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 168187/18915204. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(c (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))(c (^y.(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168188/18915258. ------ 1. ==[ start ]==> (((a b)(^c.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168189/18915357. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((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. ------ 168190/18915366. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 168191/18915393. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 168192/18916113. ------ 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)))) 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. ------ 168193/18916140. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.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. ------ 168194/18916149. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 168195/18916194. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((b a)(b a))(^y.(^z.z))) 8. ==[ alpha ]==> (((b a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 168196/18916257. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.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. ------ 168197/18916275. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((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. ------ 168198/18916284. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 168199/18916338. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(^a.a))) 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. ------ 168200/18916383. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) 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. ------ 168201/18916392. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 168202/18916419. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 168203/18916446. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(^a.a))(^b.(^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. ------ 168204/18916509. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c (a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c (a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (a b))) REDUCED to normal form. ------ 168205/18916536. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b ((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(b (a a))) REDUCED to normal form. ------ 168206/18916563. ------ 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. ------ 168207/18916590. ------ 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 a))(a a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 168208/18916617. ------ 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 (^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. ------ 168209/18916644. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))(((a a) a)((^x.x) a))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a) a)) REDUCED to normal form. ------ 168210/18916671. ------ 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 (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^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))((^y.y)(a (a a)))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(a (a a)))) 7. ==[ beta ]==> (((a a)((a a) a))(a (a a))) REDUCED to normal form. ------ 168211/18916698. ------ 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 (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^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)(^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. ------ 168212/18916752. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^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))) REDUCED to normal form. ------ 168213/18916779. ------ 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)))) 5. ==[ beta ]==> ((b (a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 168214/18916923. ------ 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 (a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (a a))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168215/18917004. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168216/18917148. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((b c)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b c)(^y.y)) 8. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 168217/18917175. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.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. ------ 168218/18917247. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 168219/18917391. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c (^y.a))) REDUCED to normal form. ------ 168220/18917418. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b (^z.b))) 3. ==[ beta ]==> (((a a)(^y.b))(b (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.b))) REDUCED to normal form. ------ 168221/18917490. ------ 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.(^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. ------ 168222/18917526. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 168223/18917553. ------ 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. ------ 168224/18917778. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(c ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))(c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a b)(a a))(c (^y.y))) 6. ==[ alpha ]==> (((a b)(a a))(c (^x.x))) REDUCED to normal form. ------ 168225/18917805. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b ((a a) a))) 3. ==[ beta ]==> (((a a)(a b))(b ((a a) a))) REDUCED to normal form. ------ 168226/18917832. ------ 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. ------ 168227/18917886. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(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. ------ 168228/18917913. ------ 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. ------ 168229/18917940. ------ 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. ------ 168230/18917994. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)((a a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 168231/18918084. ------ 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. ------ 168232/18918165. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> (b ((a a)(^x1.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 168233/18918498. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.a))) REDUCED to normal form. ------ 168234/18918525. ------ 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.(^x2.x2))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 168235/18918570. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^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. ------ 168236/18918579. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 168237/18918606. ------ 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. ------ 168238/18918633. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 168239/18918678. ------ 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. ------ 168240/18918687. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.(^x2.x2))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 168241/18918714. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 168242/18918741. ------ 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))(^x1.(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. ------ 168243/18918813. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z)) b)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(b b)) REDUCED to normal form. ------ 168244/18918831. ------ 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 (^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. ------ 168245/18918858. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 168246/18918885. ------ 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. ------ 168247/18918966. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c c)) REDUCED to normal form. ------ 168248/18919101. ------ 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 ((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b ((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b ((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(b a)) REDUCED to normal form. ------ 168249/18919128. ------ 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. ------ 168250/18919155. ------ 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. ------ 168251/18919209. ------ 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. ------ 168252/18919227. ------ 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 (^y.y))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 168253/18919245. ------ 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 ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((((^z.z) a)(^x1.x1))(^y.y)) 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. ------ 168254/18919632. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^a.(^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. ------ 168255/18919650. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(^x1.x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((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. ------ 168256/18919659. ------ 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. ------ 168257/18919677. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((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. ------ 168258/18919686. ------ 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. ------ 168259/18919704. ------ 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)((^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. ------ 168260/18919730. ------ 1. ==[ start ]==> (^a.((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (^x.((^y.x)(b (^z.z)))) 3. ==[ beta ]==> (^x.x) REDUCED to normal form. ------ 168261/18919731. ------ 1. ==[ start ]==> (a ((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168262/18919788. ------ 1. ==[ start ]==> ((^a.b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 168263/18920229. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168264/18929886. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^z.(^x1.(x1 x1)))((^z.(^x1.(x1 x1)))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.(x1 x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.(y y)) 6. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168265/18930390. ------ 1. ==[ start ]==> ((^a.a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.a)(b (^z.z))) 4. ==[ alpha ]==> ((^x.a)(b (^y.y))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 168266/18930417. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^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))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 168267/18930444. ------ 1. ==[ start ]==> ((^a.b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 168268/18930447. ------ 1. ==[ start ]==> ((a b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 168269/18930885. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168270/18930888. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 168271/18931209. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 168272/18931311. ------ 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. ------ 168273/18931716. ------ 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. ------ 168274/18932100. ------ 1. ==[ start ]==> ((^a.(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(b (b (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 168275/18932874. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((a a)(a a)))((^z.(^x1.x1))((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a)(a a)))((^x1.(^y1.y1))((a a)(a a))))) 5. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))((^x1.(^y1.y1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^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. ------ 168276/18934305. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b ((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 168277/18935037. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.((^y.y) x))) 3. ==[ eta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 168278/18935982. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 168279/18936060. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 168280/18936558. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(b a))) 3. ==[ beta ]==> (b (^y.(b a))) 4. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 168281/18936846. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^b.(b 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. ------ 168282/18937059. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((^y.a)(^z.(a a)))((^y.a)(^z.(a a))))(((^y.a)(^z.(a a)))((^y.a)(^z.(a a))))) 4. ==[ alpha ]==> ((((^x.a)(^y.(a a)))((^z.a)(^x1.(a a))))(((^y1.a)(^z1.(a a)))((^x2.a)(^y2.(a a))))) 5. ==[ beta ]==> ((a ((^z.a)(^x1.(a a))))(((^y1.a)(^z1.(a a)))((^x2.a)(^y2.(a a))))) 6. ==[ alpha ]==> ((a ((^x.a)(^y.(a a))))(((^z.a)(^x1.(a a)))((^y1.a)(^z1.(a a))))) 7. ==[ beta ]==> ((a a)(((^z.a)(^x1.(a a)))((^y1.a)(^z1.(a a))))) 8. ==[ alpha ]==> ((a a)(((^x.a)(^y.(a a)))((^z.a)(^x1.(a a))))) 9. ==[ beta ]==> ((a a)(a ((^z.a)(^x1.(a a))))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)(^y.(a a))))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 168283/18937872. ------ 1. ==[ start ]==> (((a (a a))(b a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 168284/18938139. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(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. ------ 168285/18938556. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(z z)))) 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. ------ 168286/18938952. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(a y))) 3. ==[ eta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 168287/18939141. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.y))) REDUCED to normal form. ------ 168288/18939300. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (^c.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (^x1.a))) 3. ==[ eta ]==> ((^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. ------ 168289/18939798. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)(^y.((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(^x.((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)(^x.(^z.z))) 10. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 168290/18939942. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 168291/18940119. ------ 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. ------ 168292/18940221. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 168293/18940329. ------ 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. ------ 168294/18940437. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 168295/18940542. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.(z z)))) 3. ==[ beta ]==> ((a (^z.(z z)))((a (^z.(z z)))(^y.y))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(y y)))(^z.z))) REDUCED to normal form. ------ 168296/18940545. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(z z)))) REDUCED to normal form. ------ 168297/18940941. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 168298/18940986. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.b)) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.b)) REDUCED to normal form. ------ 168299/18941013. ------ 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)(^y1.(y1 y1))) 4. ==[ alpha ]==> ((^x.x)(^y.(y y))) 5. ==[ beta ]==> (^y.(y y)) 6. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168300/18941052. ------ 1. ==[ start ]==> ((a a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 168301/18941079. ------ 1. ==[ start ]==> ((a (a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a a))(^y.y)) 4. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 168302/18941097. ------ 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. ------ 168303/18941106. ------ 1. ==[ start ]==> ((a b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> ((a b)(a (a (^y.y)))) 4. ==[ alpha ]==> ((a b)(a (a (^x.x)))) REDUCED to normal form. ------ 168304/18941124. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 168305/18941151. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.(^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)) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 168306/18941178. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 168307/18941349. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 168308/18941547. ------ 1. ==[ start ]==> ((a (^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 168309/18941655. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((((^y.y) b)(a (a a)))(((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> ((b (a (a a)))(((^y.y) b)(a (a a)))) 8. ==[ alpha ]==> ((b (a (a a)))(((^x.x) b)(a (a a)))) 9. ==[ beta ]==> ((b (a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 168310/18941682. ------ 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)))((^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. ------ 168311/18941736. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(^z.z))(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. ------ 168312/18941763. ------ 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. ------ 168313/18941790. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^x1.x1)))) 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. ------ 168314/18941844. ------ 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)(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. ------ 168315/18941871. ------ 1. ==[ start ]==> ((a (^b.(^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. ------ 168316/18941970. ------ 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. ------ 168317/18942096. ------ 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. ------ 168318/18942123. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y) a)((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(^y.a))) 5. ==[ beta ]==> (a ((b a)(^y.a))) 6. ==[ alpha ]==> (a ((b a)(^x.a))) REDUCED to normal form. ------ 168319/18942150. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 168320/18942177. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 168321/18942204. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 168322/18942258. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 168323/18942294. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> (((a a)(^x.x))(b ((^z.z) b))) 8. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y) b))) 9. ==[ beta ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 168324/18942321. ------ 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. ------ 168325/18942348. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(b (^z.z)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 168326/18942375. ------ 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. ------ 168327/18942762. ------ 1. ==[ start ]==> ((a (^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(b (b (^y.y)))) REDUCED to normal form. ------ 168328/18942951. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.b)(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 168329/18943032. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a) a)((a a)(^z.z)))) IRREDUCIBLE: cycle. ------ 168330/18943113. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168331/18943140. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a b)((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((a b)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 168332/18943167. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 168333/18943203. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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. ------ 168334/18943230. ------ 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))(^y.(^z.z)))) REDUCED to normal form. ------ 168335/18943257. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((^y.a)(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b)(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 168336/18943284. ------ 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.(y1 y1)))) REDUCED to normal form. ------ 168337/18943311. ------ 1. ==[ start ]==> (((a b)(^a.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 168338/18943347. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(^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)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 168339/18943374. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 168340/18943401. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 168341/18943455. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(b a))) 7. ==[ beta ]==> (a ((^y.(^z.z))(b a))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(b a))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 168342/18943482. ------ 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. ------ 168343/18943500. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b) b)(((^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. ------ 168344/18943509. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 168345/18943536. ------ 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)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 168346/18943923. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 168347/18944247. ------ 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) 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. ------ 168348/18944391. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 168349/18944418. ------ 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. ------ 168350/18944445. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 168351/18944499. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)(^z.b))) REDUCED to normal form. ------ 168352/18944526. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.b))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 168353/18944607. ------ 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)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168354/18944634. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 168355/18944688. ------ 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. ------ 168356/18944724. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b)(^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. ------ 168357/18944751. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(^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. ------ 168358/18944832. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.a))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.a))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 9. ==[ beta ]==> ((^y.(a a))(^z.a)) 10. ==[ alpha ]==> ((^x.(a a))(^y.a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168359/18944859. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.b)(^y.b))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 168360/18944886. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 168361/18944913. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 168362/18944967. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 168363/18945057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b)(a a))) 5. ==[ beta ]==> (b (((^z.z) b)(a a))) 6. ==[ alpha ]==> (b (((^x.x) b)(a a))) 7. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 168364/18945138. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 168365/18945246. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^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. ------ 168366/18945273. ------ 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))((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. ------ 168367/18945327. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 168368/18945390. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 168369/18945417. ------ 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)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 168370/18945444. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.a))((b a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 168371/18945471. ------ 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))(^y1.(y1 y1)))) REDUCED to normal form. ------ 168372/18945534. ------ 1. ==[ start ]==> (((a a)(b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.b)((a a) a))) 3. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 168373/18945588. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 168374/18945615. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a b))(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a b))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 168375/18945642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.a)(b a))) 5. ==[ beta ]==> (((a a) a)((^y.a)(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(b a))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 168376/18945669. ------ 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 (^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. ------ 168377/18945696. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)((^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. ------ 168378/18945723. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b)(^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) 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. ------ 168379/18945750. ------ 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)))(^z1.(^x2.x2)))) 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. ------ 168380/18945975. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (b a))) 3. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 168381/18946083. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 168382/18946110. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 168383/18946137. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 168384/18946191. ------ 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)((a a) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)((a a) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)((a a) a))) 7. ==[ beta ]==> (((a a)(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 168385/18946272. ------ 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) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)((a a)(^y1.y1)))) 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. ------ 168386/18946389. ------ 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. ------ 168387/18946452. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 168388/18946479. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 168389/18946533. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 168390/18946560. ------ 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.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 168391/18946587. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 168392/18946614. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 168393/18946641. ------ 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.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(a (^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. ------ 168394/18946686. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 168395/18946722. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 168396/18946893. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(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. ------ 168397/18947001. ------ 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))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168398/18947010. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 168399/18947055. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((a b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(a (a a)))) 5. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 168400/18947082. ------ 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)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^y1.y1)(^z1.z1)))) 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. ------ 168401/18947136. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (a a))(a b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (a a))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (a a))(a b))) REDUCED to normal form. ------ 168402/18947217. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a a)(b a))) 3. ==[ beta ]==> (b ((a a)(b a))) REDUCED to normal form. ------ 168403/18947253. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 168404/18947280. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 168405/18947334. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^y1.(y1 y1)))) REDUCED to normal form. ------ 168406/18947361. ------ 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. ------ 168407/18947397. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 168408/18947424. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(a b))) REDUCED to normal form. ------ 168409/18947451. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 168410/18947478. ------ 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.(^z.z))((a a)(^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. ------ 168411/18947505. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.x1)(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(b a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(b a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^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. ------ 168412/18947559. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))(^a.(^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. ------ 168413/18947586. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 168414/18947613. ------ 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.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 168415/18947667. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))(^z1.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. ------ 168416/18947694. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((b (a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> ((b (a a))((^x.b)(^y.b))) 7. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 168417/18947721. ------ 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. ------ 168418/18947757. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(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. ------ 168419/18947892. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (((a a) a)(a (a a)))) REDUCED to normal form. ------ 168420/18948000. ------ 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))((^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. ------ 168421/18948063. ------ 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. ------ 168422/18948117. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.a))) REDUCED to normal form. ------ 168423/18948144. ------ 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) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 168424/18948225. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) 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. ------ 168425/18948252. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 168426/18948306. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 168427/18948360. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b) c)) REDUCED to normal form. ------ 168428/18948477. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.b))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 168429/18948504. ------ 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.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 168430/18948531. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^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. ------ 168431/18948747. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(b (^z.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 168432/18948801. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 168433/18949188. ------ 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. ------ 168434/18949215. ------ 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)(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))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 168435/18949251. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 168436/18949269. ------ 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. ------ 168437/18949350. ------ 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)((^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. ------ 168438/18949467. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 168439/18949494. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.a))) 7. ==[ beta ]==> ((b (^x.a))(^z.a)) 8. ==[ alpha ]==> ((b (^x.a))(^y.a)) REDUCED to normal form. ------ 168440/18949521. ------ 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 z)))) REDUCED to normal form. ------ 168441/18949584. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^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. ------ 168442/18949611. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a b)) REDUCED to normal form. ------ 168443/18949638. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(^z.z))) 5. ==[ beta ]==> ((a b)((^y.b)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.b)(^y.y))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 168444/18949692. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 168445/18949719. ------ 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))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 168446/18949746. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 168447/18949773. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 168448/18949800. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^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. ------ 168449/18949962. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (^c.a))) 2. ==[ alpha ]==> ((a ((^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. ------ 168450/18950358. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 168451/18950376. ------ 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. ------ 168452/18950403. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1) 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. ------ 168453/18950457. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b b)((a a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b b)((a a)((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b b)((a a)(^y.y))) 10. ==[ alpha ]==> ((b b)((a a)(^x.x))) REDUCED to normal form. ------ 168454/18950493. ------ 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)(^x2.x2))(^y2.y2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 168455/18950547. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 168456/18950574. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 168457/18950601. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 168458/18950655. ------ 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. ------ 168459/18950682. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a) c)) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a) c)) 5. ==[ beta ]==> ((b (^x.(x x)))(a c)) REDUCED to normal form. ------ 168460/18950763. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 168461/18950781. ------ 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. ------ 168462/18950826. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.a))) REDUCED to normal form. ------ 168463/18950853. ------ 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. ------ 168464/18950880. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 168465/18950907. ------ 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 y1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 168466/18950934. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 168467/18950961. ------ 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))((^x1.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. ------ 168468/18950988. ------ 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. ------ 168469/18951015. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(^z.z))) 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. ------ 168470/18951069. ------ 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.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.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. ------ 168471/18951096. ------ 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 z)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^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. ------ 168472/18951177. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^b.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. ------ 168473/18951204. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.(y y)))) REDUCED to normal form. ------ 168474/18951600. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 168475/18951618. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 168476/18951627. ------ 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. ------ 168477/18951645. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a b)) 3. ==[ beta ]==> ((a (a (^y.y)))(a b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(a b)) REDUCED to normal form. ------ 168478/18951654. ------ 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. ------ 168479/18951672. ------ 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)(a (a a))) 4. ==[ alpha ]==> ((^x.x)(a (a a))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 168480/18951765. ------ 1. ==[ start ]==> ((^a.b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 168481/18952206. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168482/18962385. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168483/18962430. ------ 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. ------ 168484/18962433. ------ 1. ==[ start ]==> ((a b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 168485/18962442. ------ 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. ------ 168486/18962466. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 168487/18962511. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b (^z.z)) c)) 3. ==[ beta ]==> (((b (^z.z)) c)(^y.y)) 4. ==[ alpha ]==> (((b (^x.x)) c)(^y.y)) REDUCED to normal form. ------ 168488/18962871. ------ 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. ------ 168489/18962874. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 168490/18963288. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) 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)(^x.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 168491/18963321. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^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)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168492/18963753. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y)) b)) 3. ==[ beta ]==> ((((b (^y.y)) b)((b (^y.y)) b))((b (^y.y)) b)) 4. ==[ alpha ]==> ((((b (^x.x)) b)((b (^y.y)) b))((b (^z.z)) b)) REDUCED to normal form. ------ 168493/18964899. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^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. ------ 168494/18965286. ------ 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. ------ 168495/18966840. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 168496/18967023. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 168497/18967662. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 168498/18968046. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z)) c)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 168499/18968553. ------ 1. ==[ start ]==> (((a b)(^c.a))(^c.(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(b a))) REDUCED to normal form. ------ 168500/18969363. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 168501/18970125. ------ 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. ------ 168502/18970542. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 168503/18971793. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.((^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. ------ 168504/18972090. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 168505/18972423. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.d)) 3. ==[ beta ]==> ((b (a (a a)))(^y.d)) 4. ==[ alpha ]==> ((b (a (a a)))(^x.d)) REDUCED to normal form. ------ 168506/18972540. ------ 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 ]==> ((^y.(y (^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^z.(^x1.(x1 x1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z)) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168507/18972927. ------ 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))) REDUCED to normal form. ------ 168508/18972945. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^a.(^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. ------ 168509/18972972. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^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. ------ 168510/18972981. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.b)) REDUCED to normal form. ------ 168511/18972999. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 168512/18973056. ------ 1. ==[ start ]==> ((a (^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 168513/18973083. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 168514/18973101. ------ 1. ==[ start ]==> ((a b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a b)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 168515/18973110. ------ 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. ------ 168516/18973137. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 168517/18973155. ------ 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. ------ 168518/18973182. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y)) c)) REDUCED to normal form. ------ 168519/18973245. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.b)(^b.(^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. ------ 168520/18973524. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(b ((^a.(^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 (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 168521/18973542. ------ 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)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 168522/18973560. ------ 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) 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. ------ 168523/18973632. ------ 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))((^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. ------ 168524/18973713. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((b a)((a a) a))) 3. ==[ beta ]==> ((a b)((b a)((a a) a))) REDUCED to normal form. ------ 168525/18973740. ------ 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. ------ 168526/18973767. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 168527/18973794. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 168528/18973821. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 168529/18973848. ------ 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. ------ 168530/18973956. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((b b)((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((b b)((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> ((b b)((a a)(^y.y))) 6. ==[ alpha ]==> ((b b)((a a)(^x.x))) REDUCED to normal form. ------ 168531/18973992. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^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)(^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. ------ 168532/18974082. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(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. ------ 168533/18974217. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 168534/18974289. ------ 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)(^y.y))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 168535/18974397. ------ 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 ]==> (((^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) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 168536/18974424. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x)) b)) REDUCED to normal form. ------ 168537/18974460. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.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. ------ 168538/18974514. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 168539/18974595. ------ 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. ------ 168540/18974622. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 168541/18974676. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 168542/18974928. ------ 1. ==[ start ]==> (((^a.b) a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 168543/18975090. ------ 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. ------ 168544/18975117. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a b) a)(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b) a)(a ((^x.x) b))) 5. ==[ beta ]==> (((a b) a)(a b)) REDUCED to normal form. ------ 168545/18975135. ------ 1. ==[ start ]==> (((^a.a)(a b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(c (^y.(a a)))) 3. ==[ beta ]==> ((a b)(c (^y.(a a)))) 4. ==[ alpha ]==> ((a b)(c (^x.(a a)))) REDUCED to normal form. ------ 168546/18975144. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 168547/18975297. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 168548/18975342. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 168549/18975369. ------ 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))(^z.b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((a a)(^y.b))) REDUCED to normal form. ------ 168550/18975396. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)(^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a b)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 168551/18975477. ------ 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. ------ 168552/18975504. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) 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. ------ 168553/18975540. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168554/18975567. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 168555/18975621. ------ 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))(^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. ------ 168556/18975756. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.b))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.b))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 168557/18975783. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(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. ------ 168558/18975900. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c ((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(c b)) REDUCED to normal form. ------ 168559/18975918. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 168560/18975927. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((a a)(a a)))) REDUCED to normal form. ------ 168561/18975954. ------ 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. ------ 168562/18976017. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y) c)) 3. ==[ beta ]==> (((a (^x.x))(a b)) c) REDUCED to normal form. ------ 168563/18976143. ------ 1. ==[ start ]==> (((^a.b) c)((a b)(a b))) 2. ==[ alpha ]==> (((^x.b) c)((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 168564/18976377. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b)(a (^a.a)))) 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. ------ 168565/18976485. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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. ------ 168566/18976620. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.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) REDUCED to normal form. ------ 168567/18976719. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b) b)) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 168568/18977196. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a b)((a a) a))) REDUCED to normal form. ------ 168569/18977304. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (b a))) REDUCED to normal form. ------ 168570/18977322. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a b))(c (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a b))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 168571/18977331. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 168572/18977403. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a 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. ------ 168573/18977511. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 168574/18977529. ------ 1. ==[ start ]==> (((a a)(b a))((a b)(^c.a))) 2. ==[ alpha ]==> (((a a)(b a))((a b)(^x.a))) REDUCED to normal form. ------ 168575/18977556. ------ 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)(^z.b))) REDUCED to normal form. ------ 168576/18977583. ------ 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)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a (a a))((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(a a)))) 9. ==[ beta ]==> ((a (a a))(^y.(a a))) 10. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 168577/18977610. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 168578/18977664. ------ 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))(^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. ------ 168579/18977691. ------ 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. ------ 168580/18977718. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) b) a)) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) b) a)) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^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. ------ 168581/18977745. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 168582/18977889. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((a a)((^z.a)(^x1.b))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 168583/18978087. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a)(a (^z.z)))) REDUCED to normal form. ------ 168584/18978114. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 168585/18978195. ------ 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. ------ 168586/18978222. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(a b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 168587/18978276. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 168588/18978303. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(b a))) REDUCED to normal form. ------ 168589/18978330. ------ 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. ------ 168590/18978375. ------ 1. ==[ start ]==> (((^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 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. ------ 168591/18978420. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 168592/18978447. ------ 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))(^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. ------ 168593/18978474. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 168594/18978528. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.b))) 7. ==[ beta ]==> ((a b)((^y.y)(^z.b))) 8. ==[ alpha ]==> ((a b)((^x.x)(^y.b))) 9. ==[ beta ]==> ((a b)(^y.b)) 10. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 168595/18978555. ------ 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. ------ 168596/18978582. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 168597/18978636. ------ 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))))) 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. ------ 168598/18978690. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a) b)) REDUCED to normal form. ------ 168599/18978717. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((a b)(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 168600/18978726. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^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. ------ 168601/18978753. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))(^x2.(x2 x2)))) 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. ------ 168602/18978888. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.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. ------ 168603/18979005. ------ 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))(a (^x1.x1)))) REDUCED to normal form. ------ 168604/18979032. ------ 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))) 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. ------ 168605/18979059. ------ 1. ==[ start ]==> (((a a)(^b.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 168606/18979086. ------ 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)(^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. ------ 168607/18979167. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)((^z.z)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168608/18979194. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 168609/18979221. ------ 1. ==[ start ]==> (((a b)(^c.a))((a a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(b a))) REDUCED to normal form. ------ 168610/18979320. ------ 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) 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. ------ 168611/18979392. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) b)((^y.y)(^z.a))) 6. ==[ alpha ]==> (((a a) b)((^x.x)(^y.a))) 7. ==[ beta ]==> (((a a) b)(^y.a)) 8. ==[ alpha ]==> (((a a) b)(^x.a)) REDUCED to normal form. ------ 168612/18979419. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))(^x1.b))) REDUCED to normal form. ------ 168613/18979446. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) 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. ------ 168614/18979527. ------ 1. ==[ start ]==> ((((a a) a)(a b))((b a) a)) REDUCED to normal form. ------ 168615/18979554. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 168616/18979752. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.a))(^c.(^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 ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168617/18979995. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c (^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168618/18980031. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) 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. ------ 168619/18980103. ------ 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))(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. ------ 168620/18980157. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(a (a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(a (a a)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 168621/18980238. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(a b))) 3. ==[ beta ]==> (b ((^y.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 168622/18980346. ------ 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.(^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. ------ 168623/18980580. ------ 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 a)) REDUCED to normal form. ------ 168624/18980607. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b) c)) 2. ==[ alpha ]==> (((a b)(a b))((^x.b) c)) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 168625/18980796. ------ 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. ------ 168626/18980886. ------ 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.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(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. ------ 168627/18980967. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168628/18981183. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^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. ------ 168629/18981210. ------ 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)((^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. ------ 168630/18981246. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 168631/18981273. ------ 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. ------ 168632/18981354. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(a ((^y.y)(^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. ------ 168633/18981381. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 168634/18981453. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(a a))) 3. ==[ beta ]==> ((^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. ------ 168635/18981579. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 168636/18981606. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 168637/18981633. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((a b) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b) a)) 5. ==[ beta ]==> ((a b)((a b) a)) REDUCED to normal form. ------ 168638/18981660. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a) b)) REDUCED to normal form. ------ 168639/18981687. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z)) c)) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y)) c)) 7. ==[ beta ]==> ((b a)((^y.y) c)) 8. ==[ alpha ]==> ((b a)((^x.x) c)) 9. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 168640/18981876. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b a)((^y.(^z.z)) c)) 6. ==[ alpha ]==> ((b a)((^x.(^y.y)) c)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 168641/18982047. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 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. ------ 168642/18982128. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 168643/18982236. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 168644/18982353. ------ 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 ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 168645/18982452. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b (^y.(^z.z)))) 7. ==[ beta ]==> ((b b)(b (^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 168646/18982461. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((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. ------ 168647/18982533. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(z z))(a (^x1.x1)))) 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. ------ 168648/18982542. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d c)) REDUCED to normal form. ------ 168649/18982569. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c d)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c d)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c d)) REDUCED to normal form. ------ 168650/18982641. ------ 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.(^x2.x2))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168651/18982704. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(c a)) REDUCED to normal form. ------ 168652/18982758. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 168653/18982794. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 168654/18982821. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 168655/18982902. ------ 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. ------ 168656/18982929. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) 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. ------ 168657/18982956. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 168658/18982983. ------ 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)))) 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. ------ 168659/18983010. ------ 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. ------ 168660/18983118. ------ 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)) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y)) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x)) a)) 5. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 168661/18983190. ------ 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 (^y.y))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 168662/18983208. ------ 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 ]==> ((^y.(y (^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(z z)))) 5. ==[ beta ]==> ((a (^z.(z z)))(^y.y)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 168663/18983595. ------ 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. ------ 168664/18983613. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^a.(^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. ------ 168665/18983622. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b a)) REDUCED to normal form. ------ 168666/18983640. ------ 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. ------ 168667/18983649. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a b)) REDUCED to normal form. ------ 168668/18983667. ------ 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)((^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. ------ 168669/18994464. ------ 1. ==[ start ]==> (((a a)(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 168670/18994479. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 168671/18994905. ------ 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) a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 168672/18994983. ------ 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. ------ 168673/18996147. ------ 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.(^z1.z1)) x1))) 3. ==[ eta ]==> (((a (^x.x))((^y.y)(^z.z)))(^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))) REDUCED to normal form. ------ 168674/18996279. ------ 1. ==[ start ]==> ((^a.(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((b a)((^y.y)(^z.z))) b) 4. ==[ alpha ]==> (((b a)((^x.x)(^y.y))) b) 5. ==[ beta ]==> (((b a)(^y.y)) b) 6. ==[ alpha ]==> (((b a)(^x.x)) b) REDUCED to normal form. ------ 168675/18996666. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(((b a)(^z.(^x1.x1)))((b a)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((b a)(^y.(^z.z)))((b a)(^x1.(^y1.y1))))) REDUCED to normal form. ------ 168676/18996912. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^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. ------ 168677/18997548. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((((^z.z)(^x1.x1))((a a)(^y1.y1)))(((^z.z)(^x1.x1))((a a)(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1))))(^x2.x2)) 5. ==[ beta ]==> ((((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1))))(^x2.x2)) 6. ==[ alpha ]==> ((((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1))))(^z1.z1)) 7. ==[ beta ]==> ((((a a)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1))))(^z1.z1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(((^y.y)(^z.z))((a a)(^x1.x1))))(^y1.y1)) 9. ==[ beta ]==> ((((a a)(^x.x))((^z.z)((a a)(^x1.x1))))(^y1.y1)) 10. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)((a a)(^z.z))))(^x1.x1)) 11. ==[ beta ]==> ((((a a)(^x.x))((a a)(^z.z)))(^x1.x1)) 12. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 168678/18998028. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((a a)(a a)))) REDUCED to normal form. ------ 168679/18998730. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 168680/18998853. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^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. ------ 168681/18999744. ------ 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. ------ 168682/19000566. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 168683/19000593. ------ 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.(^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. ------ 168684/19001646. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 168685/19001898. ------ 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.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.((z z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 168686/19003299. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168687/19004103. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(^b.(^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. ------ 168688/19004118. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 168689/19004220. ------ 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. ------ 168690/19004463. ------ 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. ------ 168691/19004541. ------ 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 ]==> (((a a)((^z.z) a))(((a a)((^z.z) a))(^y.y))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)((^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. ------ 168692/19004958. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.x1)) 3. ==[ beta ]==> (((^z.z)(^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. ------ 168693/19004967. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 168694/19004994. ------ 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. ------ 168695/19005087. ------ 1. ==[ start ]==> (((^a.a) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (a ((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168696/19005114. ------ 1. ==[ start ]==> (((a a) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 168697/19005132. ------ 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. ------ 168698/19005141. ------ 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. ------ 168699/19005159. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 168700/19005168. ------ 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 ((^z.z)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 168701/19005213. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 168702/19005276. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 168703/19005357. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(^a.a))(^b.(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. ------ 168704/19005438. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 168705/19005465. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 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. ------ 168706/19005492. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 168707/19005582. ------ 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. ------ 168708/19005609. ------ 1. ==[ start ]==> (((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 a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^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. ------ 168709/19005636. ------ 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. ------ 168710/19005663. ------ 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. ------ 168711/19005906. ------ 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. ------ 168712/19005933. ------ 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) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 168713/19005960. ------ 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)))) REDUCED to normal form. ------ 168714/19005987. ------ 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. ------ 168715/19006023. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^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. ------ 168716/19006050. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.(^z1.z1)))) 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. ------ 168717/19006104. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 9. ==[ beta ]==> (b (^y.(y y))) 10. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 168718/19006113. ------ 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. ------ 168719/19006140. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 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. ------ 168720/19006158. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b a)(^c.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. ------ 168721/19006185. ------ 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. ------ 168722/19006221. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 168723/19006239. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 168724/19006248. ------ 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. ------ 168725/19006482. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 168726/19006653. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 168727/19006707. ------ 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. ------ 168728/19006734. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(a a))(^b.b))) 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. ------ 168729/19006761. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 168730/19006797. ------ 1. ==[ start ]==> (((a a)((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(b (b (^x.x)))) REDUCED to normal form. ------ 168731/19006824. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^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. ------ 168732/19006851. ------ 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. ------ 168733/19006878. ------ 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. ------ 168734/19006905. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 168735/19006932. ------ 1. ==[ start ]==> ((((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)))) REDUCED to normal form. ------ 168736/19006959. ------ 1. ==[ start ]==> ((a (a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a (a b))((b a)(^y.y))) 4. ==[ alpha ]==> ((a (a b))((b a)(^x.x))) REDUCED to normal form. ------ 168737/19007166. ------ 1. ==[ start ]==> (((a a)(^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(c (^y.(a a)))) REDUCED to normal form. ------ 168738/19007238. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(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))) REDUCED to normal form. ------ 168739/19007274. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 168740/19007301. ------ 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) 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. ------ 168741/19007319. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((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. ------ 168742/19007328. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 168743/19007346. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 168744/19007517. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 168745/19007562. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))(^c.(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 a) REDUCED to normal form. ------ 168746/19007643. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 168747/19007787. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 168748/19007814. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 168749/19007895. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.(y y))(^z.(^x1.(^y1.y1))))((^y.(y y))(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 9. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 10. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3))))) 11. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3))))) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168750/19007922. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 168751/19007949. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))(^c.(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. ------ 168752/19008012. ------ 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. ------ 168753/19008039. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b)(a (^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. ------ 168754/19008066. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a) a))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> ((a ((a a) a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 168755/19008093. ------ 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)(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. ------ 168756/19008120. ------ 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)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (a 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. ------ 168757/19008147. ------ 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. ------ 168758/19008174. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a b)(a b))) REDUCED to normal form. ------ 168759/19008201. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 168760/19008228. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 168761/19008399. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 168762/19008408. ------ 1. ==[ start ]==> (((a b) c)((^b.b)(a (^a.a)))) 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. ------ 168763/19008435. ------ 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. ------ 168764/19008480. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 168765/19008516. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 168766/19008543. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.b)(a b))) 3. ==[ beta ]==> ((a (^y.b))((^z.b)(a b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.b)(a b))) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 168767/19008561. ------ 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.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 168768/19008597. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168769/19008624. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((b a)(b a))) REDUCED to normal form. ------ 168770/19008642. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^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. ------ 168771/19008651. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 168772/19008678. ------ 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.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 168773/19008705. ------ 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)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 168774/19009074. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a)) a)) 5. ==[ beta ]==> (b ((^z.(a a)) a)) 6. ==[ alpha ]==> (b ((^x.(a a)) a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 168775/19009353. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168776/19009407. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 168777/19009425. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^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. ------ 168778/19009434. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(a a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 168779/19009461. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 168780/19009533. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^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. ------ 168781/19010100. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 168782/19010154. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 168783/19010352. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 168784/19010397. ------ 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))((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. ------ 168785/19010406. ------ 1. ==[ start ]==> (((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 a))) 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. ------ 168786/19010424. ------ 1. ==[ start ]==> ((a (^b.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 168787/19010703. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168788/19010748. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z)) c)) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z)) 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. ------ 168789/19011216. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 168790/19011243. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.a))) REDUCED to normal form. ------ 168791/19011270. ------ 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.(^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. ------ 168792/19011342. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^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. ------ 168793/19011351. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 168794/19011378. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.b)(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(a (a a)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 168795/19012053. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b (^y.(^z.z)))) 3. ==[ beta ]==> ((b b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 168796/19012098. ------ 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.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. ------ 168797/19012125. ------ 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.(^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. ------ 168798/19012134. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 168799/19012161. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b)((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 168800/19012179. ------ 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 a)(b a))(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 168801/19012242. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 168802/19012260. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.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. ------ 168803/19012269. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(a b))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 168804/19012323. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 168805/19012368. ------ 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. ------ 168806/19012377. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 168807/19012404. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 168808/19012548. ------ 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. ------ 168809/19012575. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(a ((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 168810/19012602. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(a a))) REDUCED to normal form. ------ 168811/19012629. ------ 1. ==[ start ]==> (((a b)(a b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a b)(a (^x.x)))) REDUCED to normal form. ------ 168812/19012656. ------ 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. ------ 168813/19012683. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^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)(^x.x))(^y.y))((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(a (a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 168814/19012737. ------ 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 a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a ((a a) a))) REDUCED to normal form. ------ 168815/19012764. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 168816/19012791. ------ 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)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a)(a a))) REDUCED to normal form. ------ 168817/19012908. ------ 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)(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(z2 z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))(^z2.(z2 z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168818/19012989. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168819/19013133. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 168820/19013160. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 168821/19013286. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 168822/19013403. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c (^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))(c (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(c (^y.a))) REDUCED to normal form. ------ 168823/19013475. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a b)(^x1.x1))) 3. ==[ beta ]==> ((^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. ------ 168824/19013484. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 168825/19013511. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.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) REDUCED to normal form. ------ 168826/19013538. ------ 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) 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. ------ 168827/19013790. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 168828/19013817. ------ 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. ------ 168829/19013871. ------ 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. ------ 168830/19013898. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b a)((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> ((b a)((^x.x)(a (^y.y)))) 9. ==[ beta ]==> ((b a)(a (^y.y))) 10. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 168831/19013925. ------ 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. ------ 168832/19013979. ------ 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)(^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. ------ 168833/19014069. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 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. ------ 168834/19014150. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 168835/19014258. ------ 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. ------ 168836/19014393. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((^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. ------ 168837/19014420. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(y y)) c)) 5. ==[ beta ]==> ((^y.(y y)) c) 6. ==[ alpha ]==> ((^x.(x x)) c) 7. ==[ beta ]==> (c c) REDUCED to normal form. ------ 168838/19014483. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 168839/19014555. ------ 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. ------ 168840/19014564. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 168841/19014591. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 168842/19014618. ------ 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. ------ 168843/19014663. ------ 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)(^x2.x2)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168844/19014672. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^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. ------ 168845/19014699. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 168846/19014726. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 168847/19014780. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 168848/19014798. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 168849/19014816. ------ 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. ------ 168850/19014843. ------ 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 (^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. ------ 168851/19014870. ------ 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.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. ------ 168852/19014897. ------ 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. ------ 168853/19014978. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c c)) REDUCED to normal form. ------ 168854/19015113. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b ((^y.y) a))) 3. ==[ beta ]==> ((b (a (a a)))(b ((^y.y) a))) 4. ==[ alpha ]==> ((b (a (a a)))(b ((^x.x) a))) 5. ==[ beta ]==> ((b (a (a a)))(b a)) REDUCED to normal form. ------ 168855/19015140. ------ 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. ------ 168856/19015194. ------ 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 (^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)))) REDUCED to normal form. ------ 168857/19015212. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^b.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. ------ 168858/19015221. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)((^y.y) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a a) a)) REDUCED to normal form. ------ 168859/19015617. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 168860/19015635. ------ 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)(^y.y))((^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. ------ 168861/19015644. ------ 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. ------ 168862/19015662. ------ 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))) REDUCED to normal form. ------ 168863/19015671. ------ 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. ------ 168864/19015689. ------ 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)((a a) a)) 4. ==[ alpha ]==> ((^x.x)((a a) a)) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 168865/19015742. ------ 1. ==[ start ]==> (^a.((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (^x.((^y.(y y))((x x)(x x)))) 3. ==[ beta ]==> (^x.(((x x)(x x))((x x)(x x)))) REDUCED to normal form. ------ 168866/19015743. ------ 1. ==[ start ]==> (a ((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (a ((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (a (((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 168867/19016691. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^a.(^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. ------ 168868/19023495. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^a.(^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. ------ 168869/19025475. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.((^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))) REDUCED to normal form. ------ 168870/19026423. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a))) a) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a))) a) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 168871/19026429. ------ 1. ==[ start ]==> ((^a.a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 4. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 168872/19026456. ------ 1. ==[ start ]==> ((^a.(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.a)(b (^z.z)))((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.a)(b (^y.y)))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> (a ((^z.a)(b (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168873/19026483. ------ 1. ==[ start ]==> ((^a.b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 168874/19026753. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 168875/19026924. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 168876/19026945. ------ 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) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 168877/19027248. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 168878/19027374. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(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. ------ 168879/19027377. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^a.(^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. ------ 168880/19027782. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a a)(^x.((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)(^x.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 168881/19028139. ------ 1. ==[ start ]==> ((^a.(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(c ((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 168882/19028913. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.a)((^x1.x1) b))((^z.a)((^x1.x1) b)))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)((^z.z) b))((^x1.a)((^y1.y1) b)))) 5. ==[ beta ]==> (((^y.a)((^z.z) b))((^x1.a)((^y1.y1) b))) 6. ==[ alpha ]==> (((^x.a)((^y.y) b))((^z.a)((^x1.x1) b))) 7. ==[ beta ]==> (a ((^z.a)((^x1.x1) b))) 8. ==[ alpha ]==> (a ((^x.a)((^y.y) b))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 168883/19030437. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.((z z)(z z)))) 5. ==[ beta ]==> (b (^z.((z z)(z z)))) 6. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 168884/19031103. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))((^y.y) a))(^x1.x1)) 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)) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 168885/19032912. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^b.(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(x a))) REDUCED to normal form. ------ 168886/19033098. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((((^y.(y y))(^z.b))((^y.(y y))(^z.b)))(((^y.(y y))(^z.b))((^y.(y y))(^z.b)))) 4. ==[ alpha ]==> ((((^x.(x x))(^y.b))((^z.(z z))(^x1.b)))(((^y1.(y1 y1))(^z1.b))((^x2.(x2 x2))(^y2.b)))) 5. ==[ beta ]==> ((((^y.b)(^y.b))((^z.(z z))(^x1.b)))(((^y1.(y1 y1))(^z1.b))((^x2.(x2 x2))(^y2.b)))) 6. ==[ alpha ]==> ((((^x.b)(^y.b))((^z.(z z))(^x1.b)))(((^y1.(y1 y1))(^z1.b))((^x2.(x2 x2))(^y2.b)))) 7. ==[ beta ]==> ((b ((^z.(z z))(^x1.b)))(((^y1.(y1 y1))(^z1.b))((^x2.(x2 x2))(^y2.b)))) 8. ==[ alpha ]==> ((b ((^x.(x x))(^y.b)))(((^z.(z z))(^x1.b))((^y1.(y1 y1))(^z1.b)))) 9. ==[ beta ]==> ((b ((^y.b)(^y.b)))(((^z.(z z))(^x1.b))((^y1.(y1 y1))(^z1.b)))) 10. ==[ alpha ]==> ((b ((^x.b)(^y.b)))(((^z.(z z))(^x1.b))((^y1.(y1 y1))(^z1.b)))) 11. ==[ beta ]==> ((b b)(((^z.(z z))(^x1.b))((^y1.(y1 y1))(^z1.b)))) 12. ==[ alpha ]==> ((b b)(((^x.(x x))(^y.b))((^z.(z z))(^x1.b)))) 13. ==[ beta ]==> ((b b)(((^y.b)(^y.b))((^z.(z z))(^x1.b)))) 14. ==[ alpha ]==> ((b b)(((^x.b)(^y.b))((^z.(z z))(^x1.b)))) 15. ==[ beta ]==> ((b b)(b ((^z.(z z))(^x1.b)))) 16. ==[ alpha ]==> ((b b)(b ((^x.(x x))(^y.b)))) 17. ==[ beta ]==> ((b b)(b ((^y.b)(^y.b)))) 18. ==[ alpha ]==> ((b b)(b ((^x.b)(^y.b)))) 19. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 168887/19033686. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 168888/19033938. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 168889/19034178. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 168890/19034181. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 168891/19035018. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) a)((^y.y) b)) a) 4. ==[ beta ]==> ((a ((^y.y) b)) a) 5. ==[ alpha ]==> ((a ((^x.x) b)) a) 6. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 168892/19036158. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 168893/19036161. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 168894/19036287. ------ 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.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 168895/19036395. ------ 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. ------ 168896/19036503. ------ 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 z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 168897/19036581. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^b.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. ------ 168898/19037007. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 168899/19037052. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 168900/19037106. ------ 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))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 168901/19037118. ------ 1. ==[ start ]==> ((a a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 168902/19037145. ------ 1. ==[ start ]==> ((a (a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 168903/19037172. ------ 1. ==[ start ]==> ((a b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 168904/19037190. ------ 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. ------ 168905/19037217. ------ 1. ==[ start ]==> (((^a.a) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) b)((a (a (^y.y))) a)) 3. ==[ beta ]==> (b ((a (a (^y.y))) a)) 4. ==[ alpha ]==> (b ((a (a (^x.x))) a)) REDUCED to normal form. ------ 168906/19037226. ------ 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. ------ 168907/19037244. ------ 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) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 168908/19037271. ------ 1. ==[ start ]==> (((a a) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a) b)((b (^x.x)) c)) REDUCED to normal form. ------ 168909/19037442. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 168910/19037613. ------ 1. ==[ start ]==> ((a (^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.(x x)))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 168911/19037631. ------ 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)(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 168912/19037721. ------ 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) a))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((^y.y) a))(((a a)(a a))((^y.y) a))) 6. ==[ alpha ]==> ((((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))((^y.y) a))) 8. ==[ alpha ]==> ((((a a)(a a)) a)(((a a)(a a))((^x.x) a))) 9. ==[ beta ]==> ((((a a)(a a)) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 168913/19037748. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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. ------ 168914/19037802. ------ 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)(^y.y))((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. ------ 168915/19037829. ------ 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. ------ 168916/19037856. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(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. ------ 168917/19037910. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((a a) a)(b a))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(b a))) REDUCED to normal form. ------ 168918/19037937. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 168919/19038063. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(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))))) REDUCED to normal form. ------ 168920/19038162. ------ 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. ------ 168921/19038189. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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)))) REDUCED to normal form. ------ 168922/19038216. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 168923/19038243. ------ 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))(^x1.b))) REDUCED to normal form. ------ 168924/19038270. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a))((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 168925/19038297. ------ 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. ------ 168926/19038360. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 168927/19038387. ------ 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. ------ 168928/19038414. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((^y.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)((a a)(a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 168929/19038441. ------ 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. ------ 168930/19038468. ------ 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)((^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. ------ 168931/19038828. ------ 1. ==[ start ]==> ((a (^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(c ((a a)(a a)))) REDUCED to normal form. ------ 168932/19039017. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 168933/19039098. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)((^z.z)(a a)))) IRREDUCIBLE: cycle. ------ 168934/19039179. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 168935/19039206. ------ 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))) 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. ------ 168936/19039233. ------ 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)((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. ------ 168937/19039296. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 168938/19039323. ------ 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 REDUCED to normal form. ------ 168939/19039350. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 168940/19039377. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 168941/19039467. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))(a b))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a b))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 168942/19039494. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 168943/19039548. ------ 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. ------ 168944/19039566. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 168945/19039575. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)(a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b)(a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 168946/19039602. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (a a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 168947/19039989. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 168948/19040313. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 168949/19040457. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) c)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b) c)(b (^x.(^y.y)))) REDUCED to normal form. ------ 168950/19040484. ------ 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. ------ 168951/19040511. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(^y.(y y)))) REDUCED to normal form. ------ 168952/19040565. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.a))) REDUCED to normal form. ------ 168953/19040592. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)(^z.b))) 3. ==[ beta ]==> ((a (^y.b))((a b)(^z.b))) 4. ==[ alpha ]==> ((a (^x.b))((a b)(^y.b))) REDUCED to normal form. ------ 168954/19040646. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168955/19040700. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 168956/19040727. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 168957/19040817. ------ 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)(^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. ------ 168958/19040844. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 168959/19040925. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(a a))(^c.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. ------ 168960/19040952. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a b) a)((^y.b)(^z.b))) 4. ==[ alpha ]==> (((a b) a)((^x.b)(^y.b))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 168961/19041006. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(^a.a))(^c.(^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. ------ 168962/19041123. ------ 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. ------ 168963/19041204. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((b a)((^z.z) a))) 3. ==[ beta ]==> (b ((b a)((^z.z) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 168964/19041312. ------ 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. ------ 168965/19041339. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1)(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. ------ 168966/19041393. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) a)(b a))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(b a))) 5. ==[ beta ]==> (((a b)(a b))(a (b a))) REDUCED to normal form. ------ 168967/19041483. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 168968/19041510. ------ 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)))(^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)))) REDUCED to normal form. ------ 168969/19041537. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)(^x1.a))) REDUCED to normal form. ------ 168970/19041600. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 168971/19041627. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 168972/19041681. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 168973/19041708. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.(y y))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 168974/19041735. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 168975/19041762. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(a (^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. ------ 168976/19041789. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^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. ------ 168977/19041816. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 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. ------ 168978/19041861. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 168979/19042149. ------ 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.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. ------ 168980/19042158. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 168981/19042176. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 168982/19042203. ------ 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) 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. ------ 168983/19042257. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((a b)((^y.y)(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x)(^y.y)))) 9. ==[ beta ]==> (((a a)(a a))((a b)(^y.y))) 10. ==[ alpha ]==> (((a a)(a a))((a b)(^x.x))) REDUCED to normal form. ------ 168984/19042338. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 168985/19042455. ------ 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)))(^z1.z1))) REDUCED to normal form. ------ 168986/19042518. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 168987/19042545. ------ 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. ------ 168988/19042572. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 168989/19042599. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 168990/19042626. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 168991/19042653. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(((^z.z)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((a b)(^x.x))((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> (((a b)(^x.x))((a a)((^y.y)(a a)))) 9. ==[ beta ]==> (((a b)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 168992/19042680. ------ 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) REDUCED to normal form. ------ 168993/19042707. ------ 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))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 168994/19042752. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 168995/19042761. ------ 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)))(^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. ------ 168996/19042959. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(d ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(d ((^z.z)(a a)))) 3. ==[ beta ]==> (b (d ((^z.z)(a a)))) 4. ==[ alpha ]==> (b (d ((^x.x)(a a)))) 5. ==[ beta ]==> (b (d (a a))) REDUCED to normal form. ------ 168997/19043067. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^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. ------ 168998/19043103. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z)) c)) 3. ==[ beta ]==> ((b a)((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((b a)((^x.(^y.y)) c)) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 168999/19043121. ------ 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) a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(((^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 ((a a)((^y.y) a))) 8. ==[ alpha ]==> (b ((a a)((^x.x) a))) 9. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 169000/19043148. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((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. ------ 169001/19043202. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)((a a) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)((a a) a))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a) a)) REDUCED to normal form. ------ 169002/19043283. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((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. ------ 169003/19043346. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a)(^z.z))) REDUCED to normal form. ------ 169004/19043400. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.a))) REDUCED to normal form. ------ 169005/19043427. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)(^z.(z z)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(^y.(y y)))) REDUCED to normal form. ------ 169006/19043463. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 169007/19043490. ------ 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.(^y1.y1))((a a) 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. ------ 169008/19043517. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(y y))(a b))) 3. ==[ beta ]==> ((a (b a))((^y.(y y))(a b))) 4. ==[ alpha ]==> ((a (b a))((^x.(x x))(a b))) 5. ==[ beta ]==> ((a (b a))((a b)(a b))) REDUCED to normal form. ------ 169009/19043544. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) a) REDUCED to normal form. ------ 169010/19043571. ------ 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.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 169011/19043598. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(b a))) 3. ==[ beta ]==> ((((a a) a)(a b))(b a)) REDUCED to normal form. ------ 169012/19043679. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 169013/19043760. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))(^c.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. ------ 169014/19043787. ------ 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. ------ 169015/19043823. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(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. ------ 169016/19043958. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((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. ------ 169017/19044066. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169018/19044183. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 169019/19044210. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a b)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.a))) REDUCED to normal form. ------ 169020/19044291. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (a a))(^y.a))) REDUCED to normal form. ------ 169021/19044318. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.b))(a (^z.b))) 4. ==[ alpha ]==> (((a b)(^x.b))(a (^y.b))) REDUCED to normal form. ------ 169022/19044372. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 169023/19044426. ------ 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. ------ 169024/19044453. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b) c)) REDUCED to normal form. ------ 169025/19044516. ------ 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. ------ 169026/19044543. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.a))) 7. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 169027/19044570. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 169028/19044597. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 169029/19044813. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c (^z.b))) 3. ==[ beta ]==> ((b (a (^y.y)))(c (^z.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c (^y.b))) REDUCED to normal form. ------ 169030/19044840. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(b (^x.(a a)))) REDUCED to normal form. ------ 169031/19044867. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 169032/19045182. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z)) d)) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z)) d)) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y)) d)) 5. ==[ beta ]==> ((b c)((^y.y) d)) 6. ==[ alpha ]==> ((b c)((^x.x) d)) 7. ==[ beta ]==> ((b c) d) REDUCED to normal form. ------ 169033/19045254. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c ((a a) a))) 3. ==[ beta ]==> ((b (^y.y))(c ((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))(c ((a a) a))) REDUCED to normal form. ------ 169034/19045281. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(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. ------ 169035/19045317. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 169036/19045335. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b)(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b)(a a))) REDUCED to normal form. ------ 169037/19045344. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 169038/19045416. ------ 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 (a a)))) 3. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 169039/19045533. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b)(^x1.x1))) REDUCED to normal form. ------ 169040/19045560. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a)(^a.(^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. ------ 169041/19045587. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 169042/19045650. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 169043/19045677. ------ 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))) 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. ------ 169044/19045704. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(a b))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^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. ------ 169045/19045731. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 169046/19045758. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 169047/19045785. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^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. ------ 169048/19045812. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (((a b)(a a))((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 169049/19045839. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 169050/19046442. ------ 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.y1))(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 169051/19046469. ------ 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. ------ 169052/19046523. ------ 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. ------ 169053/19046613. ------ 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. ------ 169054/19046640. ------ 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) a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) 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. ------ 169055/19046667. ------ 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))(^x1.(x1 x1)))) REDUCED to normal form. ------ 169056/19046721. ------ 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)(^z1.z1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 169057/19046748. ------ 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. ------ 169058/19046775. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a c)) REDUCED to normal form. ------ 169059/19046847. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 169060/19046946. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(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. ------ 169061/19046973. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a (^b.(^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)))) REDUCED to normal form. ------ 169062/19047000. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(a a))) 3. ==[ beta ]==> ((((a a) a)(b a))((a a)(a a))) REDUCED to normal form. ------ 169063/19047027. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 169064/19047054. ------ 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.y1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 169065/19047081. ------ 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. ------ 169066/19047135. ------ 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.(^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. ------ 169067/19047162. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(^b.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. ------ 169068/19047189. ------ 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 z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^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. ------ 169069/19047270. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.a))) REDUCED to normal form. ------ 169070/19047279. ------ 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 ]==> (((a a)((^z.z) a))(^y.y)) 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. ------ 169071/19047666. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^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. ------ 169072/19047684. ------ 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. ------ 169073/19047693. ------ 1. ==[ start ]==> (((a (a (^a.a))) 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. ------ 169074/19047711. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b a)) 3. ==[ beta ]==> ((a (a (^y.y)))(b a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(b a)) REDUCED to normal form. ------ 169075/19047720. ------ 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. ------ 169076/19047738. ------ 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)(a b)) 4. ==[ alpha ]==> ((^x.x)(a b)) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 169077/19047792. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 169078/19047894. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 169079/19057533. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 169080/19058481. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a))) b) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a))) b) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) b) REDUCED to normal form. ------ 169081/19058505. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169082/19058586. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 169083/19058589. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 169084/19058631. ------ 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)) a) b)(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 169085/19058748. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 169086/19059453. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^a.(^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. ------ 169087/19059873. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((((^y.(^z.z)) a) a)(((^y.(^z.z)) a) a))(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (((((^x.(^y.y)) a) a)(((^z.(^x1.x1)) a) a))(((^y1.(^z1.z1)) a) a)) 5. ==[ beta ]==> ((((^y.y) a)(((^z.(^x1.x1)) a) a))(((^y1.(^z1.z1)) a) a)) 6. ==[ alpha ]==> ((((^x.x) a)(((^y.(^z.z)) a) a))(((^x1.(^y1.y1)) a) a)) 7. ==[ beta ]==> ((a (((^y.(^z.z)) a) a))(((^x1.(^y1.y1)) a) a)) 8. ==[ alpha ]==> ((a (((^x.(^y.y)) a) a))(((^z.(^x1.x1)) a) a)) 9. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a) a)) 10. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a) a)) 11. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) a)) 12. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) a)) 13. ==[ beta ]==> ((a a)((^y.y) a)) 14. ==[ alpha ]==> ((a a)((^x.x) a)) 15. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 169088/19060206. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 169089/19060650. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 169090/19060773. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.(^y1.y1)))(a (a a)))((^z.(^x1.(^y1.y1)))(a (a a))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.(^x1.x1)))(a (a a)))((^y1.(^z1.(^x2.x2)))(a (a a))))) 5. ==[ beta ]==> (^x.((^z.(^x1.x1))((^y1.(^z1.(^x2.x2)))(a (a a))))) 6. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a))))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169091/19060980. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)(^x1.x1))(((^z.z) a)(^x1.x1)))) 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 (^x.x))(a (^z.z))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 169092/19062504. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.(^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. ------ 169093/19062837. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.((^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. ------ 169094/19062855. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.(^z.(y y)))) 3. ==[ beta ]==> (b (^y.(^z.(y y)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 169095/19063248. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((b a) c)) 3. ==[ beta ]==> (((b a) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((b a) c)(^x.(^y.y))) REDUCED to normal form. ------ 169096/19063827. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^a.(^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. ------ 169097/19063851. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169098/19064166. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a) b)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a) b)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 169099/19064700. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(b a))) REDUCED to normal form. ------ 169100/19064979. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(^d.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.a))) REDUCED to normal form. ------ 169101/19066698. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^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. ------ 169102/19066905. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^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. ------ 169103/19067085. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.b))) 5. ==[ beta ]==> ((a b)(^y.(^z.b))) 6. ==[ alpha ]==> ((a b)(^x.(^y.b))) REDUCED to normal form. ------ 169104/19067805. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y) a)(^z.((z z) z))) 4. ==[ alpha ]==> (((^x.x) a)(^y.((y y) y))) 5. ==[ beta ]==> (a (^y.((y y) y))) 6. ==[ alpha ]==> (a (^x.((x x) x))) REDUCED to normal form. ------ 169105/19068093. ------ 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.((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169106/19068225. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 169107/19068228. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 169108/19068462. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(z z)))) REDUCED to normal form. ------ 169109/19069047. ------ 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. ------ 169110/19069092. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(^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)))) REDUCED to normal form. ------ 169111/19069119. ------ 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)) REDUCED to normal form. ------ 169112/19069173. ------ 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))((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 169113/19069203. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 169114/19069230. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 169115/19069257. ------ 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. ------ 169116/19069284. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 169117/19069302. ------ 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. ------ 169118/19069329. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) b)) 5. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 169119/19069419. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 169120/19069446. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 169121/19069527. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(a a))(^c.(^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. ------ 169122/19069608. ------ 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. ------ 169123/19069734. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 169124/19069779. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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)))) REDUCED to normal form. ------ 169125/19069860. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((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 (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 169126/19069887. ------ 1. ==[ start ]==> (((a (a a)) a)((b a)((a a) a))) REDUCED to normal form. ------ 169127/19069914. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 169128/19069941. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))((a a)(a a))) REDUCED to normal form. ------ 169129/19069968. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 169130/19069995. ------ 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. ------ 169131/19070103. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((b b)((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 169132/19070148. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169133/19070283. ------ 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.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169134/19070364. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 169135/19070436. ------ 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))(^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)(^x.x))((^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. ------ 169136/19070463. ------ 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. ------ 169137/19070571. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) a)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) a)) 5. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 169138/19070661. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 169139/19070769. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(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. ------ 169140/19070904. ------ 1. ==[ start ]==> ((a (^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 169141/19071075. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 169142/19071237. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(b a))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(b a))) 5. ==[ beta ]==> ((((a a) a) b)(b a)) REDUCED to normal form. ------ 169143/19071264. ------ 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. ------ 169144/19071291. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.b))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.b))(a b)) REDUCED to normal form. ------ 169145/19071345. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(b (^z.z)))) REDUCED to normal form. ------ 169146/19071444. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 169147/19071471. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 169148/19071489. ------ 1. ==[ start ]==> (((a a)(a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 169149/19071543. ------ 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))(^y1.b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.b))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 169150/19071570. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)(^x.(a a)))) REDUCED to normal form. ------ 169151/19071651. ------ 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. ------ 169152/19071678. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) 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. ------ 169153/19071687. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169154/19071714. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 169155/19071849. ------ 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)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 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. ------ 169156/19071930. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.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. ------ 169157/19072065. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 169158/19072074. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(c b)) REDUCED to normal form. ------ 169159/19072101. ------ 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. ------ 169160/19072164. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 169161/19072191. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y) c)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) c)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) c)) 5. ==[ beta ]==> ((a ((a a) a)) c) REDUCED to normal form. ------ 169162/19072290. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)(((^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. ------ 169163/19072524. ------ 1. ==[ start ]==> (((^a.b)(^b.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 a)) REDUCED to normal form. ------ 169164/19072686. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.b)(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.b)(a b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)(a b))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 169165/19072767. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 169166/19072866. ------ 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. ------ 169167/19072893. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) b) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b) b)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b) b)) 5. ==[ beta ]==> (((a (^x.x))(a a))(b b)) REDUCED to normal form. ------ 169168/19072920. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.(^z.z))) c)) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 169169/19073199. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 169170/19073343. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)((^y.y)(^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. ------ 169171/19073451. ------ 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))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 169172/19073478. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a (b a))) REDUCED to normal form. ------ 169173/19073532. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 169174/19073550. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(a (^y.(a a)))) 3. ==[ beta ]==> (b (a (^y.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 169175/19073676. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(a a))(^b.(^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. ------ 169176/19073703. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 169177/19073730. ------ 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)(^z.b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a 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. ------ 169178/19073757. ------ 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.(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^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. ------ 169179/19073838. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 169180/19073865. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a a)(^b.b))) 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))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 169181/19073892. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b a)) REDUCED to normal form. ------ 169182/19073946. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a) c)) REDUCED to normal form. ------ 169183/19074036. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((a a)((^z.b)(^x1.a))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.a))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 169184/19074117. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(a a))(^c.(^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. ------ 169185/19074234. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 169186/19074261. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a)(a (^x1.x1)))) REDUCED to normal form. ------ 169187/19074342. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a b)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)(^y.y))) REDUCED to normal form. ------ 169188/19074369. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)((a a) a))) 5. ==[ beta ]==> ((^y.b)(((a a) a)((a a) a))) 6. ==[ alpha ]==> ((^x.b)(((a a) a)((a a) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 169189/19074423. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 169190/19074450. ------ 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) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 169191/19074477. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.z))(b a))) REDUCED to normal form. ------ 169192/19074522. ------ 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))(a (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169193/19074549. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 169194/19074567. ------ 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. ------ 169195/19074594. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 169196/19074621. ------ 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.(x1 x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 169197/19074648. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a 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. ------ 169198/19074675. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 169199/19074702. ------ 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))(^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))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.b)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.b)) REDUCED to normal form. ------ 169200/19074729. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 169201/19074837. ------ 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)) REDUCED to normal form. ------ 169202/19074864. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a) b)) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a) b)) 3. ==[ beta ]==> ((a b)((b a) b)) REDUCED to normal form. ------ 169203/19075035. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 169204/19075152. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a)(a a))) REDUCED to normal form. ------ 169205/19075179. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 169206/19075206. ------ 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) 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. ------ 169207/19075233. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(a (a a)))) REDUCED to normal form. ------ 169208/19075314. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))((a (a a))(a b))) 6. ==[ alpha ]==> ((^x.(a a))((a (a a))(a b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169209/19075341. ------ 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.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(a (a a))) REDUCED to normal form. ------ 169210/19075359. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 169211/19075368. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 169212/19075395. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 169213/19075539. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)(^b.(^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. ------ 169214/19075593. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))(^y.b))) 3. ==[ beta ]==> ((a (b a))((a (a a))(^y.b))) 4. ==[ alpha ]==> ((a (b a))((a (a a))(^x.b))) REDUCED to normal form. ------ 169215/19075620. ------ 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.(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 169216/19075701. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a) a)) REDUCED to normal form. ------ 169217/19075728. ------ 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)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 169218/19075899. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 169219/19076178. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((b b)((a (^x.x))(a a))) REDUCED to normal form. ------ 169220/19076205. ------ 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. ------ 169221/19076250. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169222/19076304. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 169223/19076385. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (b ((^y.(y y))((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. ------ 169224/19076754. ------ 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 a)) REDUCED to normal form. ------ 169225/19076781. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b) c)) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b) c)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b) c)) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 169226/19077114. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.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. ------ 169227/19077222. ------ 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.(^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. ------ 169228/19077330. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.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. ------ 169229/19077357. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 169230/19077393. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(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. ------ 169231/19077420. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b)(a a))) REDUCED to normal form. ------ 169232/19077501. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 169233/19077528. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 169234/19077600. ------ 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 (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169235/19077726. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 169236/19077780. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(^z.b))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(^z.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.b))) 5. ==[ beta ]==> ((a b)((a a)(^y.b))) 6. ==[ alpha ]==> ((a b)((a a)(^x.b))) REDUCED to normal form. ------ 169237/19077807. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b) a)) REDUCED to normal form. ------ 169238/19077834. ------ 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. ------ 169239/19077996. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 169240/19078023. ------ 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)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 169241/19078050. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z)) c)) 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. ------ 169242/19078194. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.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 REDUCED to normal form. ------ 169243/19078275. ------ 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. ------ 169244/19078383. ------ 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.(^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. ------ 169245/19078500. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 169246/19078599. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c (^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c (^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c (^z.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(c (^z.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c (^y.(y y)))) 7. ==[ beta ]==> ((b b)(c (^y.(y y)))) 8. ==[ alpha ]==> ((b b)(c (^x.(x x)))) REDUCED to normal form. ------ 169247/19078608. ------ 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. ------ 169248/19078635. ------ 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)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169249/19078680. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^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)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 169250/19078743. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c d)) REDUCED to normal form. ------ 169251/19078788. ------ 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)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169252/19078905. ------ 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. ------ 169253/19078923. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 169254/19078941. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 169255/19078968. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z)) b)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(b b)) REDUCED to normal form. ------ 169256/19078995. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a 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. ------ 169257/19079076. ------ 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. ------ 169258/19079103. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 169259/19079130. ------ 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 (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 169260/19079157. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.(y y)))) REDUCED to normal form. ------ 169261/19079211. ------ 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) a) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a b)) REDUCED to normal form. ------ 169262/19079238. ------ 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. ------ 169263/19079319. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a) b)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a) b)) 5. ==[ beta ]==> ((a a)((^y.a) b)) 6. ==[ alpha ]==> ((a a)((^x.a) b)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 169264/19079337. ------ 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 (^y.y))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 169265/19079355. ------ 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 ]==> ((b (^z.a))(^y.y)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 169266/19079742. ------ 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. ------ 169267/19079760. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (^x1.x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 169268/19079769. ------ 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. ------ 169269/19079787. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (^a.(^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. ------ 169270/19079796. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b a)) REDUCED to normal form. ------ 169271/19079814. ------ 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. ------ 169272/19079868. ------ 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 a)))(a (^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 169273/19087638. ------ 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. ------ 169274/19090680. ------ 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. ------ 169275/19090692. ------ 1. ==[ start ]==> (((^a.a) b)(^b.(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. ------ 169276/19091133. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 169277/19091184. ------ 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. ------ 169278/19091535. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a a)((^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. ------ 169279/19092375. ------ 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. ------ 169280/19092480. ------ 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 ]==> (((a (^y.(^z.z)))(a (a a))) b) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 169281/19092867. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(((a (^z.(^x1.x1)))(^y1.(y1 y1)))((a (^z.(^x1.x1)))(^y1.(y1 y1))))) 4. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2))))) REDUCED to normal form. ------ 169282/19093536. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 169283/19093749. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((((a a) a)((^z.z)(a a)))(((a a) a)((^z.z)(a a))))(^y.y)) 4. ==[ alpha ]==> (((((a a) a)((^x.x)(a a)))(((a a) a)((^y.y)(a a))))(^z.z)) 5. ==[ beta ]==> (((((a a) a)(a a))(((a a) a)((^y.y)(a a))))(^z.z)) 6. ==[ alpha ]==> (((((a a) a)(a a))(((a a) a)((^x.x)(a a))))(^y.y)) 7. ==[ beta ]==> (((((a a) a)(a a))(((a a) a)(a a)))(^y.y)) 8. ==[ alpha ]==> (((((a a) a)(a a))(((a a) a)(a a)))(^x.x)) REDUCED to normal form. ------ 169284/19094958. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 169285/19095054. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 169286/19095930. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 169287/19095945. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169288/19096227. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^b.(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. ------ 169289/19096821. ------ 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.(^z1.z1))))) REDUCED to normal form. ------ 169290/19098126. ------ 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 y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 169291/19098339. ------ 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. ------ 169292/19098342. ------ 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)))(^y.(a a))) REDUCED to normal form. ------ 169293/19098792. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^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. ------ 169294/19099008. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.(x1 x1)))) REDUCED to normal form. ------ 169295/19099395. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(z b))) REDUCED to normal form. ------ 169296/19099500. ------ 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. ------ 169297/19099899. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.a))) 5. ==[ beta ]==> (a (^y.(^z.a))) 6. ==[ alpha ]==> (a (^x.(^y.a))) REDUCED to normal form. ------ 169298/19100196. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 169299/19100340. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 169300/19100742. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^z.z))(a (^x1.x1)))(((a (^z.z))(a (^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a (^z.z))(a (^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 169301/19101141. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^a.(^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. ------ 169302/19101186. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.b)) 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. ------ 169303/19101195. ------ 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. ------ 169304/19101267. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.a)) 2. ==[ alpha ]==> (((^x.(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. ------ 169305/19101315. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (a ((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> (a ((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> (a (((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 169306/19101342. ------ 1. ==[ start ]==> (((a a) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 169307/19101369. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 169308/19101387. ------ 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. ------ 169309/19101396. ------ 1. ==[ start ]==> (((^a.a) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((^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. ------ 169310/19101423. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a (^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169311/19101441. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 169312/19101468. ------ 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)((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. ------ 169313/19101531. ------ 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 (^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 169314/19101720. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 169315/19101810. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 169316/19101837. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 169317/19101864. ------ 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. ------ 169318/19101891. ------ 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. ------ 169319/19101927. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a)) d)) 3. ==[ beta ]==> ((^y.y)((^x1.(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. ------ 169320/19102134. ------ 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. ------ 169321/19102161. ------ 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))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x)) a)((a (a a)) b)) REDUCED to normal form. ------ 169322/19102188. ------ 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. ------ 169323/19102206. ------ 1. ==[ start ]==> (((^a.(a a)) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 169324/19102215. ------ 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. ------ 169325/19102242. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^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. ------ 169326/19102278. ------ 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)(^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)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169327/19102332. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 169328/19102341. ------ 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. ------ 169329/19102368. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 169330/19102386. ------ 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)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 169331/19102395. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 169332/19102413. ------ 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. ------ 169333/19102449. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(^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)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 169334/19102467. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(^x1.(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 169335/19102476. ------ 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. ------ 169336/19102503. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 169337/19102710. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1)) 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. ------ 169338/19102800. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.(^a.a)))(^b.(^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. ------ 169339/19102881. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 169340/19102908. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 169341/19102935. ------ 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. ------ 169342/19102962. ------ 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))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169343/19102989. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(^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. ------ 169344/19103052. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (b (^z.z)))) REDUCED to normal form. ------ 169345/19103079. ------ 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. ------ 169346/19103106. ------ 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. ------ 169347/19103133. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 169348/19103160. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(a a))(b ((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b ((^x.x) a))) 5. ==[ beta ]==> ((((a a) a)(a a))(b a)) REDUCED to normal form. ------ 169349/19103187. ------ 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. ------ 169350/19103547. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^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. ------ 169351/19103556. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)((^z.z) 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. ------ 169352/19103574. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 169353/19103745. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 169354/19103790. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169355/19103817. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 169356/19103871. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) a)) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 7. ==[ beta ]==> ((b (^y.y)) a) 8. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 169357/19103961. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 169358/19104015. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 169359/19104042. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 169360/19104096. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 169361/19104150. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 169362/19104177. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 169363/19104240. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 169364/19104267. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a))(a a))) REDUCED to normal form. ------ 169365/19104294. ------ 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)))) 5. ==[ beta ]==> ((a ((a a) a))(b (a (^y.y)))) 6. ==[ alpha ]==> ((a ((a a) a))(b (a (^x.x)))) REDUCED to normal form. ------ 169366/19104321. ------ 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) 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. ------ 169367/19104348. ------ 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 (a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b a)(a (a a)))) 5. ==[ beta ]==> ((a (a a))((b a)(a (a a)))) REDUCED to normal form. ------ 169368/19104375. ------ 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)(^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. ------ 169369/19104402. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 169370/19104429. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a b)(a b))) 3. ==[ beta ]==> (((a a)(a a))((a b)(a b))) REDUCED to normal form. ------ 169371/19104456. ------ 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.y)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 169372/19104627. ------ 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 a))(^z.z))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 169373/19104636. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(a a))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 169374/19104663. ------ 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. ------ 169375/19104690. ------ 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) 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. ------ 169376/19104708. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(y y)))) REDUCED to normal form. ------ 169377/19104735. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((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. ------ 169378/19104744. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 169379/19104771. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 169380/19104789. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a b)(^y.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(^y.b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.b))) REDUCED to normal form. ------ 169381/19104825. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169382/19104852. ------ 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 a)(^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. ------ 169383/19104879. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b)(^x.a))((b a)(b a))) REDUCED to normal form. ------ 169384/19104906. ------ 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.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 169385/19104933. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((^y1.y1) 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. ------ 169386/19105383. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) 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. ------ 169387/19105635. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 169388/19105662. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(a (^y.(a a)))) REDUCED to normal form. ------ 169389/19105689. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 169390/19105716. ------ 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)))(a (^x2.x2)))) 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. ------ 169391/19105761. ------ 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))(^y1.(y1 y1)))) REDUCED to normal form. ------ 169392/19106040. ------ 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)))(^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. ------ 169393/19106058. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a) c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a) c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169394/19106328. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169395/19106355. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 169396/19106580. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(c (^d.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(c (^z.a))) REDUCED to normal form. ------ 169397/19106634. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.x1))) REDUCED to normal form. ------ 169398/19106652. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 169399/19106931. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 169400/19106976. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 169401/19107246. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169402/19107300. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 169403/19107471. ------ 1. ==[ start ]==> (((a b)(^c.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 169404/19107525. ------ 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.(^y1.y1))))) REDUCED to normal form. ------ 169405/19107570. ------ 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.(^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. ------ 169406/19107606. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 169407/19108137. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 169408/19108281. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c (^y.(a a)))) 3. ==[ beta ]==> ((b b)(c (^y.(a a)))) 4. ==[ alpha ]==> ((b b)(c (^x.(a a)))) REDUCED to normal form. ------ 169409/19108308. ------ 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. ------ 169410/19108353. ------ 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))(^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. ------ 169411/19108362. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 169412/19108389. ------ 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))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 169413/19108407. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)(^y.a))) 3. ==[ beta ]==> (((b a)(b a))((a b)(^y.a))) 4. ==[ alpha ]==> (((b a)(b a))((a b)(^x.a))) REDUCED to normal form. ------ 169414/19108470. ------ 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)(^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. ------ 169415/19108488. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((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. ------ 169416/19108497. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 169417/19108551. ------ 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))((^z1.z1)(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. ------ 169418/19108596. ------ 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)(^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. ------ 169419/19108605. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^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. ------ 169420/19108632. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 169421/19108659. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 169422/19108776. ------ 1. ==[ start ]==> (((a (a a))(b a))(c (a b))) REDUCED to normal form. ------ 169423/19108803. ------ 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 ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b ((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(b ((^z.z)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(b (a a))) REDUCED to normal form. ------ 169424/19108830. ------ 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)))) 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. ------ 169425/19108857. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(a a))) 3. ==[ beta ]==> (((a b)(a b))((a a)(a a))) REDUCED to normal form. ------ 169426/19108884. ------ 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)(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. ------ 169427/19108911. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a) a) a)) REDUCED to normal form. ------ 169428/19108965. ------ 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 (a 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. ------ 169429/19108992. ------ 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 a) a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((b (a (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 169430/19109019. ------ 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. ------ 169431/19109046. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 169432/19109136. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a) a)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a)(^x2.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169433/19109217. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 169434/19109325. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((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. ------ 169435/19109361. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.a))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.a))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 169436/19109388. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 169437/19109496. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 169438/19109514. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(a a)) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(a a)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(a a)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 169439/19109712. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 169440/19109739. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b)(a a))) 3. ==[ beta ]==> ((b (^y.a))((^z.b)(a a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.b)(a a))) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 169441/19110099. ------ 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. ------ 169442/19110126. ------ 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))) 5. ==[ beta ]==> ((b a)(((a a) a)(a a))) REDUCED to normal form. ------ 169443/19110153. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^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 (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 169444/19110207. ------ 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. ------ 169445/19110297. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(^z.z))) 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. ------ 169446/19110378. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.(y1 y1)))) 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. ------ 169447/19110486. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^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. ------ 169448/19110648. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 169449/19110711. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.(y y)))) REDUCED to normal form. ------ 169450/19110738. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b (^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b (^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169451/19110783. ------ 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.x1))(^y1.y1))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.y1))) 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. ------ 169452/19110792. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 169453/19110819. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a (^z.z))(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 169454/19110846. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 169455/19110891. ------ 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))((a a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169456/19110900. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 169457/19110927. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 169458/19110954. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 169459/19111008. ------ 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.(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. ------ 169460/19111044. ------ 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)))) 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. ------ 169461/19111071. ------ 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. ------ 169462/19111098. ------ 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. ------ 169463/19111125. ------ 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) a))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) b)((a (^x.x)) a)) REDUCED to normal form. ------ 169464/19111152. ------ 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. ------ 169465/19111341. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (a (^y.y)))) 3. ==[ beta ]==> ((b (a (a a)))(c (a (^y.y)))) 4. ==[ alpha ]==> ((b (a (a a)))(c (a (^x.x)))) REDUCED to normal form. ------ 169466/19111368. ------ 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)) a)(b ((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(b ((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(b a)) REDUCED to normal form. ------ 169467/19111422. ------ 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. ------ 169468/19111449. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 169469/19111845. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)(^a.(^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. ------ 169470/19111863. ------ 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 ]==> (((^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. ------ 169471/19111872. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (^y.y))) REDUCED to normal form. ------ 169472/19111890. ------ 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 (^x.x))) b) REDUCED to normal form. ------ 169473/19111899. ------ 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. ------ 169474/19111917. ------ 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)((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. ------ 169475/19111971. ------ 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)(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. ------ 169476/19111997. ------ 1. ==[ start ]==> (^a.((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169477/19111998. ------ 1. ==[ start ]==> (a ((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 169478/19113378. ------ 1. ==[ start ]==> ((^a.((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^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))) 4. ==[ alpha ]==> (((^x.((^y.(^z.z)) a))(^x1.((^y1.(^z1.z1)) a)))(^x2.((^y2.(^z2.z2)) a))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x2.((^y2.(^z2.z2)) a))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((^y.y)(^z.((^x1.(^y1.y1)) a))) 8. ==[ alpha ]==> ((^x.x)(^y.((^z.(^x1.x1)) a))) 9. ==[ beta ]==> (^y.((^z.(^x1.x1)) a)) 10. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 11. ==[ beta ]==> (^x.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169479/19122711. ------ 1. ==[ start ]==> ((^a.a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^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. ------ 169480/19122738. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))((a a)(a a)))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))((a a)(a a)))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 169481/19122765. ------ 1. ==[ start ]==> ((^a.b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 169482/19122813. ------ 1. ==[ start ]==> (((^a.a) b)(^c.(^a.(a (^a.a))))) 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. ------ 169483/19122822. ------ 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. ------ 169484/19122846. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a (^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 ]==> (((^z.z)(^y.y))(^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. ------ 169485/19123254. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 169486/19123530. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169487/19123668. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^c.((^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. ------ 169488/19124088. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((^y.y)((^z.(^x1.x1)) a))((^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)))((^x2.x2)((^y2.(^z2.z2)) a))) 5. ==[ beta ]==> ((((^y.(^z.z)) a)((^x1.x1)((^y1.(^z1.z1)) a)))((^x2.x2)((^y2.(^z2.z2)) a))) 6. ==[ alpha ]==> ((((^x.(^y.y)) a)((^z.z)((^x1.(^y1.y1)) a)))((^z1.z1)((^x2.(^y2.y2)) a))) 7. ==[ beta ]==> (((^y.y)((^z.z)((^x1.(^y1.y1)) a)))((^z1.z1)((^x2.(^y2.y2)) a))) 8. ==[ alpha ]==> (((^x.x)((^y.y)((^z.(^x1.x1)) a)))((^y1.y1)((^z1.(^x2.x2)) a))) 9. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a))) 10. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)((^y1.(^z1.z1)) a))) 11. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)((^y1.(^z1.z1)) a))) 12. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.(^y1.y1)) a))) 13. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) a))) 14. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 15. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 16. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 17. ==[ beta ]==> ((^y.(^z.z)) a) 18. ==[ alpha ]==> ((^x.(^y.y)) a) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169489/19124091. ------ 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))(^x.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 169490/19125195. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((^z.(z z))(a (^x1.(^y1.y1))))((^z.(z z))(a (^x1.(^y1.y1)))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2)))))) 5. ==[ beta ]==> (((^y.(y y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^z1.(^x2.x2)))(a (^z1.(^x2.x2))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))) REDUCED to normal form. ------ 169491/19126386. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 169492/19126626. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> (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. ------ 169493/19127070. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.((^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. ------ 169494/19127412. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 169495/19127463. ------ 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)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.x2))) 5. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.x2))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169496/19127745. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169497/19128348. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 169498/19128357. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 169499/19128381. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 169500/19128663. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(z1 (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(z1 (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169501/19129221. ------ 1. ==[ start ]==> (((a b)((a a) a))(^b.(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(x a))) REDUCED to normal form. ------ 169502/19129380. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a)))(((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a)))(((^x2.(^y2.y2))(^z2.a))((^x3.(^y3.y3))(^z3.a)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(^z1.a)))(((^x2.(^y2.y2))(^z2.a))((^x3.(^y3.y3))(^z3.a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.a)))(((^y1.(^z1.z1))(^x2.a))((^y2.(^z2.z2))(^x3.a)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.a))(((^y1.(^z1.z1))(^x2.a))((^y2.(^z2.z2))(^x3.a)))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a)))) 11. ==[ beta ]==> (((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 15. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169503/19130247. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(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. ------ 169504/19130460. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 169505/19130931. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.((^z1.z1)(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(y1 y1))) REDUCED to normal form. ------ 169506/19131327. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(a z))) 3. ==[ eta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 169507/19131516. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.z))) REDUCED to normal form. ------ 169508/19132038. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^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. ------ 169509/19132317. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 169510/19132440. ------ 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. ------ 169511/19132461. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 169512/19132596. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 169513/19133262. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.b)) 3. ==[ beta ]==> (((^y.y) b)(^z.b)) 4. ==[ alpha ]==> (((^x.x) b)(^y.b)) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 169514/19133280. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 169515/19133316. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 169516/19133388. ------ 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))((a a)(a a)))(^y.(y y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(x x))) REDUCED to normal form. ------ 169517/19133427. ------ 1. ==[ start ]==> ((a a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 169518/19133454. ------ 1. ==[ start ]==> ((a (a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a a))((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 169519/19133481. ------ 1. ==[ start ]==> ((a b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 169520/19133526. ------ 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. ------ 169521/19133535. ------ 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. ------ 169522/19133553. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 169523/19133562. ------ 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)))((^x1.x1)(^z.z))) 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. ------ 169524/19133580. ------ 1. ==[ start ]==> (((a a) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a) b)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a a) b)((^y.y) b)) 4. ==[ alpha ]==> (((a a) b)((^x.x) b)) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 169525/19133607. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y)) c)) REDUCED to normal form. ------ 169526/19133967. ------ 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)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 169527/19134030. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((b (^y.y))(a (^z.z)))((b (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> (((b (^x.x))(a (^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 169528/19134057. ------ 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) 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. ------ 169529/19134111. ------ 1. ==[ start ]==> (((^a.(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)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 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. ------ 169530/19134138. ------ 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. ------ 169531/19134165. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((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. ------ 169532/19134219. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 169533/19134246. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 169534/19134381. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169535/19134471. ------ 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. ------ 169536/19134498. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (a (((^y.y) b)(^z.(z z)))) 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. ------ 169537/19134525. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 169538/19134552. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)(^z.a))) REDUCED to normal form. ------ 169539/19134579. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 169540/19134606. ------ 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. ------ 169541/19134633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.(^y1.y1)))) 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. ------ 169542/19134696. ------ 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. ------ 169543/19134723. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) b))) 7. ==[ beta ]==> ((a a)(((^y.y) b)((^y.y) b))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) b))) 9. ==[ beta ]==> ((a a)(b ((^y.y) b))) 10. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 11. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 169544/19134750. ------ 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. ------ 169545/19134777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(b (^z.z)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 169546/19134804. ------ 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))((^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. ------ 169547/19135155. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.a)(^c.(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. ------ 169548/19135326. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 169549/19135407. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(a b))) IRREDUCIBLE: cycle. ------ 169550/19135488. ------ 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 (((^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. ------ 169551/19135515. ------ 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. ------ 169552/19135542. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^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. ------ 169553/19135596. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(b (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(b (^x.x)))) REDUCED to normal form. ------ 169554/19135632. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.a)((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((b (^y.y))(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 169555/19135659. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 169556/19135686. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.x))(b (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 169557/19135722. ------ 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. ------ 169558/19135803. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 169559/19135830. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> (a ((^y.b)((^z.z)(a a)))) 8. ==[ alpha ]==> (a ((^x.b)((^y.y)(a a)))) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 169560/19135884. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 169561/19135911. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 169562/19136622. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 169563/19136766. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b) c)(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 169564/19136793. ------ 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. ------ 169565/19136820. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 169566/19136874. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 169567/19136901. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> ((a (^x.b))((a a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 169568/19136955. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169569/19137036. ------ 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)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 169570/19137063. ------ 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))) REDUCED to normal form. ------ 169571/19137099. ------ 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)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 169572/19137153. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a 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)))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 169573/19137180. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))(^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. ------ 169574/19137261. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 169575/19137288. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 169576/19137342. ------ 1. ==[ start ]==> ((a (b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 169577/19137432. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b ((^z.z) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b ((^z.z) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b ((^z.z) b))) 5. ==[ beta ]==> (b (b ((^z.z) b))) 6. ==[ alpha ]==> (b (b ((^x.x) b))) 7. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 169578/19137513. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 169579/19137621. ------ 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. ------ 169580/19137648. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 169581/19137702. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a (a a))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b)(a b))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 169582/19137783. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((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. ------ 169583/19137819. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 169584/19137846. ------ 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)))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 169585/19137909. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 169586/19137936. ------ 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.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 169587/19137963. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.b)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)((a a) a))) 5. ==[ beta ]==> ((a (a a))((^y.b)((a a) a))) 6. ==[ alpha ]==> ((a (a a))((^x.b)((a a) a))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 169588/19137990. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.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. ------ 169589/19138017. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 169590/19138044. ------ 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 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. ------ 169591/19138071. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(b a))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 169592/19138098. ------ 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.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 169593/19138125. ------ 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)(^x.x))(a (^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 169594/19138170. ------ 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))((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. ------ 169595/19138179. ------ 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)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 169596/19138458. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169597/19138467. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 169598/19138485. ------ 1. ==[ start ]==> (((^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 a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 169599/19138494. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1))) b)) 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. ------ 169600/19138512. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 169601/19138566. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))(a (a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(a (a a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(a (a a)))) 9. ==[ beta ]==> (((a a)(a a))((a a)(a (a a)))) REDUCED to normal form. ------ 169602/19138647. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(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. ------ 169603/19138755. ------ 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)(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. ------ 169604/19138800. ------ 1. ==[ start ]==> (((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 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. ------ 169605/19138881. ------ 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 (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 169606/19138908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.b)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 169607/19138962. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(a b))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 169608/19138989. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (((a a)(a (a a)))((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (((a a)(a (a a)))((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (((a a)(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 169609/19139016. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 169610/19139061. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169611/19139070. ------ 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))))) 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. ------ 169612/19139097. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 169613/19139376. ------ 1. ==[ start ]==> (((^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.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169614/19139385. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1))) 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. ------ 169615/19139430. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (((a a)(^y.y))(a (^z.z)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 169616/19139439. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 169617/19139457. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((^z1.z1) 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. ------ 169618/19139511. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a) a)((^z.z)(^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. ------ 169619/19139592. ------ 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.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. ------ 169620/19139709. ------ 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.(^x2.x2)))) REDUCED to normal form. ------ 169621/19139736. ------ 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 (^x.x))((a a)(^z.a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 169622/19139772. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a) b)((^y.b)(a (a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(a (a a)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 169623/19139826. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 169624/19139853. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a b)(a b))) REDUCED to normal form. ------ 169625/19139880. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.a)((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)((^y.a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)((^y.y)(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 169626/19139907. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^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. ------ 169627/19139934. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.x)(b a))) 3. ==[ beta ]==> (((a b)((a a) a))(b a)) REDUCED to normal form. ------ 169628/19140042. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 169629/19140069. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)(^b.(^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. ------ 169630/19140096. ------ 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. ------ 169631/19140267. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^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. ------ 169632/19140375. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169633/19140456. ------ 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. ------ 169634/19140492. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 169635/19140519. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 169636/19140600. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^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. ------ 169637/19140627. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a))(^y.a))) REDUCED to normal form. ------ 169638/19140681. ------ 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 (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 169639/19140735. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 169640/19140762. ------ 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. ------ 169641/19140789. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b) c)) REDUCED to normal form. ------ 169642/19140852. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a))(^b.(^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. ------ 169643/19140906. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(^y.b))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 169644/19140933. ------ 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.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 169645/19141176. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 169646/19141491. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a) c)) 3. ==[ beta ]==> ((b c)(((a a) a) c)) REDUCED to normal form. ------ 169647/19141644. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (a a))) REDUCED to normal form. ------ 169648/19141653. ------ 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 a)) REDUCED to normal form. ------ 169649/19141725. ------ 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) 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. ------ 169650/19141833. ------ 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. ------ 169651/19141869. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b)(^z.z))) 3. ==[ beta ]==> ((b (^y.a))((a b)(^z.z))) 4. ==[ alpha ]==> ((b (^x.a))((a b)(^y.y))) REDUCED to normal form. ------ 169652/19141896. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 169653/19141959. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 169654/19141986. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 169655/19142013. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^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. ------ 169656/19142040. ------ 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. ------ 169657/19142067. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(^z.z))) 5. ==[ beta ]==> ((b a)((^y.b)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.y))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 169658/19142121. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^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))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 169659/19142148. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 169660/19142175. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.a)(^b.(^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. ------ 169661/19142229. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.b)) REDUCED to normal form. ------ 169662/19142508. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d d)) 3. ==[ beta ]==> (b (d d)) REDUCED to normal form. ------ 169663/19142751. ------ 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 ]==> (((^y.(^z.z)) a)(a ((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(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. ------ 169664/19142778. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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 ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169665/19142832. ------ 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) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> ((b b)(((^y.y) a)((^z.z) a))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((b b)(a ((^y.y) a))) 10. ==[ alpha ]==> ((b b)(a ((^x.x) a))) 11. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 169666/19142922. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 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. ------ 169667/19142949. ------ 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. ------ 169668/19142976. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.a))) REDUCED to normal form. ------ 169669/19143030. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 169670/19143057. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 169671/19143084. ------ 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. ------ 169672/19143156. ------ 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. ------ 169673/19143174. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 169674/19143255. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 169675/19143282. ------ 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 (^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 169676/19143309. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 169677/19143336. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 169678/19143363. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(a (^y.y)))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 169679/19143390. ------ 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) 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. ------ 169680/19143444. ------ 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 y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(^y1.y1))) 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. ------ 169681/19143471. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 169682/19143498. ------ 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))) 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. ------ 169683/19143570. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) b)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 169684/19143588. ------ 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 ]==> ((^y.(y (^z.z)))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^z.z))(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 169685/19143975. ------ 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. ------ 169686/19143993. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (a (^x1.x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 169687/19144002. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^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. ------ 169688/19144020. ------ 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. ------ 169689/19144029. ------ 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. ------ 169690/19144047. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b a)) 3. ==[ beta ]==> ((^y.y)(b a)) 4. ==[ alpha ]==> ((^x.x)(b a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 169691/19144101. ------ 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))) REDUCED to normal form. ------ 169692/19144136. ------ 1. ==[ start ]==> (^a.(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (^x.(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (^x.((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169693/19144137. ------ 1. ==[ start ]==> (a (((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (a ((^y.y)(^z.z))) 4. ==[ alpha ]==> (a ((^x.x)(^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 169694/19149495. ------ 1. ==[ start ]==> ((^a.(^b.b))(^a.(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169695/19154853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^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. ------ 169696/19154859. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(^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. ------ 169697/19154868. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169698/19154949. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 169699/19154994. ------ 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 (^z.z))) a)(^y.y)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 169700/19155111. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^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. ------ 169701/19155843. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^a.(^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. ------ 169702/19156569. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 169703/19157136. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (^y.(((^z.z)((^x1.x1) a))((^z.z)((^x1.x1) a)))) 4. ==[ alpha ]==> (^x.(((^y.y)((^z.z) a))((^x1.x1)((^y1.y1) a)))) 5. ==[ beta ]==> (^x.(((^z.z) a)((^x1.x1)((^y1.y1) a)))) 6. ==[ alpha ]==> (^x.(((^y.y) a)((^z.z)((^x1.x1) a)))) 7. ==[ beta ]==> (^x.(a ((^z.z)((^x1.x1) a)))) 8. ==[ alpha ]==> (^x.(a ((^y.y)((^z.z) a)))) 9. ==[ beta ]==> (^x.(a ((^z.z) a))) 10. ==[ alpha ]==> (^x.(a ((^y.y) a))) 11. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 169704/19157343. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a (a a))(^z.(^x1.(^y1.y1))))((a (a a))(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> ((^x.x)(((a (a a))(^y.(^z.(^x1.x1))))((a (a a))(^y1.(^z1.(^x2.x2)))))) 5. ==[ beta ]==> (((a (a a))(^y.(^z.(^x1.x1))))((a (a a))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 169705/19157436. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(^y1.(y1 (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 169706/19159227. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 169707/19159611. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a (^x1.(^y1.y1))) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 169708/19159893. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 169709/19159902. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^z.b)) REDUCED to normal form. ------ 169710/19160214. ------ 1. ==[ start ]==> ((^a.(^b.b))(a (^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169711/19160217. ------ 1. ==[ start ]==> ((a (^b.b))(^a.(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 169712/19160529. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 169713/19160811. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169714/19160820. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 169715/19161369. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.a))) REDUCED to normal form. ------ 169716/19162161. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^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. ------ 169717/19163079. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.(a a)))) REDUCED to normal form. ------ 169718/19163088. ------ 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)(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 169719/19163862. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.(^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. ------ 169720/19164186. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^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. ------ 169721/19164348. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(^c.a))) 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. ------ 169722/19164588. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 169723/19165011. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a) b)) 3. ==[ beta ]==> (((^z.a) b)(((^z.a) b)(^y.y))) 4. ==[ alpha ]==> (((^x.a) b)(((^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 (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 169724/19165428. ------ 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)(^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. ------ 169725/19165437. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(y (^z.z)))) REDUCED to normal form. ------ 169726/19165482. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.(^a.(^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. ------ 169727/19165536. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(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. ------ 169728/19165572. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^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. ------ 169729/19165584. ------ 1. ==[ start ]==> ((a a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 169730/19165593. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 169731/19165620. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 169732/19165647. ------ 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. ------ 169733/19165674. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 169734/19165692. ------ 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. ------ 169735/19165719. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 169736/19165728. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 169737/19165836. ------ 1. ==[ start ]==> ((a (^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 169738/19165917. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(^a.a))(^b.(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. ------ 169739/19165944. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 169740/19166025. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 169741/19166151. ------ 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. ------ 169742/19166169. ------ 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 a)(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(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. ------ 169743/19166250. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a b)(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> ((a b)(b (a (a a)))) REDUCED to normal form. ------ 169744/19166277. ------ 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. ------ 169745/19166304. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)((a a) a))) REDUCED to normal form. ------ 169746/19166331. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 169747/19166358. ------ 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)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 169748/19166385. ------ 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. ------ 169749/19166493. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> ((b b)(a ((a a)(a a)))) REDUCED to normal form. ------ 169750/19166565. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 169751/19166673. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.b)(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. ------ 169752/19166700. ------ 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. ------ 169753/19166853. ------ 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. ------ 169754/19166880. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (a a))(^b.b))) 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. ------ 169755/19167051. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (a ((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 169756/19167213. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) 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. ------ 169757/19167294. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(^z.z))) 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. ------ 169758/19167465. ------ 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 (((^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. ------ 169759/19167627. ------ 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. ------ 169760/19167654. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a b) a)((^y.y)(b a))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(b a))) 5. ==[ beta ]==> (((a b) a)(b a)) REDUCED to normal form. ------ 169761/19167681. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 169762/19167735. ------ 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.x1))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 169763/19167762. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 169764/19167834. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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 a)) REDUCED to normal form. ------ 169765/19167861. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z) 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. ------ 169766/19167879. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 169767/19167906. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 169768/19167960. ------ 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))(^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. ------ 169769/19167987. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a b)(^z.(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((a b)(^y.(a a)))) 7. ==[ beta ]==> (a ((a b)(^y.(a a)))) 8. ==[ alpha ]==> (a ((a b)(^x.(a a)))) REDUCED to normal form. ------ 169770/19168068. ------ 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))))) 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. ------ 169771/19168077. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169772/19168104. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 169773/19168158. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(b (^z1.z1)))) 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. ------ 169774/19168239. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 169775/19168320. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 169776/19168374. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(^z1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(^z1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(a a)))) 11. ==[ beta ]==> ((^y.b)(^z.(a a))) 12. ==[ alpha ]==> ((^x.b)(^y.(a a))) 13. ==[ beta ]==> b REDUCED to normal form. ------ 169777/19168455. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 169778/19168608. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 169779/19168680. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 169780/19168995. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 169781/19169076. ------ 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 a)) REDUCED to normal form. ------ 169782/19169157. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 169783/19169283. ------ 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)) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 169784/19169310. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b) b)) 3. ==[ beta ]==> ((a (a b))(((^y.y) b) b)) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b) b)) 5. ==[ beta ]==> ((a (a b))(b b)) REDUCED to normal form. ------ 169785/19169589. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 169786/19169733. ------ 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 (a a)))) REDUCED to normal form. ------ 169787/19169841. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(a a))) 8. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a a))) 9. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 169788/19169868. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 169789/19169922. ------ 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 (^x1.(^y1.y1))))) REDUCED to normal form. ------ 169790/19169940. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(b (^y.y))) 3. ==[ beta ]==> (b (b (^y.y))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 169791/19169949. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a) b)) REDUCED to normal form. ------ 169792/19170066. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 169793/19170093. ------ 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)))(((^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. ------ 169794/19170120. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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. ------ 169795/19170147. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a) a)(^x.b))) REDUCED to normal form. ------ 169796/19170174. ------ 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))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> (((a a) a)(^y.(a a))) 10. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 169797/19170255. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^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))))) REDUCED to normal form. ------ 169798/19170282. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 169799/19170336. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 169800/19170345. ------ 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)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 169801/19170426. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(a a))(^b.(^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 a)) REDUCED to normal form. ------ 169802/19170507. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 169803/19170615. ------ 1. ==[ start ]==> (((^a.(^a.(^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))((^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. ------ 169804/19170624. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a b)) REDUCED to normal form. ------ 169805/19170651. ------ 1. ==[ start ]==> (((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 a))) REDUCED to normal form. ------ 169806/19170732. ------ 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 (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 169807/19170759. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((a b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((a b)((^y.y)(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 169808/19170813. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a b))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 169809/19170840. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a (a a))(a a))) REDUCED to normal form. ------ 169810/19170867. ------ 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) a)((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. ------ 169811/19170912. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(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. ------ 169812/19170921. ------ 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.(^y1.y1))))) REDUCED to normal form. ------ 169813/19170939. ------ 1. ==[ start ]==> ((a (^b.b))(a (^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 169814/19170957. ------ 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)))(^y1.y1))) REDUCED to normal form. ------ 169815/19170984. ------ 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. ------ 169816/19171011. ------ 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 a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 169817/19171038. ------ 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.(z z)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a (a a))(a a))((a a)(^y.(y y)))) 6. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 169818/19171065. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a 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. ------ 169819/19171119. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^x1.b))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.b))) 7. ==[ beta ]==> (((a b)(^x.x))(^z.b)) 8. ==[ alpha ]==> (((a b)(^x.x))(^y.b)) REDUCED to normal form. ------ 169820/19171146. ------ 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.(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. ------ 169821/19171227. ------ 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.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 169822/19171254. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 169823/19171263. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^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. ------ 169824/19171425. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 169825/19171533. ------ 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)(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169826/19171542. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 169827/19171569. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a)(a a))) 3. ==[ beta ]==> ((b a)((b a)(a a))) REDUCED to normal form. ------ 169828/19171596. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 169829/19171623. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a) a)) REDUCED to normal form. ------ 169830/19171704. ------ 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)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))((a a) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169831/19171731. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (a a))(a b))) REDUCED to normal form. ------ 169832/19171758. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)((^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. ------ 169833/19171785. ------ 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 (^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. ------ 169834/19171812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(b a))) REDUCED to normal form. ------ 169835/19171929. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(^y.(y y)))) 3. ==[ beta ]==> (((a a) b)((a b)(^y.(y y)))) 4. ==[ alpha ]==> (((a a) b)((a b)(^x.(x x)))) REDUCED to normal form. ------ 169836/19171956. ------ 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.(^y1.y1)))) REDUCED to normal form. ------ 169837/19171983. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (b a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a (b a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((a (b a))(^y.a)) 8. ==[ alpha ]==> ((a (b a))(^x.a)) REDUCED to normal form. ------ 169838/19172010. ------ 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))(^y.b))) REDUCED to normal form. ------ 169839/19172037. ------ 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) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(a a)))) 9. ==[ beta ]==> ((a a)(a (^y.(a a)))) 10. ==[ alpha ]==> ((a a)(a (^x.(a a)))) REDUCED to normal form. ------ 169840/19172064. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 169841/19172118. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a) a)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 169842/19172145. ------ 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)(^y.y)) b)) REDUCED to normal form. ------ 169843/19172289. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 169844/19172568. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)(a b))) 3. ==[ beta ]==> ((b b)(((^y.y) a)(a b))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)(a b))) 5. ==[ beta ]==> ((b b)(a (a b))) REDUCED to normal form. ------ 169845/19172595. ------ 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. ------ 169846/19172613. ------ 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. ------ 169847/19172694. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 169848/19172775. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 169849/19172883. ------ 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 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. ------ 169850/19173144. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 169851/19173171. ------ 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 a)) REDUCED to normal form. ------ 169852/19173198. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b) c)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 169853/19173423. ------ 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)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(a (^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(a (^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169854/19173504. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 169855/19173612. ------ 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. ------ 169856/19173720. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 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. ------ 169857/19173747. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^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. ------ 169858/19173783. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (a b))) 3. ==[ beta ]==> ((a (^y.y))(b (a b))) 4. ==[ alpha ]==> ((a (^x.x))(b (a b))) REDUCED to normal form. ------ 169859/19173801. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(a a))) REDUCED to normal form. ------ 169860/19173810. ------ 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)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 169861/19173891. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y) a)) 7. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 169862/19173918. ------ 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))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 169863/19173990. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(b (^x1.b))) 3. ==[ beta ]==> ((^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. ------ 169864/19173999. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(a b))) REDUCED to normal form. ------ 169865/19174116. ------ 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 y)))) REDUCED to normal form. ------ 169866/19174143. ------ 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) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 169867/19174170. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)((a (^y.y))(^z.a))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 169868/19174197. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(^z.b))) REDUCED to normal form. ------ 169869/19174224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b) a)) 3. ==[ beta ]==> (((^y.y)(b a))((a b) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((a b) a)) 5. ==[ beta ]==> ((b a)((a b) a)) REDUCED to normal form. ------ 169870/19174251. ------ 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. ------ 169871/19174278. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z)) c)) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y)) c)) 5. ==[ beta ]==> (((a b)(a a))((^y.y) c)) 6. ==[ alpha ]==> (((a b)(a a))((^x.x) c)) 7. ==[ beta ]==> (((a b)(a a)) c) REDUCED to normal form. ------ 169872/19174413. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b) a)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b) a)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b) a)) 5. ==[ beta ]==> ((b a)((^y.b) a)) 6. ==[ alpha ]==> ((b a)((^x.b) a)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 169873/19174584. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.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. ------ 169874/19174665. ------ 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) a))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((^y1.y1) 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. ------ 169875/19174773. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169876/19174890. ------ 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) 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. ------ 169877/19174998. ------ 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) 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. ------ 169878/19175025. ------ 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. ------ 169879/19175070. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (^z.a))) 3. ==[ beta ]==> (b (a (^z.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 169880/19175178. ------ 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. ------ 169881/19175313. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 169882/19175358. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1)) 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. ------ 169883/19175385. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a 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. ------ 169884/19175412. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 169885/19175493. ------ 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. ------ 169886/19175520. ------ 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)))) 7. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 169887/19175547. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 169888/19175601. ------ 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. ------ 169889/19175628. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a) b)) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a) b)) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a) b)) 5. ==[ beta ]==> ((b (a (a a)))(a b)) REDUCED to normal form. ------ 169890/19175709. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z)) a)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y)) a)) 5. ==[ beta ]==> ((a a)((^y.(y y)) a)) 6. ==[ alpha ]==> ((a a)((^x.(x x)) a)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 169891/19175727. ------ 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. ------ 169892/19175736. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a) b)) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 169893/19176132. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (a a))) 3. ==[ beta ]==> (((^y.y) b)(b (a a))) 4. ==[ alpha ]==> (((^x.x) b)(b (a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 169894/19176150. ------ 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 ]==> (((^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. ------ 169895/19176159. ------ 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. ------ 169896/19176177. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 169897/19176186. ------ 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. ------ 169898/19176204. ------ 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)(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. ------ 169899/19176258. ------ 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 a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^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. ------ 169900/19176294. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(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 ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169901/19187019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b)) 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 ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 169902/19187043. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 169903/19187163. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 169904/19187604. ------ 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. ------ 169905/19187628. ------ 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. ------ 169906/19187979. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (^x1.x1))(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. ------ 169907/19188846. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a (a a))((^x.x) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 169908/19188924. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) b)((^z.z) a))) 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. ------ 169909/19189311. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (^y.((((^z.z) b)(^x1.a))(((^z.z) b)(^x1.a)))) 4. ==[ alpha ]==> (^x.((((^y.y) b)(^z.a))(((^x1.x1) b)(^y1.a)))) 5. ==[ beta ]==> (^x.((b (^z.a))(((^x1.x1) b)(^y1.a)))) 6. ==[ alpha ]==> (^x.((b (^y.a))(((^z.z) b)(^x1.a)))) 7. ==[ beta ]==> (^x.((b (^y.a))(b (^x1.a)))) 8. ==[ alpha ]==> (^x.((b (^y.a))(b (^z.a)))) REDUCED to normal form. ------ 169910/19189611. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 169911/19190007. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 169912/19190193. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a b)(a b))) 3. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(^y.y)) 4. ==[ alpha ]==> ((((a b)(a b))((a b)(a b)))(^x.x)) REDUCED to normal form. ------ 169913/19190376. ------ 1. ==[ start ]==> (((a b) c)(^a.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 169914/19191429. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 169915/19191498. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a)(^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 169916/19192077. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 169917/19192995. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 169918/19194345. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 169919/19194597. ------ 1. ==[ start ]==> (((a b)(a b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 169920/19194783. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 169921/19195263. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 169922/19195479. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 169923/19195866. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) 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))) REDUCED to normal form. ------ 169924/19195944. ------ 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) a))) 3. ==[ eta ]==> ((^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. ------ 169925/19196532. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 169926/19196667. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 169927/19196811. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.((^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. ------ 169928/19196919. ------ 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. ------ 169929/19197162. ------ 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. ------ 169930/19197186. ------ 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. ------ 169931/19197612. ------ 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. ------ 169932/19197657. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 169933/19197747. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^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. ------ 169934/19197777. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 169935/19197786. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(^a.a))((^a.a) 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 (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 169936/19197813. ------ 1. ==[ start ]==> (((a a) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 169937/19197840. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 169938/19197867. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 169939/19197894. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 169940/19197912. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 169941/19197921. ------ 1. ==[ start ]==> (((a a) b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a) b)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a a) b)((^z.z)(^y.y))) 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. ------ 169942/19197939. ------ 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)(((^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. ------ 169943/19197966. ------ 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. ------ 169944/19198056. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.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. ------ 169945/19198137. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 169946/19198191. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 169947/19198218. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 169948/19198308. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 169949/19198335. ------ 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. ------ 169950/19198362. ------ 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. ------ 169951/19198605. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a) a)(b a))) REDUCED to normal form. ------ 169952/19198632. ------ 1. ==[ start ]==> (((a (^a.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 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x)) 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 (^x.x)) a)((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a (^x.x)) a)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.z)))) REDUCED to normal form. ------ 169953/19198659. ------ 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 (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 169954/19198686. ------ 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. ------ 169955/19198713. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 169956/19198803. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.(^x2.x2)))) 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))) REDUCED to normal form. ------ 169957/19198857. ------ 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 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 9. ==[ beta ]==> (b (^y.(y y))) 10. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 169958/19198866. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 169959/19198884. ------ 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. ------ 169960/19198893. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 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. ------ 169961/19198938. ------ 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))(^x1.b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 169962/19198974. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169963/19199181. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 169964/19199235. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(a a)) c)) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(a a)) c)) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(a a)) c)) 5. ==[ beta ]==> (a (((a a)(a a)) c)) REDUCED to normal form. ------ 169965/19199271. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 169966/19199298. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))(^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. ------ 169967/19199352. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^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. ------ 169968/19199379. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 169969/19199406. ------ 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. ------ 169970/19199460. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 169971/19199550. ------ 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. ------ 169972/19199577. ------ 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)) 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. ------ 169973/19199604. ------ 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))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 169974/19199631. ------ 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. ------ 169975/19199658. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> ((a (a b))(b ((^y.y) a))) 4. ==[ alpha ]==> ((a (a b))(b ((^x.x) a))) 5. ==[ beta ]==> ((a (a b))(b a)) REDUCED to normal form. ------ 169976/19199919. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c (^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 169977/19200018. ------ 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 a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 169978/19200027. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(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. ------ 169979/19200045. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a (^x.(a a)))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.a))) REDUCED to normal form. ------ 169980/19200216. ------ 1. ==[ start ]==> (((^a.b) b)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 169981/19200261. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(a a))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(a a))((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 169982/19200288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 169983/19200423. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> (b (((^x1.x1) b) c)) 4. ==[ alpha ]==> (b (((^x.x) b) c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 169984/19200432. ------ 1. ==[ start ]==> (((a b) b)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b) b)(^y.a)) 4. ==[ alpha ]==> (((a b) b)(^x.a)) REDUCED to normal form. ------ 169985/19200459. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 169986/19200513. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 169987/19200567. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 169988/19200648. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 169989/19200675. ------ 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. ------ 169990/19200711. ------ 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)))) 3. ==[ beta ]==> (((a a)(a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 169991/19200738. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a (b (^y.y)))) REDUCED to normal form. ------ 169992/19200765. ------ 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. ------ 169993/19200792. ------ 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)(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. ------ 169994/19200819. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))((^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. ------ 169995/19200846. ------ 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. ------ 169996/19200873. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 169997/19200900. ------ 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. ------ 169998/19200927. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(a b))) REDUCED to normal form. ------ 169999/19201107. ------ 1. ==[ start ]==> (((a b) c)(a (^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(a (^x.(^y.y)))) REDUCED to normal form. ------ 170000/19201134. ------ 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. ------ 170001/19201161. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b)(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. ------ 170002/19201179. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 170003/19201206. ------ 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)(^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. ------ 170004/19201242. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 170005/19201296. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170006/19201341. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 170007/19201350. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 170008/19201377. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(b a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((b a)(b a))) REDUCED to normal form. ------ 170009/19201404. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 170010/19201854. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z) b)) 3. ==[ beta ]==> (b ((^z.z) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170011/19202106. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 170012/19202133. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 170013/19202160. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(a (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 170014/19202187. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 170015/19202232. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)(^x1.a))) REDUCED to normal form. ------ 170016/19202511. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 170017/19202529. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170018/19202808. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.a)(^b.b))) 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. ------ 170019/19202826. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((^x.x)(a (^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. ------ 170020/19202853. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 170021/19203105. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 170022/19203402. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170023/19203447. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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) REDUCED to normal form. ------ 170024/19203474. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((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. ------ 170025/19203726. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 170026/19203942. ------ 1. ==[ start ]==> (((a b)(^c.a))(d (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d (^y.(a a)))) REDUCED to normal form. ------ 170027/19203969. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 170028/19204041. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((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. ------ 170029/19204077. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^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. ------ 170030/19204608. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 170031/19204878. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((b a)(b a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 170032/19204941. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 170033/19204959. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 170034/19204968. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 170035/19205022. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 170036/19205076. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.x1))) REDUCED to normal form. ------ 170037/19205103. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^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. ------ 170038/19205130. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 170039/19205301. ------ 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. ------ 170040/19205328. ------ 1. ==[ start ]==> (((a b)(a b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 170041/19205355. ------ 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. ------ 170042/19205382. ------ 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)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(a (^z.z)))) REDUCED to normal form. ------ 170043/19205436. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^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)((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(a (a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (a a))) REDUCED to normal form. ------ 170044/19205463. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (a a))((^y.y)(^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. ------ 170045/19205490. ------ 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 a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a ((a a) a))) REDUCED to normal form. ------ 170046/19205517. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 170047/19205607. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170048/19205688. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170049/19205796. ------ 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)(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(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. ------ 170050/19205832. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 170051/19205859. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 170052/19205967. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 170053/19205994. ------ 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.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 170054/19206066. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170055/19206183. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (^x1.b))) REDUCED to normal form. ------ 170056/19206210. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) 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)))) REDUCED to normal form. ------ 170057/19206237. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 170058/19206570. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(b ((a a) a))) REDUCED to normal form. ------ 170059/19206597. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 170060/19206624. ------ 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))) REDUCED to normal form. ------ 170061/19206678. ------ 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 (^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. ------ 170062/19206849. ------ 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. ------ 170063/19206957. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 170064/19207074. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 170065/19207119. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a) a)) 3. ==[ beta ]==> ((^y.y)((^x1.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. ------ 170066/19207173. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z)) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z)) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z)) c)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z)) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y)) c)) 7. ==[ beta ]==> ((b b)((^y.(y y)) c)) 8. ==[ alpha ]==> ((b b)((^x.(x x)) c)) 9. ==[ beta ]==> ((b b)(c c)) REDUCED to normal form. ------ 170067/19207263. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 170068/19207290. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 170069/19207317. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 170070/19207362. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170071/19207371. ------ 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. ------ 170072/19207398. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 170073/19207425. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^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. ------ 170074/19207479. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 170075/19207515. ------ 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. ------ 170076/19207542. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 170077/19207569. ------ 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. ------ 170078/19207596. ------ 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 (^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. ------ 170079/19207623. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 170080/19207650. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(a (a a)))) REDUCED to normal form. ------ 170081/19207731. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c c)) REDUCED to normal form. ------ 170082/19207893. ------ 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. ------ 170083/19207920. ------ 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. ------ 170084/19207929. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^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 ]==> (((^z.a) b)(^y.y)) 6. ==[ alpha ]==> (((^x.a) b)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 170085/19208316. ------ 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 (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170086/19208334. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((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. ------ 170087/19208343. ------ 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. ------ 170088/19208361. ------ 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. ------ 170089/19208370. ------ 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. ------ 170090/19208388. ------ 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)((^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. ------ 170091/19208442. ------ 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)) REDUCED to normal form. ------ 170092/19208478. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 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. ------ 170093/19208634. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^z.(a (a (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(a (a (^y.y))))(^z.z)) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 170094/19213854. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170095/19214169. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^b.(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. ------ 170096/19219212. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b)) c) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z)) c) 3. ==[ beta ]==> (((^y.y)(^z.z)) 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. ------ 170097/19219263. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^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))) 5. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) 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. ------ 170098/19219290. ------ 1. ==[ start ]==> ((^a.b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 170099/19219371. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^z.z)(a (a (^x1.x1))))(^y.y)) 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. ------ 170100/19219374. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 170101/19219806. ------ 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. ------ 170102/19220055. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170103/19220613. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((((^y.(^z.z))(b (^x1.x1)))((^y.(^z.z))(b (^x1.x1))))((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(b (^z1.z1))))((^x2.(^y2.y2))(b (^z2.z2)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(b (^z1.z1))))((^x2.(^y2.y2))(b (^z2.z2)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(b (^x1.x1))))((^y1.(^z1.z1))(b (^x2.x2)))) 7. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 8. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b (^z1.z1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 12. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170104/19221720. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(b a))((^z.(^x1.x1))(b a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(b a))((^x1.(^y1.y1))(b a)))) 5. ==[ beta ]==> (((^y.(^z.z))(b a))((^x1.(^y1.y1))(b a))) 6. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(b a))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 9. ==[ beta ]==> ((^y.(^z.z))(b a)) 10. ==[ alpha ]==> ((^x.(^y.y))(b a)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170105/19222569. ------ 1. ==[ start ]==> (((^a.b)(^b.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)))) REDUCED to normal form. ------ 170106/19222938. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 170107/19223151. ------ 1. ==[ start ]==> ((^a.(b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.(a a)))) 3. ==[ eta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170108/19223988. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^x1.x1)(^y1.y1))(^y.(^z.z))) 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. ------ 170109/19224297. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^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)))(^z.b)) REDUCED to normal form. ------ 170110/19224591. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)(a (^a.(^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. ------ 170111/19224594. ------ 1. ==[ start ]==> ((a (^b.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 170112/19224612. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 170113/19224906. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170114/19224909. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^b.(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. ------ 170115/19225773. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^b.(b 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)(^y.y))(^z.(z a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y a))) REDUCED to normal form. ------ 170116/19226295. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 170117/19226547. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 170118/19226799. ------ 1. ==[ start ]==> (((a b)(a b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 170119/19226985. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c (^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c (^z.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170120/19227879. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(b a)) a) 4. ==[ beta ]==> (((^y.y)(b a)) a) 5. ==[ alpha ]==> (((^x.x)(b a)) a) 6. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 170121/19228068. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.z))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.y))) 5. ==[ beta ]==> ((b a)(^y.(^z.y))) 6. ==[ alpha ]==> ((b a)(^x.(^y.x))) REDUCED to normal form. ------ 170122/19228239. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.((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)) REDUCED to normal form. ------ 170123/19228590. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> ((^y.y)(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y) y))) 5. ==[ beta ]==> (^y.((y y) y)) 6. ==[ alpha ]==> (^x.((x x) x)) REDUCED to normal form. ------ 170124/19228725. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 170125/19228869. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 170126/19229013. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 170127/19229148. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 170128/19229256. ------ 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. ------ 170129/19229364. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 170130/19229832. ------ 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)))) REDUCED to normal form. ------ 170131/19229913. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.b)) 2. ==[ alpha ]==> (((^x.(x x))((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. ------ 170132/19229949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.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. ------ 170133/19229997. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(^a.a))(^b.b))) 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))) 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. ------ 170134/19230006. ------ 1. ==[ start ]==> ((a (a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (a a))(^y.y)) 4. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 170135/19230033. ------ 1. ==[ start ]==> ((a b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a b)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> ((a b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 170136/19230087. ------ 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. ------ 170137/19230105. ------ 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. ------ 170138/19230114. ------ 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. ------ 170139/19230132. ------ 1. ==[ start ]==> (((a a) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a) b)((a (a (^x.x))) a)) REDUCED to normal form. ------ 170140/19230159. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 170141/19230186. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 170142/19230249. ------ 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. ------ 170143/19230546. ------ 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. ------ 170144/19230564. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y (^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)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 170145/19230582. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((^y.(y y))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((((^y.(^z.z)) a)(a a))(((^y.(^z.z)) a)(a a))) 6. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.(^x1.x1)) a)(a a))) 7. ==[ beta ]==> (((^y.y)(a a))(((^z.(^x1.x1)) a)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(a a))) 9. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a a))) 10. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a a))) 11. ==[ beta ]==> ((a a)((^y.y)(a a))) 12. ==[ alpha ]==> ((a a)((^x.x)(a a))) 13. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 170146/19230609. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((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. ------ 170147/19230645. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(a a)) d)) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a)) d)) 3. ==[ beta ]==> ((a b)((^y.(a a)) d)) 4. ==[ alpha ]==> ((a b)((^x.(a a)) d)) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 170148/19230663. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) 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. ------ 170149/19230690. ------ 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. ------ 170150/19230717. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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. ------ 170151/19230771. ------ 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.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. ------ 170152/19230798. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 170153/19230933. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170154/19230960. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.(^y1.y1)) 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. ------ 170155/19231023. ------ 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. ------ 170156/19231050. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 170157/19231077. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 170158/19231104. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 170159/19231131. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b a)(^z.a))) 3. ==[ beta ]==> ((a (^y.a))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 170160/19231158. ------ 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. ------ 170161/19231185. ------ 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)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 170162/19231221. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 170163/19231275. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 170164/19231302. ------ 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. ------ 170165/19231329. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((^y.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)((a a)(a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 170166/19231356. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 170167/19231707. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^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. ------ 170168/19231734. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 170169/19231860. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b) 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. ------ 170170/19231878. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.b)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170171/19231959. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))((a a) a))) IRREDUCIBLE: cycle. ------ 170172/19232040. ------ 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)((a a)(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 170173/19232067. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^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)((^y.y)(b a))) 6. ==[ alpha ]==> ((a b)((^x.x)(b a))) 7. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 170174/19232094. ------ 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.(^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. ------ 170175/19232148. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 170176/19232211. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 170177/19232238. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 170178/19232274. ------ 1. ==[ start ]==> (((a a)(a b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.y) 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. ------ 170179/19232301. ------ 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.(^x1.x1)))(a (a a)))) 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. ------ 170180/19232382. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))(a b))) 5. ==[ beta ]==> (((^y.y) a)((^z.(a a))(a b))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(a b))) 7. ==[ beta ]==> (a ((^y.(a a))(a b))) 8. ==[ alpha ]==> (a ((^x.(a a))(a b))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 170181/19232409. ------ 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. ------ 170182/19232427. ------ 1. ==[ start ]==> (((^a.b) b)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 170183/19232436. ------ 1. ==[ start ]==> (((a b)(a a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 170184/19232463. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 170185/19232643. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b) b)(((^x.x) b) c)) 3. ==[ beta ]==> (((a b) b)(b c)) REDUCED to normal form. ------ 170186/19233075. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a) e)) 2. ==[ alpha ]==> (((^x.b) c)((^y.a) e)) 3. ==[ beta ]==> (b ((^y.a) e)) 4. ==[ alpha ]==> (b ((^x.a) e)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170187/19233174. ------ 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.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. ------ 170188/19233309. ------ 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. ------ 170189/19233345. ------ 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. ------ 170190/19233372. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.(^z.z)))) REDUCED to normal form. ------ 170191/19233426. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b a)(^z.(z z)))) REDUCED to normal form. ------ 170192/19233453. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 170193/19233507. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170194/19233534. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 170195/19233561. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 170196/19233615. ------ 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)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 170197/19233651. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))((^x1.x1) 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. ------ 170198/19233678. ------ 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)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a a)(a a))) REDUCED to normal form. ------ 170199/19233705. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(^z.z))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.y))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 170200/19233732. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x)(^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. ------ 170201/19233759. ------ 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)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.a))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170202/19233813. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 170203/19233840. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 170204/19233867. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 170205/19233894. ------ 1. ==[ start ]==> ((a (b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 170206/19233984. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (c (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 170207/19234065. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (b (((^z.z) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 170208/19234173. ------ 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)))) 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. ------ 170209/19234200. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 170210/19234254. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)(a b))((^y.y)(a a))) 8. ==[ alpha ]==> (((a b)(a b))((^x.x)(a a))) 9. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 170211/19234335. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((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))))) REDUCED to normal form. ------ 170212/19234398. ------ 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)(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 170213/19234515. ------ 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.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 170214/19234542. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 170215/19234596. ------ 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))((^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. ------ 170216/19234623. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a (a a)))(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b)(a (a a)))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 170217/19234650. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.a)(b a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.a)(b a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)(b a))) 5. ==[ beta ]==> (((a a) a)((^y.a)(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(b a))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 170218/19234677. ------ 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.x1))(a (^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. ------ 170219/19234722. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 170220/19234731. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 170221/19235010. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 170222/19235037. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^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))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 170223/19235046. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.b) 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. ------ 170224/19235064. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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. ------ 170225/19235118. ------ 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) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))((^z.z) a))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))((^z.z) a))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((^y.y) a))) 9. ==[ beta ]==> (((a a)(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 170226/19235127. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 170227/19235199. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 170228/19235307. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((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. ------ 170229/19235334. ------ 1. ==[ start ]==> ((a (^b.b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 170230/19235352. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 170231/19235379. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 170232/19235460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(a (a a)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(a (a a)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 170233/19235487. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 170234/19235514. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((a a) a))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 170235/19235541. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 170236/19235568. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)((^y.y)(a a)))) 9. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a a))) REDUCED to normal form. ------ 170237/19235622. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(b 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. ------ 170238/19235649. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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))))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 170239/19235928. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(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. ------ 170240/19235964. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 170241/19235982. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 170242/19236009. ------ 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))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(a (^z1.z1)))) 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. ------ 170243/19236063. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(a (a a)))) REDUCED to normal form. ------ 170244/19236144. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (a a))(a b))) 3. ==[ beta ]==> (b ((a (a a))(a b))) REDUCED to normal form. ------ 170245/19236261. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a)(^y1.y1))) REDUCED to normal form. ------ 170246/19236288. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 170247/19236324. ------ 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) a))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 170248/19236351. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 170249/19236378. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 170250/19236405. ------ 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. ------ 170251/19236432. ------ 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)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(a b))) 7. ==[ beta ]==> ((a a)((^y.(y y))(a b))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(a b))) 9. ==[ beta ]==> ((a a)((a b)(a b))) REDUCED to normal form. ------ 170252/19236459. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.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. ------ 170253/19236486. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^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. ------ 170254/19236513. ------ 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)(^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. ------ 170255/19236594. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 170256/19236621. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((b (a a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 170257/19236819. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((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. ------ 170258/19236927. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 170259/19237008. ------ 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. ------ 170260/19237035. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 170261/19237071. ------ 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))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 170262/19237152. ------ 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 y)))) REDUCED to normal form. ------ 170263/19237179. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 170264/19237233. ------ 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)(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.b))) REDUCED to normal form. ------ 170265/19237287. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 170266/19237314. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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)) REDUCED to normal form. ------ 170267/19237341. ------ 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. ------ 170268/19237377. ------ 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. ------ 170269/19237404. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 170270/19237431. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^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. ------ 170271/19237458. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))(^c.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. ------ 170272/19237485. ------ 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)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(^x1.b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.b))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 170273/19237512. ------ 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.(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. ------ 170274/19237539. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)(^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. ------ 170275/19237728. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c (^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.b))) REDUCED to normal form. ------ 170276/19238043. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b) b)) 3. ==[ beta ]==> ((b c)((a b) b)) REDUCED to normal form. ------ 170277/19238070. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a) c)) REDUCED to normal form. ------ 170278/19238196. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (a b))) REDUCED to normal form. ------ 170279/19238277. ------ 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. ------ 170280/19238286. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a) c)) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 170281/19238385. ------ 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 (^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. ------ 170282/19238448. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 170283/19238511. ------ 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) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 170284/19238538. ------ 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 y))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 170285/19238565. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 170286/19238592. ------ 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 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. ------ 170287/19238619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(a b))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))((^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. ------ 170288/19238646. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b)(^z.z))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 170289/19238673. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 170290/19238700. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 170291/19238727. ------ 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 y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 170292/19238808. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^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. ------ 170293/19238979. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 170294/19239303. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)(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. ------ 170295/19239330. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(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. ------ 170296/19239384. ------ 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. ------ 170297/19239393. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y)) c)) 3. ==[ beta ]==> (((a (a a))(^x.x))(c c)) REDUCED to normal form. ------ 170298/19239465. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 170299/19239501. ------ 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)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 170300/19239528. ------ 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. ------ 170301/19239582. ------ 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))(^z1.(z1 z1)))) REDUCED to normal form. ------ 170302/19239609. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 170303/19239636. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 170304/19239726. ------ 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.(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. ------ 170305/19239753. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 170306/19239861. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.(x x)))) REDUCED to normal form. ------ 170307/19239888. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 170308/19239915. ------ 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 z))(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(a a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 170309/19239942. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 170310/19239996. ------ 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. ------ 170311/19240023. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(^y.y))) 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. ------ 170312/19240050. ------ 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.(^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. ------ 170313/19240104. ------ 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 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. ------ 170314/19240122. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) a)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 170315/19240140. ------ 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. ------ 170316/19240527. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) REDUCED to normal form. ------ 170317/19240545. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 170318/19240554. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a) b)) REDUCED to normal form. ------ 170319/19240572. ------ 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)))) REDUCED to normal form. ------ 170320/19240581. ------ 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. ------ 170321/19240599. ------ 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. ------ 170322/19240653. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a b)) REDUCED to normal form. ------ 170323/19240689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 170324/19240715. ------ 1. ==[ start ]==> (^a.(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(((x x) x)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 170325/19240716. ------ 1. ==[ start ]==> (a (((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 170326/19246389. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170327/19251459. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 170328/19251465. ------ 1. ==[ start ]==> ((^a.a)(((a a) a)(^a.(^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. ------ 170329/19251492. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^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))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 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. ------ 170330/19251519. ------ 1. ==[ start ]==> ((^a.b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.b)((a (a a))(^y.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 170331/19251555. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 170332/19251600. ------ 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. ------ 170333/19251612. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 170334/19251717. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (^x.((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 170335/19252053. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 170336/19252059. ------ 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. ------ 170337/19252881. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170338/19253175. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 170339/19253355. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a)) c)) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a)) c)) 3. ==[ beta ]==> (((^y.(a a)) c) b) 4. ==[ alpha ]==> (((^x.(a a)) c) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 170340/19253673. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(b (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 170341/19253742. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.(a a))(a (^x1.x1)))((^z.(a a))(a (^x1.x1))))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(a (^z.z)))((^x1.(a a))(a (^y1.y1))))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))(a (^y1.y1))))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(a (^z.z))))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 170342/19254807. ------ 1. ==[ start ]==> (((a b) c)(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.((a a)(a a)))) REDUCED to normal form. ------ 170343/19255860. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.a))(^y.b)) REDUCED to normal form. ------ 170344/19255929. ------ 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)))(a (^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 170345/19256217. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((((^x1.x1) b) a)(^y.(^z.z))) 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. ------ 170346/19256526. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^b.(^b.b))) 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))) REDUCED to normal form. ------ 170347/19256535. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 170348/19256820. ------ 1. ==[ start ]==> ((^a.(^b.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170349/19257135. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170350/19257138. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 170351/19257147. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^b.(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. ------ 170352/19257453. ------ 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))))) REDUCED to normal form. ------ 170353/19257741. ------ 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.(^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. ------ 170354/19258533. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 170355/19259496. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170356/19259910. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(a b))) 3. ==[ beta ]==> ((b (^y.a))(^z.(a b))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(a b))) REDUCED to normal form. ------ 170357/19260108. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.b))) 5. ==[ beta ]==> ((b a)(^y.(^z.b))) 6. ==[ alpha ]==> ((b a)(^x.(^y.b))) REDUCED to normal form. ------ 170358/19260375. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1)) c)) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170359/19260657. ------ 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. ------ 170360/19260819. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^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. ------ 170361/19260963. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 170362/19261194. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 170363/19261611. ------ 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. ------ 170364/19261617. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z)) a)) 3. ==[ beta ]==> (((^z.(z z)) a)(((^z.(z z)) a)(^y.y))) 4. ==[ alpha ]==> (((^x.(x x)) 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 a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 170365/19262016. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.c)) 3. ==[ beta ]==> (((^y.y) b)(^z.c)) 4. ==[ alpha ]==> (((^x.x) b)(^y.c)) 5. ==[ beta ]==> (b (^y.c)) 6. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 170366/19262061. ------ 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)))) REDUCED to normal form. ------ 170367/19262070. ------ 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. ------ 170368/19262142. ------ 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))) REDUCED to normal form. ------ 170369/19262178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 170370/19262205. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 170371/19262217. ------ 1. ==[ start ]==> ((a a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 170372/19262244. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 170373/19262253. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 170374/19262271. ------ 1. ==[ start ]==> ((a b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 170375/19262280. ------ 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. ------ 170376/19262307. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 170377/19262352. ------ 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. ------ 170378/19262361. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 170379/19262388. ------ 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)((^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. ------ 170380/19262469. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 170381/19262802. ------ 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 (a (^y.y))))) 4. ==[ alpha ]==> ((a a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 170382/19262811. ------ 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. ------ 170383/19262883. ------ 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) a))) 3. ==[ beta ]==> ((a b)(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> ((a b)(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> ((a b)(((a a)(a a)) a)) REDUCED to normal form. ------ 170384/19262910. ------ 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. ------ 170385/19262937. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 170386/19262964. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b a)((a a) a))) REDUCED to normal form. ------ 170387/19262991. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 170388/19263018. ------ 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. ------ 170389/19263126. ------ 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 b)((a (a a))((^y.y) b))) 4. ==[ alpha ]==> ((b b)((a (a a))((^x.x) b))) 5. ==[ beta ]==> ((b b)((a (a a)) b)) REDUCED to normal form. ------ 170390/19263171. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170391/19263333. ------ 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. ------ 170392/19263459. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 170393/19263513. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^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)((^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. ------ 170394/19263540. ------ 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. ------ 170395/19263630. ------ 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.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.(^x2.x2)) 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. ------ 170396/19263765. ------ 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. ------ 170397/19263846. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.(a a))(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 170398/19263927. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 170399/19264098. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 170400/19264107. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a)) c)) 2. ==[ alpha ]==> ((a (a b))((^x.(a a)) c)) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 170401/19264260. ------ 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. ------ 170402/19264287. ------ 1. ==[ start ]==> (((a b) a)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 170403/19264314. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(b a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(b a))) 5. ==[ beta ]==> (((a a)(^x.b))(b a)) REDUCED to normal form. ------ 170404/19264368. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a ((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 170405/19264395. ------ 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.y))((a a)(a a)))) REDUCED to normal form. ------ 170406/19264422. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(b (^z.z)))) 6. ==[ alpha ]==> ((^x.a)((a a)(b (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 170407/19264494. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 170408/19264512. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) 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. ------ 170409/19264539. ------ 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)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 170410/19264566. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 170411/19264620. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> (a (((^y.y)(a a))(^z.b))) 8. ==[ alpha ]==> (a (((^x.x)(a a))(^y.b))) 9. ==[ beta ]==> (a ((a a)(^y.b))) 10. ==[ alpha ]==> (a ((a a)(^x.b))) REDUCED to normal form. ------ 170412/19264647. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 170413/19264674. ------ 1. ==[ start ]==> (((a b)(a a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 170414/19264710. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 170415/19264737. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 170416/19264791. ------ 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.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 8. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170417/19264872. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170418/19264926. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 170419/19265007. ------ 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))(^y1.b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.b))) 9. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.b))) 10. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 11. ==[ beta ]==> ((^y.(a a))(^z.b)) 12. ==[ alpha ]==> ((^x.(a a))(^y.b)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 170420/19265268. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.z) c)) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.z) c)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y) c)) 5. ==[ beta ]==> ((a (a a))((^y.y) c)) 6. ==[ alpha ]==> ((a (a a))((^x.x) c)) 7. ==[ beta ]==> ((a (a a)) c) REDUCED to normal form. ------ 170421/19265313. ------ 1. ==[ start ]==> (((^a.b) c)((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b) c)((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 170422/19265547. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 170423/19265556. ------ 1. ==[ start ]==> (((a b) c)((a a)((a a)(a a)))) REDUCED to normal form. ------ 170424/19265628. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b)(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. ------ 170425/19265655. ------ 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) 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. ------ 170426/19265790. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 170427/19265889. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 170428/19265943. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(a a)) a)) 3. ==[ beta ]==> ((a (a b))(((a a)(a a)) a)) REDUCED to normal form. ------ 170429/19265970. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) b) b)) 3. ==[ beta ]==> (((a (a a))((a a) a))(b b)) REDUCED to normal form. ------ 170430/19266222. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170431/19266366. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((b a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((b a) a)) REDUCED to normal form. ------ 170432/19266474. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(a b))) REDUCED to normal form. ------ 170433/19266501. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.b))((^z.z)(a a))) 6. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(a a))) 7. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 170434/19266555. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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. ------ 170435/19266573. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(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. ------ 170436/19266582. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 170437/19266609. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.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. ------ 170438/19266681. ------ 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)))(a (^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 170439/19266699. ------ 1. ==[ start ]==> (((a a)(b a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))((b a)(^x.a))) REDUCED to normal form. ------ 170440/19266726. ------ 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))(^x1.(x1 x1)))) REDUCED to normal form. ------ 170441/19266753. ------ 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)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(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 (a a))(((^y.y)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(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. ------ 170442/19266780. ------ 1. ==[ start ]==> (((a (a a))(a b))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((a b)(^x.a))) REDUCED to normal form. ------ 170443/19266807. ------ 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)(^z.b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a 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. ------ 170444/19266834. ------ 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)))(((^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. ------ 170445/19266861. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 170446/19266915. ------ 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))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 170447/19266969. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) b) a)) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 170448/19266978. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b)(^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. ------ 170449/19267059. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(y1 y1)))) 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. ------ 170450/19267140. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170451/19267248. ------ 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))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170452/19267257. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 170453/19267275. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.a)(^b.b))) 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. ------ 170454/19267284. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 170455/19267365. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 170456/19267392. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(a (a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 170457/19267446. ------ 1. ==[ start ]==> (((a b)(^b.(^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. ------ 170458/19267473. ------ 1. ==[ start ]==> ((((^a.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))(a b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(a b))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a b))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(a b)) REDUCED to normal form. ------ 170459/19267500. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a (a a))(a a))) REDUCED to normal form. ------ 170460/19267554. ------ 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))) REDUCED to normal form. ------ 170461/19267572. ------ 1. ==[ start ]==> ((a (^b.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 170462/19267617. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 170463/19267644. ------ 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. ------ 170464/19267671. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 170465/19267698. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.(z z)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^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. ------ 170466/19267725. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 170467/19267752. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 170468/19267779. ------ 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))(^x1.b))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.b))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.b))) 7. ==[ beta ]==> (((a a)(a (a a)))(^y.b)) 8. ==[ alpha ]==> (((a a)(a (a a)))(^x.b)) REDUCED to normal form. ------ 170469/19267806. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 170470/19267887. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((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. ------ 170471/19267896. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.a)(a (^a.(^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. ------ 170472/19267923. ------ 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)))(^z2.z2))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2)))(^z2.z2))) 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. ------ 170473/19268058. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)(^c.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. ------ 170474/19268175. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(b (b a))) REDUCED to normal form. ------ 170475/19268202. ------ 1. ==[ start ]==> ((((^a.a) b) a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) 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. ------ 170476/19268229. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(a a))) REDUCED to normal form. ------ 170477/19268256. ------ 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))(a (^z1.z1)))) REDUCED to normal form. ------ 170478/19268337. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(((a a) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))(((a a) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 170479/19268364. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)((a a) a))) 5. ==[ beta ]==> ((((a a) a)(^x.b))((a a) a)) REDUCED to normal form. ------ 170480/19268391. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(a b))) REDUCED to normal form. ------ 170481/19268418. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a ((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 170482/19268445. ------ 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 (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 170483/19268490. ------ 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))(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. ------ 170484/19268562. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 170485/19268589. ------ 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)(^x1.(x1 x1)))) REDUCED to normal form. ------ 170486/19268616. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a) a)(^b.(^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. ------ 170487/19268670. ------ 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))(^x1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.b))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (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. ------ 170488/19268697. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a (^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 170489/19268724. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 170490/19268778. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a) a)) REDUCED to normal form. ------ 170491/19268922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))(^c.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. ------ 170492/19269201. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (a a))((a a) a))) 3. ==[ beta ]==> ((b b)((a (a a))((a a) a))) REDUCED to normal form. ------ 170493/19269228. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(a b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (a b))) REDUCED to normal form. ------ 170494/19269273. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 170495/19269282. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 170496/19269327. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 170497/19269408. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 170498/19269516. ------ 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))((^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. ------ 170499/19269615. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b) c)) REDUCED to normal form. ------ 170500/19269831. ------ 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 a)) REDUCED to normal form. ------ 170501/19270056. ------ 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))(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170502/19270137. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170503/19270245. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)((^z1.z1)(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. ------ 170504/19270353. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 170505/19270380. ------ 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.(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. ------ 170506/19270416. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c ((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(c ((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(c ((a a) a))) REDUCED to normal form. ------ 170507/19270434. ------ 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))(^z1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.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. ------ 170508/19270443. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (a b))) REDUCED to normal form. ------ 170509/19270524. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 170510/19270551. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.b))((^z.z) a)) 8. ==[ alpha ]==> (((a a)(^x.b))((^y.y) a)) 9. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 170511/19270632. ------ 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 (^x1.x1))((a a) a))) REDUCED to normal form. ------ 170512/19270659. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(a b))) 3. ==[ beta ]==> ((b (^y.a))((a a)(a b))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(a b))) REDUCED to normal form. ------ 170513/19270749. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(^z.a)) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.a)) REDUCED to normal form. ------ 170514/19270776. ------ 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 y)))) REDUCED to normal form. ------ 170515/19270803. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^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. ------ 170516/19270857. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(^z.b))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(^y.b))) 5. ==[ beta ]==> ((b a)((a a)(^y.b))) 6. ==[ alpha ]==> ((b a)((a a)(^x.b))) REDUCED to normal form. ------ 170517/19270884. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a b) a)) REDUCED to normal form. ------ 170518/19270911. ------ 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. ------ 170519/19270938. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 170520/19271073. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 170521/19271127. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((a ((^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. ------ 170522/19271217. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.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. ------ 170523/19271298. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170524/19271406. ------ 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. ------ 170525/19271541. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) 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)((^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. ------ 170526/19271568. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 170527/19271631. ------ 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. ------ 170528/19271658. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170529/19271703. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 170530/19271712. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 170531/19271811. ------ 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) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170532/19271820. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c d)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c d)) REDUCED to normal form. ------ 170533/19271946. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 170534/19272018. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^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. ------ 170535/19272045. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y)) b)) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y)) b)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x)) b)) 5. ==[ beta ]==> (((a (a a)) b)(b b)) REDUCED to normal form. ------ 170536/19272072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a) c)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a) c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a) c)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a) c)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) c)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 170537/19272153. ------ 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. ------ 170538/19272180. ------ 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.(^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. ------ 170539/19272234. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 170540/19272261. ------ 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. ------ 170541/19272288. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 170542/19272360. ------ 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. ------ 170543/19272369. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y)) a)) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 170544/19272765. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 170545/19272783. ------ 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 ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170546/19272792. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (a a))) REDUCED to normal form. ------ 170547/19272810. ------ 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 (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 170548/19272819. ------ 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. ------ 170549/19272837. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(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. ------ 170550/19272891. ------ 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. ------ 170551/19272927. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 170552/19272954. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 170553/19273560. ------ 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))))(^y1.(y1 (y1 (^z1.z1)))))(((^z.(z (z (^x1.x1))))(^y1.(y1 (y1 (^z1.z1)))))(^y.y))) 6. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.(z (z (^x1.x1)))))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 7. ==[ beta ]==> (((^z.(z (z (^x1.x1))))((^z.(z (z (^x1.x1))))(^y.y)))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 8. ==[ alpha ]==> (((^x.(x (x (^y.y))))((^z.(z (z (^x1.x1))))(^y1.y1)))(((^z1.(z1 (z1 (^x2.x2))))(^y2.(y2 (y2 (^z2.z2)))))(^x3.x3))) 9. ==[ beta ]==> ((((^z.(z (z (^x1.x1))))(^y1.y1))(((^z.(z (z (^x1.x1))))(^y1.y1))(^y.y)))(((^z1.(z1 (z1 (^x2.x2))))(^y2.(y2 (y2 (^z2.z2)))))(^x3.x3))) 10. ==[ alpha ]==> ((((^x.(x (x (^y.y))))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(((^y2.(y2 (y2 (^z2.z2))))(^x3.(x3 (x3 (^y3.y3)))))(^z3.z3))) 11. ==[ beta ]==> ((((^z.z)((^z.z)(^y.y)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(((^y2.(y2 (y2 (^z2.z2))))(^x3.(x3 (x3 (^y3.y3)))))(^z3.z3))) 12. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(((^y2.(y2 (y2 (^z2.z2))))(^x3.(x3 (x3 (^y3.y3)))))(^z3.z3))) 13. ==[ beta ]==> ((((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(((^y2.(y2 (y2 (^z2.z2))))(^x3.(x3 (x3 (^y3.y3)))))(^z3.z3))) 14. ==[ alpha ]==> ((((^x.x)(^y.y))(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1)))(((^x2.(x2 (x2 (^y2.y2))))(^z2.(z2 (z2 (^x3.x3)))))(^y3.y3))) 15. ==[ beta ]==> (((^y.y)(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1)))(((^x2.(x2 (x2 (^y2.y2))))(^z2.(z2 (z2 (^x3.x3)))))(^y3.y3))) 16. ==[ alpha ]==> (((^x.x)(((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1)))(((^z1.(z1 (z1 (^x2.x2))))(^y2.(y2 (y2 (^z2.z2)))))(^x3.x3))) 17. ==[ beta ]==> ((((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1))(((^z1.(z1 (z1 (^x2.x2))))(^y2.(y2 (y2 (^z2.z2)))))(^x3.x3))) 18. ==[ alpha ]==> ((((^x.(x (x (^y.y))))(^z.z))(^x1.x1))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 19. ==[ beta ]==> ((((^z.z)((^z.z)(^y.y)))(^x1.x1))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 20. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(^x1.x1))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 21. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))(((^y1.(y1 (y1 (^z1.z1))))(^x2.(x2 (x2 (^y2.y2)))))(^z2.z2))) 22. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.(z1 (z1 (^x2.x2)))))(^y2.y2))) 23. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.(z1 (z1 (^x2.x2)))))(^y2.y2))) 24. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(z (z (^x1.x1))))(^y1.(y1 (y1 (^z1.z1)))))(^x2.x2))) 25. ==[ beta ]==> ((^y.y)(((^z.(z (z (^x1.x1))))(^y1.(y1 (y1 (^z1.z1)))))(^x2.x2))) 26. ==[ alpha ]==> ((^x.x)(((^y.(y (y (^z.z))))(^x1.(x1 (x1 (^y1.y1)))))(^z1.z1))) 27. ==[ beta ]==> (((^y.(y (y (^z.z))))(^x1.(x1 (x1 (^y1.y1)))))(^z1.z1)) 28. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.(z (z (^x1.x1)))))(^y1.y1)) 29. ==[ beta ]==> (((^z.(z (z (^x1.x1))))((^z.(z (z (^x1.x1))))(^y.y)))(^y1.y1)) 30. ==[ alpha ]==> (((^x.(x (x (^y.y))))((^z.(z (z (^x1.x1))))(^y1.y1)))(^z1.z1)) 31. ==[ beta ]==> ((((^z.(z (z (^x1.x1))))(^y1.y1))(((^z.(z (z (^x1.x1))))(^y1.y1))(^y.y)))(^z1.z1)) 32. ==[ alpha ]==> ((((^x.(x (x (^y.y))))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.y2)) 33. ==[ beta ]==> ((((^z.z)((^z.z)(^y.y)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.y2)) 34. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.y2)) 35. ==[ beta ]==> ((((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.y2)) UNREDUCED: maximal number of reductions reached. ------ 170554/19283118. ------ 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. ------ 170555/19283706. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 170556/19283730. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170557/19283877. ------ 1. ==[ start ]==> (((a a) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 170558/19284309. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 170559/19284315. ------ 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. ------ 170560/19284318. ------ 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. ------ 170561/19284666. ------ 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)(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. ------ 170562/19285560. ------ 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.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(a (^z.z)))(^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. ------ 170563/19285611. ------ 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 ]==> ((((a a)(a a))(a (^y.y))) b) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 170564/19285998. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.((((a a)(a a))(^z.(^x1.x1)))(((a a)(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1))))) REDUCED to normal form. ------ 170565/19286721. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 170566/19286880. ------ 1. ==[ start ]==> ((^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))) 3. ==[ beta ]==> (((((^z.z)(a a))((a a) a))(((^z.z)(a a))((a a) a)))(^y.y)) 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)) 7. ==[ beta ]==> ((((a a)((a a) a))((a a)((a a) a)))(^y.y)) 8. ==[ alpha ]==> ((((a a)((a a) a))((a a)((a a) a)))(^x.x)) REDUCED to normal form. ------ 170567/19287063. ------ 1. ==[ start ]==> (((a b) c)(^d.(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(a a)))) REDUCED to normal form. ------ 170568/19288185. ------ 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)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 170569/19288467. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z))) a)(^y1.y1)) 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. ------ 170570/19288791. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 170571/19289403. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(^a.(^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. ------ 170572/19289709. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^b.(^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. ------ 170573/19290006. ------ 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.(^y2.y2))))) REDUCED to normal form. ------ 170574/19291059. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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)))) REDUCED to normal form. ------ 170575/19291311. ------ 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 y)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 170576/19291470. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170577/19292193. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 170578/19292580. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(y b))) REDUCED to normal form. ------ 170579/19292631. ------ 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 (^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170580/19292913. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 170581/19293219. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 170582/19293246. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(^c.a))) 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. ------ 170583/19293381. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 170584/19293525. ------ 1. ==[ start ]==> ((((^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)))) 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. ------ 170585/19293633. ------ 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. ------ 170586/19293867. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 170587/19293873. ------ 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. ------ 170588/19293876. ------ 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. ------ 170589/19294272. ------ 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)))) REDUCED to normal form. ------ 170590/19294326. ------ 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. ------ 170591/19294434. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(^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. ------ 170592/19294461. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 170593/19294491. ------ 1. ==[ start ]==> ((a (^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 170594/19294518. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^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. ------ 170595/19294527. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 170596/19294554. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 170597/19294581. ------ 1. ==[ start ]==> (((^a.a) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (b ((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> (b ((^x.a)(b (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170598/19294608. ------ 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. ------ 170599/19294626. ------ 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. ------ 170600/19294635. ------ 1. ==[ start ]==> (((a a) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.x)(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. ------ 170601/19294653. ------ 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)((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. ------ 170602/19294662. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) a)((^x1.x1)(^z.z))) 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. ------ 170603/19294680. ------ 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. ------ 170604/19294707. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 170605/19294770. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 170606/19294851. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(^a.a))(^b.(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. ------ 170607/19294878. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 170608/19294959. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.a))(^b.b))) 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. ------ 170609/19295049. ------ 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. ------ 170610/19295067. ------ 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)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 170611/19295076. ------ 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. ------ 170612/19295085. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.(y y))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (((^y.(y (^z.z))) a)((^y.(y (^z.z))) a)) 6. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z (^x1.x1))) a)) 7. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1))) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) a)) 9. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 170613/19295319. ------ 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. ------ 170614/19295346. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a) a)(b a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a) a)(b a))) REDUCED to normal form. ------ 170615/19295373. ------ 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 (^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. ------ 170616/19295400. ------ 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. ------ 170617/19295427. ------ 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)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 170618/19295517. ------ 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)(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(^x2.x2))) 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. ------ 170619/19295571. ------ 1. ==[ start ]==> (((^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.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 170620/19295580. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 170621/19295598. ------ 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. ------ 170622/19295607. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (a a))) REDUCED to normal form. ------ 170623/19295634. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 170624/19295652. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 170625/19295949. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b (^z.z)) b)) 3. ==[ beta ]==> (((^y.a)(^y.a))((b (^z.z)) b)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b (^z.z)) b)) 5. ==[ beta ]==> (a ((b (^z.z)) b)) 6. ==[ alpha ]==> (a ((b (^x.x)) b)) REDUCED to normal form. ------ 170626/19295985. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.a))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 170627/19296012. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(y y))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(x x))) REDUCED to normal form. ------ 170628/19296120. ------ 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. ------ 170629/19296147. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170630/19296291. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 170631/19296318. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 170632/19296345. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b (^x.x))(a a))) REDUCED to normal form. ------ 170633/19296372. ------ 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. ------ 170634/19296381. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a)) c)) 3. ==[ beta ]==> ((^y.b)((^z.(a a)) c)) 4. ==[ alpha ]==> ((^x.b)((^y.(a a)) c)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170635/19296732. ------ 1. ==[ start ]==> (((^a.b)(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((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. ------ 170636/19296759. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 170637/19296930. ------ 1. ==[ start ]==> (((^a.b) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 170638/19297002. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 170639/19297056. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(a a))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 170640/19297137. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 170641/19297146. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 170642/19297173. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 170643/19297200. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 170644/19297281. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 170645/19297308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.b)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.b)(^z.(a a)))) 7. ==[ beta ]==> (((^y.b)(^z.(a a)))((^y.b)(^z.(a a)))) 8. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b)(^x1.(a a)))) 9. ==[ beta ]==> (b ((^z.b)(^x1.(a a)))) 10. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170646/19297335. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 170647/19297389. ------ 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. ------ 170648/19297452. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b ((a a)(a a)))) REDUCED to normal form. ------ 170649/19297479. ------ 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. ------ 170650/19297506. ------ 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))(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. ------ 170651/19297533. ------ 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)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)(a (^z.z)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)(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. ------ 170652/19297560. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a) a)((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> ((((a a) a) a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 170653/19297587. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)(a (a a)))) REDUCED to normal form. ------ 170654/19297614. ------ 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. ------ 170655/19297641. ------ 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. ------ 170656/19297821. ------ 1. ==[ start ]==> (((a b) c)(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)(b (^x.(a a)))) REDUCED to normal form. ------ 170657/19297893. ------ 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.(^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. ------ 170658/19297920. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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. ------ 170659/19297929. ------ 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) 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. ------ 170660/19297974. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(^a.a))(^b.(^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)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 170661/19298010. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^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. ------ 170662/19298037. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 170663/19298055. ------ 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) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 170664/19298064. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 170665/19298091. ------ 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))((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. ------ 170666/19298118. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((b a)(b a))) REDUCED to normal form. ------ 170667/19298568. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 170668/19298847. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 170669/19298874. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b (^b.b))) 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))) REDUCED to normal form. ------ 170670/19298946. ------ 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)))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 170671/19299225. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 170672/19299243. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) b) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170673/19299522. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 170674/19299549. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.a)(^b.b))) 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. ------ 170675/19299567. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 170676/19299855. ------ 1. ==[ start ]==> (((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.x1))))) REDUCED to normal form. ------ 170677/19300116. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170678/19300161. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a a)(^a.(^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. ------ 170679/19300188. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((^y.y)((a (^z1.(^x2.x2))) 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. ------ 170680/19300467. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.a)(^a.(^a.(^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))))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 170681/19300485. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^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 (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 170682/19300764. ------ 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.(^x2.x2))))) REDUCED to normal form. ------ 170683/19301547. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 170684/19301592. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 170685/19301655. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 170686/19301673. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> (b (((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 170687/19301682. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 170688/19301736. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 170689/19301781. ------ 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 (^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. ------ 170690/19301790. ------ 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))((^z1.z1)(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. ------ 170691/19301817. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^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. ------ 170692/19302042. ------ 1. ==[ start ]==> (((a b)(a b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(b ((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(b (a a))) REDUCED to normal form. ------ 170693/19302069. ------ 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. ------ 170694/19302096. ------ 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))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 170695/19302150. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a) a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a) a)) REDUCED to normal form. ------ 170696/19302177. ------ 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)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((b (a (^x.x)))(a (a a))) REDUCED to normal form. ------ 170697/19302204. ------ 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)(^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. ------ 170698/19302231. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 170699/19302321. ------ 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. ------ 170700/19302402. ------ 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))(^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. ------ 170701/19302510. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170702/19302546. ------ 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))) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 170703/19302573. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(^a.(^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. ------ 170704/19302681. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 170705/19302708. ------ 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))(^z1.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. ------ 170706/19302780. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b) b)) 3. ==[ beta ]==> (b ((^z.b) b)) 4. ==[ alpha ]==> (b ((^x.b) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170707/19302924. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (^z.b))) 3. ==[ beta ]==> ((b (^y.a))(b (^z.b))) 4. ==[ alpha ]==> ((b (^x.a))(b (^y.b))) REDUCED to normal form. ------ 170708/19302951. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 170709/19303311. ------ 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))) 5. ==[ beta ]==> ((b a)(b ((a a) a))) REDUCED to normal form. ------ 170710/19303338. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(a (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (a b))) REDUCED to normal form. ------ 170711/19303392. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(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. ------ 170712/19303563. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 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. ------ 170713/19303671. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170714/19303788. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (a ((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 170715/19303887. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z)) b)) 7. ==[ beta ]==> ((b b)((^y.(^z.z)) b)) 8. ==[ alpha ]==> ((b b)((^x.(^y.y)) b)) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 170716/19303977. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 170717/19304004. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (^z.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.a))) REDUCED to normal form. ------ 170718/19304031. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(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. ------ 170719/19304076. ------ 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) 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. ------ 170720/19304085. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 170721/19304112. ------ 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. ------ 170722/19304139. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 170723/19304193. ------ 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.(^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. ------ 170724/19304256. ------ 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. ------ 170725/19304283. ------ 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.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. ------ 170726/19304310. ------ 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. ------ 170727/19304337. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(a (^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. ------ 170728/19304364. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(b a))((a (^x.x)) a)) REDUCED to normal form. ------ 170729/19304391. ------ 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. ------ 170730/19304607. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b ((^z.z) a))) 3. ==[ beta ]==> (((^y.y)(a a))(b ((^z.z) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b ((^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. ------ 170731/19304625. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 170732/19304634. ------ 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. ------ 170733/19304643. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z)) a)) 5. ==[ beta ]==> (((^z.(z z)) a)(^y.y)) 6. ==[ alpha ]==> (((^x.(x x)) a)(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 170734/19305030. ------ 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. ------ 170735/19305048. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1)) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((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) REDUCED to normal form. ------ 170736/19305057. ------ 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)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 170737/19305075. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((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. ------ 170738/19305084. ------ 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. ------ 170739/19305102. ------ 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)) 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. ------ 170740/19305156. ------ 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)))((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.x))) REDUCED to normal form. ------ 170741/19305192. ------ 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 ]==> (((^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. ------ 170742/19305219. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 170743/19305236. ------ 1. ==[ start ]==> (^a.((^a.b)(b a))) 2. ==[ alpha ]==> (^x.((^y.b)(b x))) 3. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 170744/19305237. ------ 1. ==[ start ]==> (a ((^a.b)(b a))) 2. ==[ alpha ]==> (a ((^x.b)(b a))) 3. ==[ beta ]==> (a b) REDUCED to normal form. ------ 170745/19305834. ------ 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))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 170746/19309992. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((^x.(x (^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.x1)) 5. ==[ beta ]==> ((^x1.x1)(^y.(^z.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170747/19315392. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^z.(^x1.(x1 x1)))((^z.(^x1.(x1 x1)))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.(x1 x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.(y y)) 6. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 170748/19315998. ------ 1. ==[ start ]==> (((^a.b)(b a)) a) 2. ==[ alpha ]==> (((^x.b)(b a)) a) 3. ==[ beta ]==> (b a) REDUCED to normal form. ------ 170749/19316004. ------ 1. ==[ start ]==> ((^a.a)((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 3. ==[ beta ]==> ((^y.b)(b a)) 4. ==[ alpha ]==> ((^x.b)(b a)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170750/19316058. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 170751/19316139. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^z.(^x1.x1))((^y1.(^z1.z1)) a))(^y.y)) 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. ------ 170752/19316160. ------ 1. ==[ start ]==> (((a a) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 170753/19316598. ------ 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))))((^z1.z1)(^x2.(x2 (^y2.y2)))))(^y.y)) 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)(^x1.(x1 (^y1.y1))))(^y.y))(^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 ]==> (((^z.z)(^y.y))(^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. ------ 170754/19316601. ------ 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. ------ 170755/19316610. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(y (y (^z.z))))) 5. ==[ beta ]==> ((^y.(y (y (^z.z))))(^y.(y (y (^z.z))))) 6. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(z (z (^x1.x1))))) 7. ==[ beta ]==> ((^z.(z (z (^x1.x1))))((^z.(z (z (^x1.x1))))(^y.y))) 8. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z (z (^x1.x1))))(^y1.y1))) 9. ==[ beta ]==> (((^z.(z (z (^x1.x1))))(^y1.y1))(((^z.(z (z (^x1.x1))))(^y1.y1))(^y.y))) 10. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 11. ==[ beta ]==> (((^z.z)((^z.z)(^y.y)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 12. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 13. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2))) 14. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1))) 15. ==[ beta ]==> ((^y.y)(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1))) 16. ==[ alpha ]==> ((^x.x)(((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1))) 17. ==[ beta ]==> (((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1)) 18. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.z))(^x1.x1)) 19. ==[ beta ]==> (((^z.z)((^z.z)(^y.y)))(^x1.x1)) 20. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 21. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 22. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 23. ==[ beta ]==> ((^y.y)(^z.z)) 24. ==[ alpha ]==> ((^x.x)(^y.y)) 25. ==[ beta ]==> (^y.y) 26. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170756/19316823. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 170757/19317381. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((^x.a)((a a)(a a)))((^y.a)((a a)(a a))))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a ((^y.a)((a a)(a a))))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a ((^x.a)((a a)(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) REDUCED to normal form. ------ 170758/19319733. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.((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. ------ 170759/19319919. ------ 1. ==[ start ]==> ((^a.(b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.b)(^z.b))) 3. ==[ eta ]==> (b ((^y.b)(^z.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170760/19320093. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.((z z)(z z)))) 3. ==[ beta ]==> (b (^z.((z z)(z z)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 170761/19320756. ------ 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 ]==> (((^x1.x1)((^y1.y1) b))(^y.(^z.z))) 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. ------ 170762/19320759. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 170763/19321092. ------ 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)(^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. ------ 170764/19321359. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170765/19321407. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 170766/19321674. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170767/19322010. ------ 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 ]==> (((^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. ------ 170768/19322568. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(y a))) REDUCED to normal form. ------ 170769/19322673. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((((^y.b)(^z.(z z)))((^y.b)(^z.(z z))))(((^y.b)(^z.(z z)))((^y.b)(^z.(z z))))) 4. ==[ alpha ]==> ((((^x.b)(^y.(y y)))((^z.b)(^x1.(x1 x1))))(((^y1.b)(^z1.(z1 z1)))((^x2.b)(^y2.(y2 y2))))) 5. ==[ beta ]==> ((b ((^z.b)(^x1.(x1 x1))))(((^y1.b)(^z1.(z1 z1)))((^x2.b)(^y2.(y2 y2))))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.(y y))))(((^z.b)(^x1.(x1 x1)))((^y1.b)(^z1.(z1 z1))))) 7. ==[ beta ]==> ((b b)(((^z.b)(^x1.(x1 x1)))((^y1.b)(^z1.(z1 z1))))) 8. ==[ alpha ]==> ((b b)(((^x.b)(^y.(y y)))((^z.b)(^x1.(x1 x1))))) 9. ==[ beta ]==> ((b b)(b ((^z.b)(^x1.(x1 x1))))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(^y.(y y))))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 170770/19322847. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(b z))) 3. ==[ eta ]==> (((^x.b)(^y.b)) b) 4. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170771/19323342. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.(^c.(^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. ------ 170772/19323594. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.(^c.(^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. ------ 170773/19324674. ------ 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. ------ 170774/19324863. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 170775/19325664. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 170776/19325808. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^b.(^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. ------ 170777/19325943. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 170778/19326051. ------ 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. ------ 170779/19326156. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^x1.(x1 x1)))(((^z.z)(^x1.(x1 x1)))(^y.y))) 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)(^z.(z z)))(^x1.x1))(((^y.y)(^z.(z z)))(^x1.x1))) 8. ==[ alpha ]==> ((((^x.x)(^y.(y y)))(^z.z))(((^x1.x1)(^y1.(y1 y1)))(^z1.z1))) 9. ==[ beta ]==> (((^y.(y y))(^z.z))(((^x1.x1)(^y1.(y1 y1)))(^z1.z1))) 10. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.(x1 x1)))(^y1.y1))) 11. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.(x1 x1)))(^y1.y1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.(x1 x1)))(^y1.y1))) 13. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.(x1 x1)))(^y1.y1))) 14. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(z z)))(^x1.x1))) 15. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.x1)) 16. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z)) 17. ==[ beta ]==> ((^y.(y y))(^z.z)) 18. ==[ alpha ]==> ((^x.(x x))(^y.y)) 19. ==[ beta ]==> ((^y.y)(^y.y)) 20. ==[ alpha ]==> ((^x.x)(^y.y)) 21. ==[ beta ]==> (^y.y) 22. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170780/19326159. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(z z)))) REDUCED to normal form. ------ 170781/19326168. ------ 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. ------ 170782/19326555. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^a.(^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. ------ 170783/19326627. ------ 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)(^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. ------ 170784/19326717. ------ 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. ------ 170785/19326744. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 170786/19326762. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.a)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.y)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170787/19326774. ------ 1. ==[ start ]==> ((a a)((^a.b)(b a))) 2. ==[ alpha ]==> ((a a)((^x.b)(b a))) 3. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 170788/19326792. ------ 1. ==[ start ]==> (((^a.a) a)(((a a) a)(^a.(^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. ------ 170789/19326819. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 170790/19326828. ------ 1. ==[ start ]==> ((a b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 170791/19326882. ------ 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. ------ 170792/19326909. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 170793/19326927. ------ 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. ------ 170794/19326954. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a (^y.y))) a)) REDUCED to normal form. ------ 170795/19326981. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 170796/19327008. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z)) c)) REDUCED to normal form. ------ 170797/19327071. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.b)(^b.(^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. ------ 170798/19327368. ------ 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. ------ 170799/19327377. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.(y y))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.(x x))(a (a (a (^y.y))))) 5. ==[ beta ]==> ((a (a (a (^y.y))))(a (a (a (^y.y))))) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a (a (^y.y))))) REDUCED to normal form. ------ 170800/19327404. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 170801/19327458. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(a a))((^z.z) 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. ------ 170802/19327485. ------ 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. ------ 170803/19327512. ------ 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)))((^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. ------ 170804/19327566. ------ 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)(^y.y))(a b))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 170805/19327593. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 170806/19327728. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^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. ------ 170807/19327755. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(b (^y1.y1)))) 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. ------ 170808/19327818. ------ 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. ------ 170809/19327845. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 170810/19327872. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 170811/19327899. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b (^z.(z z)))) REDUCED to normal form. ------ 170812/19327926. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (^a.(^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)))) REDUCED to normal form. ------ 170813/19327953. ------ 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. ------ 170814/19327980. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 170815/19328016. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 170816/19328043. ------ 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. ------ 170817/19328097. ------ 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. ------ 170818/19328124. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) b))) 7. ==[ beta ]==> ((a a)(((^y.y) b)((^y.y) b))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) b))) 9. ==[ beta ]==> ((a a)(b ((^y.y) b))) 10. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 11. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 170819/19328151. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 170820/19328277. ------ 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. ------ 170821/19328502. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 170822/19328529. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(a a))(^b.b))) 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))) 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. ------ 170823/19328556. ------ 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. ------ 170824/19328673. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.b)(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 170825/19328754. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)((^z.z)(^x1.x1)))) IRREDUCIBLE: cycle. ------ 170826/19328835. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170827/19328862. ------ 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. ------ 170828/19328889. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^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. ------ 170829/19328943. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a ((^y.y) b))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(a ((^x.x) b))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(a b)) REDUCED to normal form. ------ 170830/19329033. ------ 1. ==[ start ]==> (((a b)(^a.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 170831/19329069. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 170832/19329096. ------ 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) 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. ------ 170833/19329123. ------ 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)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 170834/19329204. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 170835/19329222. ------ 1. ==[ start ]==> (((^a.b) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 170836/19329231. ------ 1. ==[ start ]==> (((a b)(a a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 170837/19329438. ------ 1. ==[ start ]==> (((a b) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 170838/19329465. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) b) c)) 3. ==[ beta ]==> (((a a) a)(((^y.y) b) c)) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b) c)) 5. ==[ beta ]==> (((a a) a)(b c)) REDUCED to normal form. ------ 170839/19329717. ------ 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)(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. ------ 170840/19329744. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 170841/19329870. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a))) d)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.(^x1.x1))) d)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) d)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) d)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 170842/19329969. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 170843/19330104. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 170844/19330167. ------ 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. ------ 170845/19330221. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 170846/19330248. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b a)(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.b))((b a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.b))((b a)(^y.(y y)))) REDUCED to normal form. ------ 170847/19330302. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170848/19330329. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a b)(^y.b))) REDUCED to normal form. ------ 170849/19330356. ------ 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. ------ 170850/19330446. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 170851/19330473. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 170852/19330500. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)((a a)(a a)))) 5. ==[ beta ]==> ((a (a b))((a a)(a a))) REDUCED to normal form. ------ 170853/19330554. ------ 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)(^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. ------ 170854/19330581. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.(^z.z)))(^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. ------ 170855/19330662. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 170856/19330689. ------ 1. ==[ start ]==> ((a (b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((a (b a))((^x.b)(^y.b))) 3. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 170857/19330860. ------ 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. ------ 170858/19330923. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 170859/19330968. ------ 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)))) REDUCED to normal form. ------ 170860/19330995. ------ 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)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 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. ------ 170861/19331049. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a) a)(a b))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)(a b))) REDUCED to normal form. ------ 170862/19331130. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (b (((^y.y) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 170863/19331256. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 170864/19331337. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 170865/19331364. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.b)((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a a) a)((^y.b)((a a) a))) 6. ==[ alpha ]==> (((a a) a)((^x.b)((a a) a))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 170866/19331418. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 170867/19331445. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(y y))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 170868/19331472. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 170869/19331517. ------ 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))((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. ------ 170870/19331526. ------ 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))))((^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. ------ 170871/19331832. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 170872/19331859. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 170873/19331913. ------ 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 a))((^y.y)(a a)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a)(a (^z.z)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)(a (^y.y)))) 7. ==[ beta ]==> (((a a)(a a))((b a)(a (^y.y)))) 8. ==[ alpha ]==> (((a a)(a a))((b a)(a (^x.x)))) REDUCED to normal form. ------ 170874/19331949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1)) d)) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1)) d)) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) d)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 170875/19331994. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a b)((^x1.x1)(^y1.y1)))) 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. ------ 170876/19332102. ------ 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) 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. ------ 170877/19332129. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 170878/19332147. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 170879/19332174. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(a (^y.y))) REDUCED to normal form. ------ 170880/19332201. ------ 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.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(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. ------ 170881/19332255. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 170882/19332282. ------ 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. ------ 170883/19332309. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 170884/19332363. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 170885/19332408. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^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. ------ 170886/19332417. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) a) REDUCED to normal form. ------ 170887/19332444. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 170888/19332777. ------ 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 ]==> (((^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. ------ 170889/19332786. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^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. ------ 170890/19332804. ------ 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)((b a)(a a))) 4. ==[ alpha ]==> ((^x.x)((b a)(a a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 170891/19332858. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)((^x1.x1) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)((^z.z) a))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a) a)) REDUCED to normal form. ------ 170892/19332939. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^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. ------ 170893/19333047. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((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. ------ 170894/19333083. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((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. ------ 170895/19333119. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 170896/19333146. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 170897/19333173. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((a (b a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.b)(a (a a)))) 5. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 170898/19333227. ------ 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.(^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))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 170899/19333254. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(x x))(a b))) 3. ==[ beta ]==> ((((a a) a)(a b))((a b)(a b))) REDUCED to normal form. ------ 170900/19333281. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.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. ------ 170901/19333308. ------ 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.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 170902/19333335. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(b a)) REDUCED to normal form. ------ 170903/19333416. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 170904/19333443. ------ 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. ------ 170905/19333614. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(a (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(a (b a))) 3. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 170906/19333722. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 170907/19333803. ------ 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))) 5. ==[ beta ]==> (((a a)(a a))(a (a b))) REDUCED to normal form. ------ 170908/19333830. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.y1)(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. ------ 170909/19333947. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)(^y.a))) REDUCED to normal form. ------ 170910/19333974. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 170911/19334028. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))(^x1.a))) REDUCED to normal form. ------ 170912/19334082. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 170913/19334109. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a a)(^c.(^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. ------ 170914/19334136. ------ 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. ------ 170915/19334172. ------ 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. ------ 170916/19334199. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 170917/19334253. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^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. ------ 170918/19334307. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 170919/19334334. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 170920/19334838. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((b c)(((^y.y)(a a)) a)) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a)) a)) 5. ==[ beta ]==> ((b c)((a a) a)) REDUCED to normal form. ------ 170921/19334865. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b) b)) REDUCED to normal form. ------ 170922/19335072. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b)(a a))) 3. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 170923/19335081. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b) b)) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 170924/19335108. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a) c)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a) c)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a) c)) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 170925/19335180. ------ 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) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^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. ------ 170926/19335306. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 170927/19335333. ------ 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) 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. ------ 170928/19335360. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((a b)((^y.(y y))(a (a a)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(a (a a)))) 7. ==[ beta ]==> ((a b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 170929/19335387. ------ 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)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 170930/19335414. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^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. ------ 170931/19335441. ------ 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. ------ 170932/19335468. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a b)(a a))((^y.b)(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))((^x.b)(^y.y))) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 170933/19335495. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 170934/19335522. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(^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. ------ 170935/19335576. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.a)(^b.(^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. ------ 170936/19335603. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 170937/19335630. ------ 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 (^x.x)))(^z.b)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.b)) REDUCED to normal form. ------ 170938/19335774. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((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)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 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. ------ 170939/19336125. ------ 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)(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))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 170940/19336179. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1))(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z))(a a))) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(a a))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(a a))) 9. ==[ beta ]==> ((b b)((^y.y)(a a))) 10. ==[ alpha ]==> ((b b)((^x.x)(a a))) 11. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 170941/19336188. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 170942/19336260. ------ 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. ------ 170943/19336323. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 170944/19336377. ------ 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) a)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.a))) REDUCED to normal form. ------ 170945/19336404. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 170946/19336431. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 170947/19336485. ------ 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. ------ 170948/19336521. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^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. ------ 170949/19336548. ------ 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))(^y1.(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. ------ 170950/19336575. ------ 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.(^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. ------ 170951/19336656. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.a))) REDUCED to normal form. ------ 170952/19336683. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 170953/19336710. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(a (^b.(^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)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 170954/19336737. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a a)(a a))) REDUCED to normal form. ------ 170955/19336791. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))((^z1.z1) 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. ------ 170956/19336818. ------ 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. ------ 170957/19336845. ------ 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 y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^y.y))) 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. ------ 170958/19336899. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 170959/19336926. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.(z z))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(y y))) REDUCED to normal form. ------ 170960/19336935. ------ 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. ------ 170961/19337322. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(^a.(^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. ------ 170962/19337349. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y)) a)) REDUCED to normal form. ------ 170963/19337367. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 170964/19337376. ------ 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. ------ 170965/19337394. ------ 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)(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. ------ 170966/19337448. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b a)) REDUCED to normal form. ------ 170967/19337484. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 170968/19337511. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 170969/19337529. ------ 1. ==[ start ]==> (((^a.b)(b a))(a a)) 2. ==[ alpha ]==> (((^x.b)(b a))(a a)) 3. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 170970/19348299. ------ 1. ==[ start ]==> (((^a.b)(b a)) b) 2. ==[ alpha ]==> (((^x.b)(b a)) b) 3. ==[ beta ]==> (b b) REDUCED to normal form. ------ 170971/19348323. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170972/19348341. ------ 1. ==[ start ]==> ((^a.(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((a a) a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 170973/19348368. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 170974/19348404. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 170975/19348488. ------ 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)(^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. ------ 170976/19348809. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 170977/19348920. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.(^z.(z (^x1.x1))))(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 (^z1.z1))))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 170978/19349352. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^a.(^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. ------ 170979/19350024. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 170980/19351683. ------ 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. ------ 170981/19352043. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 170982/19352403. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^b.(^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. ------ 170983/19352778. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b)(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. ------ 170984/19353066. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x1.x1))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 170985/19353078. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.((^a.a) b))) 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. ------ 170986/19353402. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^b.(^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. ------ 170987/19353669. ------ 1. ==[ start ]==> ((^a.(^b.b))(c (^d.a))) 2. ==[ alpha ]==> ((^x.(^y.y))(c (^z.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 170988/19354023. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^z1.(a (^x2.(^y2.y2))))) 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. ------ 170989/19354320. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^b.(^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. ------ 170990/19354329. ------ 1. ==[ start ]==> (((a a)(^b.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 170991/19357839. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 170992/19358043. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 170993/19358361. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 170994/19358478. ------ 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 ]==> ((^y.(y (^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^z.(^x1.(x1 x1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z)) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 170995/19358883. ------ 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))) REDUCED to normal form. ------ 170996/19358937. ------ 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)(^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. ------ 170997/19358991. ------ 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 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. ------ 170998/19359027. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.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. ------ 170999/19359054. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 171000/19359072. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 171001/19359102. ------ 1. ==[ start ]==> ((a (^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(b a))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 171002/19359120. ------ 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. ------ 171003/19359147. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))(^b.b))) 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. ------ 171004/19359156. ------ 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. ------ 171005/19359183. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 171006/19359237. ------ 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.(^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. ------ 171007/19359264. ------ 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)((^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. ------ 171008/19359291. ------ 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. ------ 171009/19359426. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 171010/19359507. ------ 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. ------ 171011/19359588. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 171012/19359678. ------ 1. ==[ start ]==> (((^a.(a a)) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)(b ((^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. ------ 171013/19359696. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 8. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 9. ==[ beta ]==> (((^z.z)(^x1.(x1 (^y1.y1))))(^y.y)) 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. ------ 171014/19359759. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a b)((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 171015/19359786. ------ 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. ------ 171016/19359813. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(b (a (a a)))) REDUCED to normal form. ------ 171017/19359840. ------ 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)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 171018/19359867. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 171019/19359894. ------ 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. ------ 171020/19360002. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((b b)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((b b)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((b b)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 171021/19360128. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(a (^y1.(y1 (^z1.z1))))) 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. ------ 171022/19360263. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 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. ------ 171023/19360335. ------ 1. ==[ start ]==> (((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))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 171024/19360362. ------ 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. ------ 171025/19360416. ------ 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. ------ 171026/19360443. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (a a))(^b.b))) 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. ------ 171027/19360506. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(b (^x2.x2)))) 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. ------ 171028/19360641. ------ 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. ------ 171029/19360668. ------ 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.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 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. ------ 171030/19360803. ------ 1. ==[ start ]==> ((a (^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 171031/19360974. ------ 1. ==[ start ]==> (((^a.b) a)((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 171032/19361136. ------ 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. ------ 171033/19361163. ------ 1. ==[ start ]==> (((a b) a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b) a)((a b)(a a))) REDUCED to normal form. ------ 171034/19361190. ------ 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. ------ 171035/19361244. ------ 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 (^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. ------ 171036/19361271. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a ((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(a b)) REDUCED to normal form. ------ 171037/19361298. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 171038/19361325. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(b (^z.z)))) REDUCED to normal form. ------ 171039/19361388. ------ 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. ------ 171040/19361415. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(b (^z.a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(b (^y.a))) REDUCED to normal form. ------ 171041/19361442. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 171042/19361469. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 171043/19361523. ------ 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))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 171044/19361550. ------ 1. ==[ start ]==> (((a b)(a a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 171045/19361586. ------ 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. ------ 171046/19361613. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 171047/19361667. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)((^z1.z1) b))) 5. ==[ beta ]==> ((^y.y)((^y1.a)((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 7. ==[ beta ]==> ((^y.a)((^z.z) b)) 8. ==[ alpha ]==> ((^x.a)((^y.y) b)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 171048/19361802. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b)(^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))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 171049/19361829. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 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. ------ 171050/19361964. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 171051/19362171. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y) c)) 3. ==[ beta ]==> ((((a a) a) a)((^y.y) c)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x) c)) 5. ==[ beta ]==> ((((a a) a) a) c) REDUCED to normal form. ------ 171052/19362189. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)((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 (^x.(^y.y))) a)) REDUCED to normal form. ------ 171053/19362423. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (^z.z))) 3. ==[ beta ]==> (b (c (^z.z))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 171054/19362432. ------ 1. ==[ start ]==> (((a b) c)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> (((a b) c)((a (^x.x)) b)) REDUCED to normal form. ------ 171055/19362459. ------ 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. ------ 171056/19362531. ------ 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)(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. ------ 171057/19362666. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 171058/19362765. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 171059/19362792. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.a))(^b.b))) 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. ------ 171060/19362819. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((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. ------ 171061/19362846. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(a a)) a)) REDUCED to normal form. ------ 171062/19362873. ------ 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) b) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b) b)) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) b)) 7. ==[ beta ]==> ((^y.y)(((^z.z) b) b)) 8. ==[ alpha ]==> ((^x.x)(((^y.y) b) b)) 9. ==[ beta ]==> (((^y.y) b) b) 10. ==[ alpha ]==> (((^x.x) b) b) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 171063/19363179. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 171064/19363242. ------ 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)))(a (^x1.x1)))) REDUCED to normal form. ------ 171065/19363350. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a b)((a a) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a b)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a b)((a a) a))) REDUCED to normal form. ------ 171066/19363377. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a) a)(a b))) REDUCED to normal form. ------ 171067/19363431. ------ 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. ------ 171068/19363458. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a (b a))) REDUCED to normal form. ------ 171069/19363485. ------ 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.(^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))))) REDUCED to normal form. ------ 171070/19363512. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) b)) REDUCED to normal form. ------ 171071/19363557. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b)(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. ------ 171072/19363575. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 171073/19363602. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 171074/19363629. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y)(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 (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. ------ 171075/19363656. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(a a))(^b.(^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. ------ 171076/19363683. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a b)(^z.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a b)(^z.a))) 4. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 171077/19363710. ------ 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)(^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. ------ 171078/19363737. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b)(a (a a)))(^y.(a a))) 6. ==[ alpha ]==> (((a b)(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 171079/19363845. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 171080/19363854. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1) b))) 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)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171081/19364016. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171082/19364151. ------ 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.(^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. ------ 171083/19364160. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 171084/19364178. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.a)(^b.b))) 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. ------ 171085/19364241. ------ 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. ------ 171086/19364268. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))((^z.z) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 171087/19364322. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 171088/19364349. ------ 1. ==[ start ]==> ((((^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) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 171089/19364376. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a b)) REDUCED to normal form. ------ 171090/19364430. ------ 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)))(^z.z))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 171091/19364448. ------ 1. ==[ start ]==> ((a (^b.b))(c (^d.a))) 2. ==[ alpha ]==> ((a (^x.x))(c (^y.a))) REDUCED to normal form. ------ 171092/19364520. ------ 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)))(^y1.y1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 171093/19364547. ------ 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. ------ 171094/19364574. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.a))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 171095/19364601. ------ 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.(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. ------ 171096/19364628. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 171097/19364682. ------ 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))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.b))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.b)) 8. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.b)) REDUCED to normal form. ------ 171098/19364772. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 171099/19364799. ------ 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.z1)(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^z1.z1)(a (^x2.(^y2.y2))))) 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. ------ 171100/19364934. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 171101/19365042. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.a)(^c.(^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. ------ 171102/19365051. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(c ((a a)(^z.z)))) REDUCED to normal form. ------ 171103/19365078. ------ 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. ------ 171104/19365096. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)((^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. ------ 171105/19365105. ------ 1. ==[ start ]==> (((a a)(^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 171106/19365132. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a)(a a))) REDUCED to normal form. ------ 171107/19365213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))((a b)(a (a a)))) 6. ==[ alpha ]==> ((^x.(a a))((a b)(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171108/19365240. ------ 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)(^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. ------ 171109/19365267. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a b)(^x.a))((a a) a)) REDUCED to normal form. ------ 171110/19365294. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^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. ------ 171111/19365321. ------ 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)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a (a a))) REDUCED to normal form. ------ 171112/19365375. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(b a))) REDUCED to normal form. ------ 171113/19365438. ------ 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.(^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. ------ 171114/19365465. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^x1.a))) REDUCED to normal form. ------ 171115/19365492. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((a (b a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((a (b a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 171116/19365519. ------ 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. ------ 171117/19365573. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (a a))(^x.b))) REDUCED to normal form. ------ 171118/19365600. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) 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. ------ 171119/19365708. ------ 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)(^x1.x1)) b)) REDUCED to normal form. ------ 171120/19365735. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a)) c)) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a)) c)) 5. ==[ beta ]==> ((b (a a))((a a) c)) REDUCED to normal form. ------ 171121/19365798. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)(^b.(^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. ------ 171122/19366077. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b b)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b b)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 171123/19366104. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a (a a))((a a) a))) REDUCED to normal form. ------ 171124/19366149. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 171125/19366158. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((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))(^y.y))((a (^z.z))(a a))) REDUCED to normal form. ------ 171126/19366185. ------ 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)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 171127/19366284. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.b)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 171128/19366392. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 171129/19366491. ------ 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. ------ 171130/19366518. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b) c)) 3. ==[ beta ]==> (((a (^x.x)) b)((a b) c)) REDUCED to normal form. ------ 171131/19366761. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b) c)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 171132/19366788. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a) d)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a) d)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a) d)) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 171133/19367013. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171134/19367121. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(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. ------ 171135/19367229. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a)(^b.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. ------ 171136/19367256. ------ 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))(^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. ------ 171137/19367310. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)(^z1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 171138/19367400. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(a a))) REDUCED to normal form. ------ 171139/19367427. ------ 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)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 171140/19367508. ------ 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) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.x1))) REDUCED to normal form. ------ 171141/19367535. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 171142/19367562. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 171143/19367625. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 171144/19367652. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.a)) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.a)) REDUCED to normal form. ------ 171145/19367679. ------ 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 z)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (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. ------ 171146/19367706. ------ 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) 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. ------ 171147/19367733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))(^c.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. ------ 171148/19367760. ------ 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. ------ 171149/19367787. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b) a)) 3. ==[ beta ]==> (((a b)(a a))((a b) a)) REDUCED to normal form. ------ 171150/19367814. ------ 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. ------ 171151/19368093. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c (^z.(^x1.x1)))) 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. ------ 171152/19368174. ------ 1. ==[ start ]==> (((^a.b)(^c.(^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) REDUCED to normal form. ------ 171153/19368282. ------ 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.(^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. ------ 171154/19368417. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 171155/19368444. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 171156/19368507. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 171157/19368534. ------ 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. ------ 171158/19368579. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (^z.(z z)))) 3. ==[ beta ]==> (b (c (^z.(z z)))) 4. ==[ alpha ]==> (b (c (^x.(x x)))) REDUCED to normal form. ------ 171159/19368588. ------ 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. ------ 171160/19368615. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 171161/19368687. ------ 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 (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171162/19368723. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c d)) 3. ==[ beta ]==> ((b (^y.(y y)))(c d)) 4. ==[ alpha ]==> ((b (^x.(x x)))(c d)) REDUCED to normal form. ------ 171163/19368822. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 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. ------ 171164/19368921. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 171165/19368948. ------ 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 y1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1)) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1)) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z)) b)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 171166/19368975. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a) c)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 171167/19369056. ------ 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. ------ 171168/19369110. ------ 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 (^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.a))) REDUCED to normal form. ------ 171169/19369137. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)(^y.(y y)))) 3. ==[ beta ]==> ((b (a (a a)))((a a)(^y.(y y)))) 4. ==[ alpha ]==> ((b (a (a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 171170/19369164. ------ 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. ------ 171171/19369236. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b ((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))(b ((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 171172/19369254. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^z.z)(^x1.(x1 x1)))(^y.y)) 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. ------ 171173/19369641. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b b)) 3. ==[ beta ]==> (((^y.y) b)(b b)) 4. ==[ alpha ]==> (((^x.x) b)(b b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 171174/19369659. ------ 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. ------ 171175/19369686. ------ 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)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 171176/19369695. ------ 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. ------ 171177/19369713. ------ 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)((^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. ------ 171178/19369767. ------ 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)(a a)))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 171179/19369803. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(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. ------ 171180/19369830. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 171181/19369848. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (^y.y))) 3. ==[ beta ]==> (b (a (^y.y))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 171182/19380627. ------ 1. ==[ start ]==> (((^a.b)(b a)) c) 2. ==[ alpha ]==> (((^x.b)(b a)) c) 3. ==[ beta ]==> (b c) REDUCED to normal form. ------ 171183/19380834. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 171184/19380903. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z)) c)) 3. ==[ beta ]==> (^y.((b (^z.z)) c)) 4. ==[ alpha ]==> (^x.((b (^y.y)) c)) REDUCED to normal form. ------ 171185/19381245. ------ 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. ------ 171186/19381596. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (a a))((^x1.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. ------ 171187/19381698. ------ 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. ------ 171188/19382517. ------ 1. ==[ start ]==> ((((a a) a)(a a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((((a a) a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 171189/19382541. ------ 1. ==[ start ]==> ((^a.(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(x b))((b (^y.y))(a a))) 3. ==[ beta ]==> (((b (^y.y))(a a)) b) 4. ==[ alpha ]==> (((b (^x.x))(a a)) b) REDUCED to normal form. ------ 171190/19382928. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (^y.(((b (^z.z))(^x1.x1))((b (^z.z))(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((b (^y.y))(^z.z))((b (^x1.x1))(^y1.y1)))) REDUCED to normal form. ------ 171191/19383678. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 171192/19383810. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((((a a)(^z.z))((^x1.x1)(^y1.y1)))(((a a)(^z.z))((^x1.x1)(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> (((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1))))(^x2.x2)) 5. ==[ beta ]==> (((((a a)(^x.x))(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1))))(^x2.x2)) 6. ==[ alpha ]==> (((((a a)(^x.x))(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1))))(^z1.z1)) 7. ==[ beta ]==> (((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 171193/19385115. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) b)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 171194/19386054. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 171195/19386666. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 171196/19386963. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.(^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. ------ 171197/19388016. ------ 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. ------ 171198/19388268. ------ 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)))(^x1.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 171199/19388400. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 171200/19388718. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.((^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. ------ 171201/19389561. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a)(a a))) 3. ==[ eta ]==> ((^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. ------ 171202/19390203. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.z))) REDUCED to normal form. ------ 171203/19390380. ------ 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. ------ 171204/19390482. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.((^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. ------ 171205/19390803. ------ 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))) 5. ==[ beta ]==> ((b a)((b ((^y.y) a))(^z.z))) 6. ==[ alpha ]==> ((b a)((b ((^x.x) a))(^y.y))) 7. ==[ beta ]==> ((b a)((b a)(^y.y))) 8. ==[ alpha ]==> ((b a)((b a)(^x.x))) REDUCED to normal form. ------ 171206/19391229. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(a (^z.z)))) REDUCED to normal form. ------ 171207/19391328. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.b)) 2. ==[ alpha ]==> (((^x.(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. ------ 171208/19391364. ------ 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)) REDUCED to normal form. ------ 171209/19391391. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 171210/19391409. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.a)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.a)) 3. ==[ beta ]==> (b (^y.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 171211/19391457. ------ 1. ==[ start ]==> (((^a.a) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.b)(b a))) 3. ==[ beta ]==> (a ((^y.b)(b a))) 4. ==[ alpha ]==> (a ((^x.b)(b a))) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 171212/19391475. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((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. ------ 171213/19391502. ------ 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. ------ 171214/19391511. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 171215/19391538. ------ 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)))) 5. ==[ beta ]==> (b (((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 171216/19391565. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 171217/19391592. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 171218/19391610. ------ 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. ------ 171219/19391619. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (a (^y.y)))) REDUCED to normal form. ------ 171220/19391637. ------ 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. ------ 171221/19391646. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 171222/19391664. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 171223/19391691. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y)) c)) REDUCED to normal form. ------ 171224/19391727. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(x1 x1)))) 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. ------ 171225/19391862. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 171226/19392033. ------ 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. ------ 171227/19392069. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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 ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 171228/19392276. ------ 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. ------ 171229/19392303. ------ 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)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 171230/19392330. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^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. ------ 171231/19392357. ------ 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. ------ 171232/19392384. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.y))((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. ------ 171233/19392483. ------ 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. ------ 171234/19392528. ------ 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))) REDUCED to normal form. ------ 171235/19392555. ------ 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. ------ 171236/19392591. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (^x.a))(a (a a))) REDUCED to normal form. ------ 171237/19392609. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 171238/19392618. ------ 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. ------ 171239/19392906. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> (a (((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a) a)) 7. ==[ beta ]==> (a ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171240/19393023. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^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. ------ 171241/19393077. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 171242/19393104. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171243/19393131. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 171244/19393275. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 171245/19393302. ------ 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. ------ 171246/19393329. ------ 1. ==[ start ]==> ((a (a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((a (a b))((b (^x.x))(a a))) REDUCED to normal form. ------ 171247/19393644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(c (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c (^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(c (^z.(a a)))) 6. ==[ alpha ]==> ((^x.a)(c (^y.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 171248/19393716. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 171249/19393887. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 171250/19393932. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a) a)(^c.(^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 a) REDUCED to normal form. ------ 171251/19394013. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.z1))) 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. ------ 171252/19394094. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (b ((b (^x1.x1)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 171253/19394148. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) b) c)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b) c)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b) c)) 5. ==[ beta ]==> ((a a)(((^y.y) b) c)) 6. ==[ alpha ]==> ((a a)(((^x.x) b) c)) 7. ==[ beta ]==> ((a a)(b c)) REDUCED to normal form. ------ 171254/19394157. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 171255/19394184. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 171256/19394238. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.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. ------ 171257/19394265. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.b))) 7. ==[ beta ]==> (((^y.(a a))(^z.b))((^y.(a a))(^z.b))) 8. ==[ alpha ]==> (((^x.(a a))(^y.b))((^z.(a a))(^x1.b))) 9. ==[ beta ]==> ((a a)((^z.(a a))(^x1.b))) 10. ==[ alpha ]==> ((a a)((^x.(a a))(^y.b))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 171258/19394292. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 171259/19394319. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a)(^c.(^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. ------ 171260/19394409. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c ((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))(a b))(c b)) REDUCED to normal form. ------ 171261/19394436. ------ 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. ------ 171262/19394463. ------ 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))(^y.y))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 171263/19394490. ------ 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))(a a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a))(a a))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 171264/19394517. ------ 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 (^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)))) 5. ==[ beta ]==> ((((a a) a) a)(b (a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a) a)(b (a (^x.x)))) REDUCED to normal form. ------ 171265/19394544. ------ 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) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 171266/19394571. ------ 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. ------ 171267/19394598. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 171268/19394778. ------ 1. ==[ start ]==> (((a b) c)(c (^b.b))) 2. ==[ alpha ]==> (((a b) c)(c (^x.x))) REDUCED to normal form. ------ 171269/19394805. ------ 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. ------ 171270/19394850. ------ 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. ------ 171271/19394877. ------ 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)(^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. ------ 171272/19394886. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b)(a (^a.a)))) 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. ------ 171273/19394913. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 171274/19394931. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 171275/19394967. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171276/19394994. ------ 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 a)) REDUCED to normal form. ------ 171277/19395012. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a b)(^z.b))) 3. ==[ beta ]==> (b ((a b)(^z.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 171278/19395021. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(a b))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 171279/19395075. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((a 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. ------ 171280/19395831. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.a))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 171281/19395858. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 171282/19395903. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 171283/19396182. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 171284/19396200. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a a)(^b.b))) 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. ------ 171285/19396281. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((b a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((b a) c)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((b a) c)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((b a) c)) 5. ==[ beta ]==> ((a a)((b a) c)) REDUCED to normal form. ------ 171286/19396506. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 171287/19396578. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1))) b)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1))) b)) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1))) b)) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z))) b)) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 171288/19396812. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.z))(b a))) REDUCED to normal form. ------ 171289/19396839. ------ 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. ------ 171290/19397073. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(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. ------ 171291/19397145. ------ 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)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((a a)(^z1.(^x2.(^y2.y2))))) 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. ------ 171292/19397397. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 171293/19397451. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.a)(^a.(^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. ------ 171294/19397469. ------ 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.(^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. ------ 171295/19397748. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a (^a.(^a.(^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))))) REDUCED to normal form. ------ 171296/19398504. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c (^z.(a a)))) REDUCED to normal form. ------ 171297/19398531. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 171298/19398612. ------ 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))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 171299/19398630. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)(^y.a))) 3. ==[ beta ]==> (b ((a b)(^y.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 171300/19398639. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 171301/19398693. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.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. ------ 171302/19398738. ------ 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)(^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. ------ 171303/19398747. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 171304/19398774. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 171305/19398801. ------ 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. ------ 171306/19398999. ------ 1. ==[ start ]==> (((a b)(a b))(c (a b))) REDUCED to normal form. ------ 171307/19399026. ------ 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. ------ 171308/19399053. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 171309/19399107. ------ 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)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)(a (^z.z)))) REDUCED to normal form. ------ 171310/19399134. ------ 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) a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((b (a (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 171311/19399161. ------ 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)(^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. ------ 171312/19399188. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (a a))((^y.y)(^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. ------ 171313/19399359. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a)(^b.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. ------ 171314/19399467. ------ 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))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171315/19399503. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((b c)((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b c)((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> ((b c)((^y.y)(a a))) 6. ==[ alpha ]==> ((b c)((^x.x)(a a))) 7. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 171316/19399530. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(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. ------ 171317/19399575. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a) c)) 3. ==[ beta ]==> ((b (^y.y))(((a a) a) c)) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a) c)) REDUCED to normal form. ------ 171318/19399638. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 171319/19399665. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)(^c.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. ------ 171320/19399737. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 171321/19399881. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c (^z.a))) 3. ==[ beta ]==> ((b (^y.a))(c (^z.a))) 4. ==[ alpha ]==> ((b (^x.a))(c (^y.a))) REDUCED to normal form. ------ 171322/19399908. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (^z.b))) REDUCED to normal form. ------ 171323/19400268. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)(c ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b a)(c ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((b a)(c (^y.y))) 8. ==[ alpha ]==> ((b a)(c (^x.x))) REDUCED to normal form. ------ 171324/19400295. ------ 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. ------ 171325/19400349. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((a ((^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. ------ 171326/19400520. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> (b (((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((a a) a)(^x.x))) REDUCED to normal form. ------ 171327/19400628. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 171328/19400745. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.a))) 5. ==[ beta ]==> (a ((^y.(y y))(^z.a))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.a))) 7. ==[ beta ]==> (a ((^y.a)(^y.a))) 8. ==[ alpha ]==> (a ((^x.a)(^y.a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171329/19400844. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a) a)) 7. ==[ beta ]==> ((b b)((^y.a) a)) 8. ==[ alpha ]==> ((b b)((^x.a) a)) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 171330/19400934. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(z z)))) REDUCED to normal form. ------ 171331/19400961. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 171332/19400988. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.a))) REDUCED to normal form. ------ 171333/19401033. ------ 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. ------ 171334/19401042. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^z1.z1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.z1)))) REDUCED to normal form. ------ 171335/19401069. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 171336/19401096. ------ 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. ------ 171337/19401150. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 171338/19401168. ------ 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. ------ 171339/19401213. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(c a)) REDUCED to normal form. ------ 171340/19401240. ------ 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. ------ 171341/19401267. ------ 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)) 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. ------ 171342/19401294. ------ 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. ------ 171343/19401321. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) 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. ------ 171344/19401348. ------ 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) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 171345/19401375. ------ 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. ------ 171346/19401582. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 171347/19401591. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b ((^y.y) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(b a)) REDUCED to normal form. ------ 171348/19401987. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^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. ------ 171349/19402005. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^a.(^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. ------ 171350/19402014. ------ 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. ------ 171351/19402032. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((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. ------ 171352/19402041. ------ 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. ------ 171353/19402059. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((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. ------ 171354/19402113. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) b) REDUCED to normal form. ------ 171355/19402149. ------ 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. ------ 171356/19402176. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 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. ------ 171357/19402194. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y) a)) 3. ==[ beta ]==> (b ((^y.y) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 171358/19402220. ------ 1. ==[ start ]==> (^a.((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.(x x))((x x)(^z.z)))) 3. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 171359/19402221. ------ 1. ==[ start ]==> (a ((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (a ((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 171360/19413015. ------ 1. ==[ start ]==> ((^a.a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 4. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171361/19413042. ------ 1. ==[ start ]==> ((^a.(a a))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.b)(b a))) 3. ==[ beta ]==> (((^y.b)(b a))((^y.b)(b a))) 4. ==[ alpha ]==> (((^x.b)(b a))((^y.b)(b a))) 5. ==[ beta ]==> (b ((^y.b)(b a))) 6. ==[ alpha ]==> (b ((^x.b)(b a))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 171362/19413069. ------ 1. ==[ start ]==> ((^a.b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 171363/19413150. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^z.a)(b (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((^x.a)(b (^y.y)))(^z.z)) 5. ==[ beta ]==> (a (^z.z)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 171364/19413339. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 171365/19413648. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 171366/19413834. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171367/19414392. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((((^y.(y y))((^z.z) b))((^y.(y y))((^z.z) b)))((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> ((((^x.(x x))((^y.y) b))((^z.(z z))((^x1.x1) b)))((^y1.(y1 y1))((^z1.z1) b))) 5. ==[ beta ]==> (((((^y.y) b)((^y.y) b))((^z.(z z))((^x1.x1) b)))((^y1.(y1 y1))((^z1.z1) b))) 6. ==[ alpha ]==> (((((^x.x) b)((^y.y) b))((^z.(z z))((^x1.x1) b)))((^y1.(y1 y1))((^z1.z1) b))) 7. ==[ beta ]==> (((b ((^y.y) b))((^z.(z z))((^x1.x1) b)))((^y1.(y1 y1))((^z1.z1) b))) 8. ==[ alpha ]==> (((b ((^x.x) b))((^y.(y y))((^z.z) b)))((^x1.(x1 x1))((^y1.y1) b))) 9. ==[ beta ]==> (((b b)((^y.(y y))((^z.z) b)))((^x1.(x1 x1))((^y1.y1) b))) 10. ==[ alpha ]==> (((b b)((^x.(x x))((^y.y) b)))((^z.(z z))((^x1.x1) b))) 11. ==[ beta ]==> (((b b)(((^y.y) b)((^y.y) b)))((^z.(z z))((^x1.x1) b))) 12. ==[ alpha ]==> (((b b)(((^x.x) b)((^y.y) b)))((^z.(z z))((^x1.x1) b))) 13. ==[ beta ]==> (((b b)(b ((^y.y) b)))((^z.(z z))((^x1.x1) b))) 14. ==[ alpha ]==> (((b b)(b ((^x.x) b)))((^y.(y y))((^z.z) b))) 15. ==[ beta ]==> (((b b)(b b))((^y.(y y))((^z.z) b))) 16. ==[ alpha ]==> (((b b)(b b))((^x.(x x))((^y.y) b))) 17. ==[ beta ]==> (((b b)(b b))(((^y.y) b)((^y.y) b))) 18. ==[ alpha ]==> (((b b)(b b))(((^x.x) b)((^y.y) b))) 19. ==[ beta ]==> (((b b)(b b))(b ((^y.y) b))) 20. ==[ alpha ]==> (((b b)(b b))(b ((^x.x) b))) 21. ==[ beta ]==> (((b b)(b b))(b b)) REDUCED to normal form. ------ 171368/19415268. ------ 1. ==[ start ]==> (((^a.b)(a a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 171369/19415499. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.b)((^x1.x1)(a a)))((^z.b)((^x1.x1)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.b)((^z.z)(a a)))((^x1.b)((^y1.y1)(a a))))) 5. ==[ beta ]==> (((^y.b)((^z.z)(a a)))((^x1.b)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)((^x1.x1)(a a)))) 7. ==[ beta ]==> (b ((^z.b)((^x1.x1)(a a)))) 8. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 171370/19416771. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 171371/19416930. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))(^z.a))) 3. ==[ eta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 171372/19417767. ------ 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 ]==> (((^x1.(^y1.y1))(a (^z1.(^x2.x2))))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 171373/19418370. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171374/19418445. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^a.(^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. ------ 171375/19418685. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 171376/19419048. ------ 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)(^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)))) REDUCED to normal form. ------ 171377/19419684. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((^y.(a a))(^z.a))((^y.(a a))(^z.a)))(((^y.(a a))(^z.a))((^y.(a a))(^z.a)))) 4. ==[ alpha ]==> ((((^x.(a a))(^y.a))((^z.(a a))(^x1.a)))(((^y1.(a a))(^z1.a))((^x2.(a a))(^y2.a)))) 5. ==[ beta ]==> (((a a)((^z.(a a))(^x1.a)))(((^y1.(a a))(^z1.a))((^x2.(a a))(^y2.a)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.a)))(((^z.(a a))(^x1.a))((^y1.(a a))(^z1.a)))) 7. ==[ beta ]==> (((a a)(a a))(((^z.(a a))(^x1.a))((^y1.(a a))(^z1.a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(^y.a))((^z.(a a))(^x1.a)))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^z.(a a))(^x1.a)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(^y.a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 171378/19420128. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 171379/19420632. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 171380/19421082. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.(^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. ------ 171381/19421316. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^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. ------ 171382/19421712. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(a y))) 3. ==[ eta ]==> (((a b)((^x.x)(a a))) a) 4. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 171383/19422423. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((z z) z))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((z z) z))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((z z) z))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((z z) z))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((y y) y))) 7. ==[ beta ]==> ((b b)(^y.((y y) y))) 8. ==[ alpha ]==> ((b b)(^x.((x x) x))) REDUCED to normal form. ------ 171384/19422846. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 171385/19422981. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 171386/19423089. ------ 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. ------ 171387/19423167. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.a))(((^z.(^x1.x1))(^y1.a))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1))(^z1.a))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.a))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.a))(^y1.y1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.a))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 171388/19423728. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(^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. ------ 171389/19423773. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(y y))) 3. ==[ beta ]==> (b (^y.(y y))) 4. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 171390/19423812. ------ 1. ==[ start ]==> ((a a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 171391/19423839. ------ 1. ==[ start ]==> ((a (a a))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (a a))((^x.b)(b a))) 3. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 171392/19423857. ------ 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. ------ 171393/19423866. ------ 1. ==[ start ]==> ((a b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 171394/19423884. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(^a.a))(^b.b))) 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. ------ 171395/19423911. ------ 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. ------ 171396/19423920. ------ 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. ------ 171397/19423947. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 171398/19423992. ------ 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. ------ 171399/19424019. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 171400/19424046. ------ 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 (^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. ------ 171401/19424136. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^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. ------ 171402/19424325. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 171403/19424415. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.(y y))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.(x x))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((b ((^y.(^z.z)) a))(b ((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((b ((^x.(^y.y)) a))(b ((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((b (^y.y))(b ((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((b (^x.x))(b ((^y.(^z.z)) a))) 9. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 10. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 171404/19424442. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(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. ------ 171405/19424496. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b (^z.z))(a (^x1.x1)))) 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. ------ 171406/19424523. ------ 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. ------ 171407/19424550. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^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. ------ 171408/19424604. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((b a)((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((b a)((a a) a))) REDUCED to normal form. ------ 171409/19424631. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 171410/19424766. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171411/19424793. ------ 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) 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. ------ 171412/19424847. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^y1.(^z1.z1)) 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. ------ 171413/19424883. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 171414/19424910. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 171415/19424937. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 171416/19424964. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.a))(b (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.a))(b (^y.(y y)))) REDUCED to normal form. ------ 171417/19424991. ------ 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. ------ 171418/19425018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((b a)(^c.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. ------ 171419/19425081. ------ 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. ------ 171420/19425108. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 171421/19425162. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 171422/19425189. ------ 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))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((a ((a a) a))(b ((^y.y) b))) 6. ==[ alpha ]==> ((a ((a a) a))(b ((^x.x) b))) 7. ==[ beta ]==> ((a ((a a) a))(b b)) REDUCED to normal form. ------ 171423/19425315. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b (^z.z)) b)) 3. ==[ beta ]==> (((^y.y) b)((b (^z.z)) b)) 4. ==[ alpha ]==> (((^x.x) b)((b (^y.y)) b)) 5. ==[ beta ]==> (b ((b (^y.y)) b)) 6. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 171424/19425567. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^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 (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 171425/19425594. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(a a))(^b.b))) 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))) 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. ------ 171426/19425621. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 171427/19425711. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.b)((b (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.b)((b (^y.y))(a a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 171428/19425792. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(a (a a)))) IRREDUCIBLE: cycle. ------ 171429/19425873. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171430/19425900. ------ 1. ==[ start ]==> (((^a.a)(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a b)((a b)((^x.x)(a a)))) 5. ==[ beta ]==> ((a b)((a b)(a a))) REDUCED to normal form. ------ 171431/19425927. ------ 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. ------ 171432/19425981. ------ 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. ------ 171433/19426062. ------ 1. ==[ start ]==> (((^a.b)(a a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((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. ------ 171434/19426161. ------ 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) 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 (^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. ------ 171435/19426188. ------ 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 (a 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. ------ 171436/19426260. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) b)(((^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. ------ 171437/19426269. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(a b))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 171438/19426296. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 171439/19426476. ------ 1. ==[ start ]==> (((a b) b)((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b) b)((b (^x.x)) a)) REDUCED to normal form. ------ 171440/19426503. ------ 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. ------ 171441/19426530. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(^x.(a a)))(b c)) REDUCED to normal form. ------ 171442/19426755. ------ 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)(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. ------ 171443/19426782. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 171444/19426908. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b) c)) 2. ==[ alpha ]==> (((^x.b) c)((^y.y) c)) 3. ==[ beta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 171445/19427007. ------ 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)(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. ------ 171446/19427142. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171447/19427259. ------ 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)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 171448/19427286. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 171449/19427340. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171450/19427394. ------ 1. ==[ start ]==> (((a b)(^b.a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(^y.b))) REDUCED to normal form. ------ 171451/19427421. ------ 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.(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. ------ 171452/19427484. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((b a)(b a))) REDUCED to normal form. ------ 171453/19427511. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 171454/19427538. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 171455/19427565. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a a)(a a))) REDUCED to normal form. ------ 171456/19427619. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x)(^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. ------ 171457/19427646. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 171458/19427727. ------ 1. ==[ start ]==> ((a (b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 171459/19427898. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(b ((^z.z) b))) 3. ==[ beta ]==> (b (b ((^z.z) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 171460/19427961. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 171461/19428006. ------ 1. ==[ start ]==> (((^a.a)(b a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))((b a)((^y.y) a))) 3. ==[ beta ]==> ((b a)((b a)((^y.y) a))) 4. ==[ alpha ]==> ((b a)((b a)((^x.x) a))) 5. ==[ beta ]==> ((b a)((b a) a)) REDUCED to normal form. ------ 171462/19428033. ------ 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)(^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. ------ 171463/19428087. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a b)((a a) a))) 3. ==[ beta ]==> (((a b)(a b))((a b)((a a) a))) REDUCED to normal form. ------ 171464/19428168. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 171465/19428294. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(a a))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 171466/19428321. ------ 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)))(a (^z1.z1)))) 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. ------ 171467/19428375. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 171468/19428402. ------ 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.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 171469/19428429. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 171470/19428456. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(a b))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 171471/19428483. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 171472/19428510. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 171473/19428555. ------ 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.(^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. ------ 171474/19428564. ------ 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)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 171475/19428897. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 171476/19428951. ------ 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 (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(a a))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a a))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 171477/19428960. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1))) b)) 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. ------ 171478/19429032. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(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. ------ 171479/19429140. ------ 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 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. ------ 171480/19429167. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 171481/19429212. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 171482/19429239. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(a (^z.z))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(a (^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 171483/19429266. ------ 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.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 171484/19429347. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 171485/19429374. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 171486/19429446. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 171487/19429455. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)(a a))) REDUCED to normal form. ------ 171488/19429482. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 171489/19429815. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(b (b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (b a))) 3. ==[ beta ]==> (((^y.y) b)(b (b a))) 4. ==[ alpha ]==> (((^x.x) b)(b (b a))) 5. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 171490/19429842. ------ 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)(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. ------ 171491/19429851. ------ 1. ==[ start ]==> (((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)) 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. ------ 171492/19429896. ------ 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))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 171493/19429977. ------ 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)(^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. ------ 171494/19430085. ------ 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 (^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. ------ 171495/19430211. ------ 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) a))) 3. ==[ beta ]==> ((a (b a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (b a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 171496/19430238. ------ 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 (a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 171497/19430292. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 171498/19430319. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))(a b))) 3. ==[ beta ]==> (((a b)((a a) a))((a b)(a b))) REDUCED to normal form. ------ 171499/19430346. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 171500/19430373. ------ 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.(^z.z))((a a)(^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. ------ 171501/19430454. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 171502/19430481. ------ 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. ------ 171503/19430652. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(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. ------ 171504/19430760. ------ 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) 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. ------ 171505/19430841. ------ 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. ------ 171506/19430868. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 171507/19430922. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a a)((a a)(^y.y)))) 3. ==[ beta ]==> (((b a)(b a))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 171508/19430985. ------ 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.(^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. ------ 171509/19431012. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)(^y.a))) REDUCED to normal form. ------ 171510/19431066. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 171511/19431120. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (^x1.b))) REDUCED to normal form. ------ 171512/19431147. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 171513/19431237. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 171514/19431264. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 171515/19431291. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.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. ------ 171516/19431318. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 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. ------ 171517/19431372. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.b))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 171518/19431399. ------ 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.(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. ------ 171519/19431651. ------ 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. ------ 171520/19431876. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)(^y.(a a)))) 3. ==[ beta ]==> ((b c)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((b c)((a a)(^x.(a a)))) REDUCED to normal form. ------ 171521/19431903. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a) a)) REDUCED to normal form. ------ 171522/19432110. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(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. ------ 171523/19432119. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 171524/19432146. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b) b)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b) b)) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 171525/19432218. ------ 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 (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. ------ 171526/19432344. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 171527/19432398. ------ 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) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 171528/19432425. ------ 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. ------ 171529/19432452. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 171530/19432479. ------ 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. ------ 171531/19432506. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)(a b))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(a b))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(a b))) 5. ==[ beta ]==> (((a b)(a a))(a b)) REDUCED to normal form. ------ 171532/19432533. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 171533/19432614. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 171534/19432641. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 171535/19432812. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) 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. ------ 171536/19433163. ------ 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. ------ 171537/19433217. ------ 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. ------ 171538/19433226. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a) a)) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 171539/19433253. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171540/19433298. ------ 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) a))) 3. ==[ beta ]==> (b (((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (b (((^x.x) 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. ------ 171541/19433307. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 171542/19433415. ------ 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. ------ 171543/19433442. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.a))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.a))) REDUCED to normal form. ------ 171544/19433469. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 171545/19433523. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 171546/19433559. ------ 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.(^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. ------ 171547/19433586. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 171548/19433613. ------ 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)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 171549/19433640. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 171550/19433721. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.a))) REDUCED to normal form. ------ 171551/19433748. ------ 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 (^z.(z z)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(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. ------ 171552/19433775. ------ 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. ------ 171553/19433829. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 171554/19433856. ------ 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) a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 171555/19433883. ------ 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. ------ 171556/19433937. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 171557/19433964. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^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. ------ 171558/19433973. ------ 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 ]==> ((b ((^z.z) a))(^y.y)) 6. ==[ alpha ]==> ((b ((^x.x) a))(^y.y)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 171559/19434360. ------ 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))) REDUCED to normal form. ------ 171560/19434378. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b b)) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 171561/19434387. ------ 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. ------ 171562/19434414. ------ 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. ------ 171563/19434432. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(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. ------ 171564/19434486. ------ 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. ------ 171565/19434522. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 171566/19434549. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 171567/19434567. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (a a))) 3. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 171568/19445415. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171569/19445460. ------ 1. ==[ start ]==> ((^a.b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 171570/19445496. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171571/19445607. ------ 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. ------ 171572/19446039. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(^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. ------ 171573/19446453. ------ 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. ------ 171574/19446783. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (a a))(^b.b))) 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. ------ 171575/19446876. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^b.((^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. ------ 171576/19447116. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 171577/19447290. ------ 1. ==[ start ]==> (((^a.b) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) a)(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.b) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.b) a)(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 171578/19447668. ------ 1. ==[ start ]==> (((a b)(^a.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(b (^z.z)))) REDUCED to normal form. ------ 171579/19447890. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a b)(^z.(a a)))((a b)(^z.(a a))))) 4. ==[ alpha ]==> ((^x.x)(((a b)(^y.(a a)))((a b)(^z.(a a))))) 5. ==[ beta ]==> (((a b)(^y.(a a)))((a b)(^z.(a a)))) 6. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 171580/19448064. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (b (^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 171581/19450158. ------ 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.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x1.x1))(^y1.(^z1.(^x2.x2))))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 171582/19451076. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 171583/19451439. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 171584/19451448. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.(^x2.x2))))) REDUCED to normal form. ------ 171585/19451718. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(b a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(b a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(b a))) REDUCED to normal form. ------ 171586/19453707. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.(^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. ------ 171587/19453716. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 171588/19454103. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.b))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.b))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.b))) REDUCED to normal form. ------ 171589/19454316. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b) a)) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171590/19454490. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(^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. ------ 171591/19454814. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(^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. ------ 171592/19454823. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((y y) y))) REDUCED to normal form. ------ 171593/19454958. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 171594/19455135. ------ 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))) REDUCED to normal form. ------ 171595/19456002. ------ 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)))) REDUCED to normal form. ------ 171596/19456146. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 171597/19456164. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 171598/19456221. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 171599/19456248. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 171600/19456266. ------ 1. ==[ start ]==> ((a b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 171601/19456302. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 171602/19456356. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 171603/19456383. ------ 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)((^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. ------ 171604/19456410. ------ 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. ------ 171605/19456437. ------ 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)((^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. ------ 171606/19456482. ------ 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. ------ 171607/19456545. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.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 ]==> a REDUCED to normal form. ------ 171608/19456653. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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 a) REDUCED to normal form. ------ 171609/19456842. ------ 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 ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 171610/19456878. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a) 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)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 171611/19456905. ------ 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. ------ 171612/19456932. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 171613/19456959. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(b (a (a a)))) REDUCED to normal form. ------ 171614/19456986. ------ 1. ==[ start ]==> ((((^a.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.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((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 (^z.(^x1.x1)))(^z1.z1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 171615/19457013. ------ 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. ------ 171616/19457121. ------ 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 b)(((a a) a)(b a))) REDUCED to normal form. ------ 171617/19457256. ------ 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. ------ 171618/19457382. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a a))) REDUCED to normal form. ------ 171619/19457454. ------ 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))(^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))) REDUCED to normal form. ------ 171620/19457481. ------ 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. ------ 171621/19457508. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a 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. ------ 171622/19457562. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^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)((^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. ------ 171623/19457589. ------ 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. ------ 171624/19457625. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 171625/19457679. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (a ((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (a ((^x.x)((^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. ------ 171626/19457787. ------ 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)(^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. ------ 171627/19457922. ------ 1. ==[ start ]==> ((a (^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 171628/19458093. ------ 1. ==[ start ]==> (((^a.b) a)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 171629/19458255. ------ 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. ------ 171630/19458282. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a b) a)((a a)(a b))) REDUCED to normal form. ------ 171631/19458309. ------ 1. ==[ start ]==> (((a a)(^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))((a b)(a a))) REDUCED to normal form. ------ 171632/19458363. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(b a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(b a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 171633/19458390. ------ 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 (^y.(^z.z))))) REDUCED to normal form. ------ 171634/19458417. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.a)(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 171635/19458444. ------ 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 a)(a a)))) REDUCED to normal form. ------ 171636/19458471. ------ 1. ==[ start ]==> (((a b)(^a.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 171637/19458507. ------ 1. ==[ start ]==> (((a a)(a b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a b))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 171638/19458534. ------ 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.(^z.z)))) REDUCED to normal form. ------ 171639/19458561. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.a))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 171640/19458588. ------ 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 z)))) REDUCED to normal form. ------ 171641/19458615. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)((b a)(^y.(^z.z)))) 7. ==[ beta ]==> (a ((b a)(^y.(^z.z)))) 8. ==[ alpha ]==> (a ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 171642/19458669. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a))(^y.b))) 3. ==[ beta ]==> (((a b)(a a))((a a)(^y.b))) 4. ==[ alpha ]==> (((a b)(a a))((a a)(^x.b))) REDUCED to normal form. ------ 171643/19458696. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 171644/19458705. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171645/19458732. ------ 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 REDUCED to normal form. ------ 171646/19458786. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 9. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 171647/19458867. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 171648/19458948. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 171649/19459083. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^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. ------ 171650/19459308. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (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. ------ 171651/19459317. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y) c)) 3. ==[ beta ]==> (((a b)(a (^x.x))) c) REDUCED to normal form. ------ 171652/19459551. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) c)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) c)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 171653/19459578. ------ 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. ------ 171654/19459605. ------ 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. ------ 171655/19459704. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))((^x1.x1) 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. ------ 171656/19459785. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 171657/19459911. ------ 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)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(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 (^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. ------ 171658/19459938. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a b))((a (^y.y))(^z.z))) 4. ==[ alpha ]==> ((a (a b))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 171659/19459992. ------ 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. ------ 171660/19460019. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) b) b)) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b b)) REDUCED to normal form. ------ 171661/19460046. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (^y.(^z.z))) c)) 3. ==[ beta ]==> (((a b) a)((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 171662/19460217. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 171663/19460298. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^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. ------ 171664/19460361. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b (a a))) REDUCED to normal form. ------ 171665/19460469. ------ 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)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((a a)((^y.y)(^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. ------ 171666/19460496. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a b)((a a) a))) REDUCED to normal form. ------ 171667/19460550. ------ 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))((^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. ------ 171668/19460577. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 171669/19460604. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a a)(^x.a))(a (b a))) REDUCED to normal form. ------ 171670/19460631. ------ 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.x1))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 171671/19460694. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) 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. ------ 171672/19460721. ------ 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)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 171673/19460748. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((b a)(^z.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a)(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((b 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. ------ 171674/19460775. ------ 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))(^y.(y y)))) REDUCED to normal form. ------ 171675/19460802. ------ 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))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(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. ------ 171676/19460829. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 171677/19460856. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((a a) a)(^x.b))) REDUCED to normal form. ------ 171678/19460883. ------ 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))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)(((^y.y)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> (((a a) a)(^y.(a a))) 10. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 171679/19460964. ------ 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.(^z1.z1))))) REDUCED to normal form. ------ 171680/19460973. ------ 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.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171681/19461054. ------ 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)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 171682/19461135. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171683/19461297. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 171684/19461360. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 171685/19461387. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.b)((b a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.b)((b a)(a (^y.y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 171686/19461441. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 171687/19461468. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a b)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(^y.y))) REDUCED to normal form. ------ 171688/19461495. ------ 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. ------ 171689/19461549. ------ 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)))(^z.z))((a (a a))(a a))) REDUCED to normal form. ------ 171690/19461666. ------ 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)))(^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. ------ 171691/19461693. ------ 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. ------ 171692/19461720. ------ 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. ------ 171693/19461747. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.(z z)))) 6. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 171694/19461774. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a 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. ------ 171695/19461855. ------ 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. ------ 171696/19461882. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 171697/19461891. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.a)((a a)(^a.a)))) 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 REDUCED to normal form. ------ 171698/19461918. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(b a))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(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. ------ 171699/19462053. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 171700/19462161. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.(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. ------ 171701/19462197. ------ 1. ==[ start ]==> ((((^a.a) b) a)(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(c ((a a)(^y.y)))) 3. ==[ beta ]==> ((b a)(c ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b a)(c ((a a)(^x.x)))) REDUCED to normal form. ------ 171702/19462224. ------ 1. ==[ start ]==> (((a a)(^b.b))(b (b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (b a))) REDUCED to normal form. ------ 171703/19462242. ------ 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)(^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. ------ 171704/19462251. ------ 1. ==[ start ]==> (((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.z1))))) REDUCED to normal form. ------ 171705/19462332. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))((^z.z) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171706/19462359. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)(a (a a)))) REDUCED to normal form. ------ 171707/19462386. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)((^y.y)(^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. ------ 171708/19462413. ------ 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)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((a a) a))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 171709/19462440. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (a a))(a b))) REDUCED to normal form. ------ 171710/19462494. ------ 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 (^y1.y1))((a a)(^z1.z1)))) REDUCED to normal form. ------ 171711/19462521. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a a)(b a))) 3. ==[ beta ]==> ((b (^y.y))((a a)(b a))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(b a))) REDUCED to normal form. ------ 171712/19462557. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a)(^y.y))) 3. ==[ beta ]==> (((a a) b)((b a)(^y.y))) 4. ==[ alpha ]==> (((a a) b)((b a)(^x.x))) REDUCED to normal form. ------ 171713/19462584. ------ 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.(^z1.z1)))) REDUCED to normal form. ------ 171714/19462611. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 171715/19462638. ------ 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.(y y)))) REDUCED to normal form. ------ 171716/19462665. ------ 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.(^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. ------ 171717/19462692. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(^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))) 5. ==[ beta ]==> ((((a a) a)(a b))(^y.a)) 6. ==[ alpha ]==> ((((a a) a)(a b))(^x.a)) REDUCED to normal form. ------ 171718/19462719. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (a a))(^x.b))) REDUCED to normal form. ------ 171719/19462746. ------ 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) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 171720/19462827. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a) a)) REDUCED to normal form. ------ 171721/19462854. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y)) b)) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 171722/19462917. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 171723/19463052. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))(^c.(^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. ------ 171724/19463196. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b b)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 171725/19463223. ------ 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)(^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. ------ 171726/19463277. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a b))) REDUCED to normal form. ------ 171727/19463304. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 171728/19463322. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b (^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 171729/19463403. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^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. ------ 171730/19463511. ------ 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 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. ------ 171731/19463610. ------ 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. ------ 171732/19463637. ------ 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. ------ 171733/19463664. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b) c)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b) c)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b) c)) REDUCED to normal form. ------ 171734/19463880. ------ 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 a)) REDUCED to normal form. ------ 171735/19463907. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b) c)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b) c)) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 171736/19464051. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b (^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b (^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b (^x2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171737/19464132. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171738/19464240. ------ 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 a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.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. ------ 171739/19464348. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(^a.(^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. ------ 171740/19464429. ------ 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.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.(^x2.x2))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 171741/19464510. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(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. ------ 171742/19464519. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a (a a))) REDUCED to normal form. ------ 171743/19464546. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b)(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((a b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a b)(a a))) REDUCED to normal form. ------ 171744/19464627. ------ 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))(a (a a)))) REDUCED to normal form. ------ 171745/19464654. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b (^x.a))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.a))(a (^y.y))) REDUCED to normal form. ------ 171746/19464681. ------ 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. ------ 171747/19464744. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 171748/19464771. ------ 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.(^z.z)))) REDUCED to normal form. ------ 171749/19464798. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.a))) 7. ==[ beta ]==> ((a b)((^y.y)(^z.a))) 8. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 9. ==[ beta ]==> ((a b)(^y.a)) 10. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 171750/19464825. ------ 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 z)))) REDUCED to normal form. ------ 171751/19464852. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 171752/19464906. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)(^y.b))) 3. ==[ beta ]==> (((a b)(a a))((a a)(^y.b))) 4. ==[ alpha ]==> (((a b)(a a))((a a)(^x.b))) REDUCED to normal form. ------ 171753/19464933. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b) a)) 3. ==[ beta ]==> (((a a)(a b))((a b) a)) REDUCED to normal form. ------ 171754/19464960. ------ 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. ------ 171755/19465122. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b) a)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.b) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.b) a)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 171756/19465293. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.b))) 3. ==[ beta ]==> (b (a (^x1.b))) 4. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 171757/19465401. ------ 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. ------ 171758/19465536. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 171759/19465563. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.a)(^z.(z z))) 6. ==[ alpha ]==> ((^x.a)(^y.(y y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 171760/19465617. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(^z.a))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.a))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.a))) 9. ==[ beta ]==> ((b b)(^y.a)) 10. ==[ alpha ]==> ((b b)(^x.a)) REDUCED to normal form. ------ 171761/19465626. ------ 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. ------ 171762/19465653. ------ 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)(^x2.x2))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171763/19465707. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 171764/19465734. ------ 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. ------ 171765/19465761. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.z))) REDUCED to normal form. ------ 171766/19465806. ------ 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.(^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. ------ 171767/19465869. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c d)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c d)) REDUCED to normal form. ------ 171768/19465941. ------ 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 (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 171769/19465959. ------ 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. ------ 171770/19465986. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a c)) REDUCED to normal form. ------ 171771/19466067. ------ 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.(^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 (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 171772/19466094. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x)) b)) 3. ==[ beta ]==> ((((a a) a)(b a))(b b)) REDUCED to normal form. ------ 171773/19466121. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 171774/19466229. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 171775/19466256. ------ 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. ------ 171776/19466283. ------ 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)(^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. ------ 171777/19466337. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 171778/19466373. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y1.a))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 171779/19466760. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c a)) 3. ==[ beta ]==> (((^y.y) b)(c a)) 4. ==[ alpha ]==> (((^x.x) b)(c a)) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 171780/19466778. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^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. ------ 171781/19466787. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b b)) REDUCED to normal form. ------ 171782/19466805. ------ 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. ------ 171783/19466832. ------ 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 ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171784/19466886. ------ 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 a)))(b (^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.x))) REDUCED to normal form. ------ 171785/19466922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(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. ------ 171786/19466949. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 171787/19466967. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b 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. ------ 171788/19468905. ------ 1. ==[ start ]==> ((^a.(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((^x.(x b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x b))(^y.(^z.z))) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171789/19475925. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(x1 b))) 3. ==[ eta ]==> ((^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. ------ 171790/19477914. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 171791/19478034. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 171792/19478076. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (^x.(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (^x.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 171793/19478769. ------ 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))(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. ------ 171794/19478898. ------ 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 ]==> (((^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. ------ 171795/19479714. ------ 1. ==[ start ]==> ((^a.(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a ((^y.(^z.z)) a)) b) 4. ==[ alpha ]==> ((a ((^x.(^y.y)) a)) b) 5. ==[ beta ]==> ((a (^y.y)) b) 6. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 171796/19479717. ------ 1. ==[ start ]==> ((a (a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((a (a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 171797/19480482. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 171798/19480491. ------ 1. ==[ start ]==> (((a b) b)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 171799/19480878. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(b (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(b (^z.z)))) 6. ==[ alpha ]==> ((a (a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 171800/19480983. ------ 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 ]==> ((((b a)(a (a a)))((b a)(a (a a))))(^y.y)) 4. ==[ alpha ]==> ((((b a)(a (a a)))((b a)(a (a a))))(^x.x)) REDUCED to normal form. ------ 171801/19483866. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) REDUCED to normal form. ------ 171802/19485573. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 171803/19485918. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.((^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. ------ 171804/19486134. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 171805/19486734. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a (a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a (a b))) 3. ==[ eta ]==> ((^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. ------ 171806/19486737. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(z b))) 3. ==[ beta ]==> ((a (^y.y))(^z.(z b))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y b))) REDUCED to normal form. ------ 171807/19487241. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 171808/19487538. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 171809/19487553. ------ 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))) REDUCED to normal form. ------ 171810/19487682. ------ 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.((^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. ------ 171811/19487790. ------ 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. ------ 171812/19488375. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^b.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. ------ 171813/19488429. ------ 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. ------ 171814/19488537. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^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. ------ 171815/19488564. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 171816/19488582. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.a)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.a)) 3. ==[ beta ]==> (b (^y.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 171817/19488657. ------ 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)))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 171818/19488684. ------ 1. ==[ start ]==> (((a a) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((a a) a)((^x.b)(b a))) 3. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 171819/19488702. ------ 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. ------ 171820/19488729. ------ 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)))((^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. ------ 171821/19488738. ------ 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 171822/19488765. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 171823/19488792. ------ 1. ==[ start ]==> (((a a) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 171824/19488819. ------ 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 (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 171825/19488837. ------ 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. ------ 171826/19488846. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 171827/19488864. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 171828/19488873. ------ 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))((^y1.y1)(^x1.x1))) 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. ------ 171829/19488891. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (^x.a))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.a))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 171830/19489008. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 171831/19489062. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 171832/19489089. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^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. ------ 171833/19489476. ------ 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. ------ 171834/19489503. ------ 1. ==[ start ]==> (((a (^a.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)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) 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 (^x.x)) a)((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a (^x.x)) a)((a a)(a a))) REDUCED to normal form. ------ 171835/19489530. ------ 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 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. ------ 171836/19489557. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a) a)(b a))) REDUCED to normal form. ------ 171837/19489584. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(((^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))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^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. ------ 171838/19489710. ------ 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. ------ 171839/19489728. ------ 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 ]==> (((^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)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171840/19489755. ------ 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. ------ 171841/19489791. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 171842/19489809. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 171843/19489818. ------ 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. ------ 171844/19489845. ------ 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.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171845/19490052. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(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. ------ 171846/19490223. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 x1))) REDUCED to normal form. ------ 171847/19490250. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1)))(^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. ------ 171848/19490331. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 171849/19490502. ------ 1. ==[ start ]==> ((((a a) a)(a a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(b (b (^x.x)))) REDUCED to normal form. ------ 171850/19490529. ------ 1. ==[ start ]==> ((a (a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a (a b))(a (^y.y))) 4. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 171851/19491087. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 171852/19491132. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((^y.(a a))((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((a b)(^y.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171853/19491159. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 171854/19491213. ------ 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))(^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. ------ 171855/19491303. ------ 1. ==[ start ]==> (((a b) b)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(b (^y.y)))) 3. ==[ beta ]==> (((a b) b)(b (^y.y))) 4. ==[ alpha ]==> (((a b) b)(b (^x.x))) REDUCED to normal form. ------ 171856/19491348. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a)) b)) 5. ==[ beta ]==> ((a a)(((a a)(a a)) b)) REDUCED to normal form. ------ 171857/19491357. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 171858/19491375. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^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. ------ 171859/19491384. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 171860/19491492. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 171861/19491519. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 171862/19491663. ------ 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 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. ------ 171863/19491690. ------ 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. ------ 171864/19491717. ------ 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))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a))(a a))) REDUCED to normal form. ------ 171865/19491744. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b)(a (^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. ------ 171866/19491771. ------ 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) a))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 171867/19491798. ------ 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. ------ 171868/19491978. ------ 1. ==[ start ]==> (((a b) c)(d (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(d (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 171869/19492005. ------ 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. ------ 171870/19492032. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.(a a)))) REDUCED to normal form. ------ 171871/19492077. ------ 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))(^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. ------ 171872/19492086. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 171873/19492113. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b)(a (^a.a)))) 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. ------ 171874/19492131. ------ 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 (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 171875/19492212. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^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. ------ 171876/19492221. ------ 1. ==[ start ]==> (((a b)(^b.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. ------ 171877/19492248. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 171878/19492833. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 171879/19493382. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 171880/19493400. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171881/19493481. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 171882/19493778. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.z) a)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z) a)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z) a)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 171883/19493859. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 171884/19494012. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 171885/19494039. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.y))(b a))) REDUCED to normal form. ------ 171886/19494066. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 171887/19494273. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 171888/19494318. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a) a)(^c.(^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. ------ 171889/19494480. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(a a)) d)) 3. ==[ beta ]==> (b (((^z.z)(a a)) d)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) d)) 5. ==[ beta ]==> (b ((a a) d)) REDUCED to normal form. ------ 171890/19494597. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 171891/19494624. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.a)(^c.(^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)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 171892/19494678. ------ 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)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 171893/19495587. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 171894/19495812. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(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. ------ 171895/19495830. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 171896/19495839. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 171897/19495893. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 171898/19495947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 171899/19495974. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(a b))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 171900/19496001. ------ 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.x1)(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. ------ 171901/19496253. ------ 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 ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b ((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b (a a))) REDUCED to normal form. ------ 171902/19496307. ------ 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))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a a))) REDUCED to normal form. ------ 171903/19496334. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 171904/19496361. ------ 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. ------ 171905/19496388. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^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. ------ 171906/19496559. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 171907/19496703. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 171908/19496730. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)((^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. ------ 171909/19496775. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b) b)) 3. ==[ beta ]==> ((b (^y.y))((a b) b)) 4. ==[ alpha ]==> ((b (^x.x))((a b) b)) REDUCED to normal form. ------ 171910/19496838. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 171911/19496865. ------ 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.(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. ------ 171912/19496946. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.(a a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 171913/19497549. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a (a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(a (a b))) 3. ==[ beta ]==> ((a (^y.y))(a (a b))) 4. ==[ alpha ]==> ((a (^x.x))(a (a b))) REDUCED to normal form. ------ 171914/19497828. ------ 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)(^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. ------ 171915/19497945. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 171916/19498053. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)(^c.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. ------ 171917/19498125. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z)) c)) 3. ==[ beta ]==> (b ((^z.(z z)) c)) 4. ==[ alpha ]==> (b ((^x.(x x)) c)) 5. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 171918/19498134. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (^z.a))) REDUCED to normal form. ------ 171919/19498161. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.(y y)))) REDUCED to normal form. ------ 171920/19498188. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 171921/19498233. ------ 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))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171922/19498242. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(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. ------ 171923/19498269. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))((a (^z.z))(a (^z.z)))) 6. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 171924/19498296. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 171925/19498350. ------ 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)(^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. ------ 171926/19498368. ------ 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 (^x.(x (^y.y))))((^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. ------ 171927/19498467. ------ 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. ------ 171928/19498494. ------ 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 ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 171929/19498521. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))(a a))) REDUCED to normal form. ------ 171930/19498548. ------ 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 (^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. ------ 171931/19498575. ------ 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) a))) 3. ==[ beta ]==> (((a a)((^y.y)(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)(a a))((a (^y.y))((^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. ------ 171932/19498602. ------ 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. ------ 171933/19498683. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c c)) 3. ==[ beta ]==> ((b (a (a a)))(c c)) REDUCED to normal form. ------ 171934/19498782. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 171935/19499187. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^b.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. ------ 171936/19499205. ------ 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)) REDUCED to normal form. ------ 171937/19499214. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^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. ------ 171938/19499232. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(^a.(^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. ------ 171939/19499241. ------ 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. ------ 171940/19499259. ------ 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) REDUCED to normal form. ------ 171941/19499313. ------ 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 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. ------ 171942/19499349. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^a.(^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. ------ 171943/19499376. ------ 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. ------ 171944/19499394. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((a a) a)) 3. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 171945/19501728. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(b (^x1.x1)))(^z.(b (^x1.x1))))) 4. ==[ alpha ]==> (^x.((^y.(b (^z.z)))(^x1.(b (^y1.y1))))) 5. ==[ beta ]==> (^x.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 171946/19508361. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.x1))) 3. ==[ eta ]==> ((^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. ------ 171947/19510296. ------ 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 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)))) 5. ==[ beta ]==> ((a a)((^z.(a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 171948/19510323. ------ 1. ==[ start ]==> ((^a.b)((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.b)((^y.b)(b a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 171949/19510404. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((^z.(z z))((a a)(a a)))(^y.y)) 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. ------ 171950/19511088. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 171951/19511646. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^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)((^y1.(^z1.z1))(a (^x2.(^y2.y2)))))((^z2.(^x3.x3))(a (^y3.(^z3.z3))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1)))))((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 7. ==[ beta ]==> (((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 8. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 11. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 12. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171952/19512171. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.x)(^y.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. ------ 171953/19512546. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (^y.(((a a)(b (^z.z)))((a a)(b (^z.z))))) 4. ==[ alpha ]==> (^x.(((a a)(b (^y.y)))((a a)(b (^z.z))))) REDUCED to normal form. ------ 171954/19512549. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 171955/19512753. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^z.(a a))(a b))((^z.(a a))(a b)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(a a))(a b))((^z.(a a))(a b)))) 5. ==[ beta ]==> (((^y.(a a))(a b))((^z.(a a))(a b))) 6. ==[ alpha ]==> (((^x.(a a))(a b))((^y.(a a))(a b))) 7. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 171956/19512936. ------ 1. ==[ start ]==> (((a b) b)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 171957/19514052. ------ 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)))(^y1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)(^z.((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)(^y.((a a)(a a)))) 9. ==[ beta ]==> (^y.((a a)(a a))) 10. ==[ alpha ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 171958/19514184. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> (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. ------ 171959/19514733. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)((^y1.y1) b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 171960/19514754. ------ 1. ==[ start ]==> (((a a)(b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 171961/19515021. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.a)(b a))) 3. ==[ beta ]==> (((^x1.a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.a)(b a))(^y.(^z.z))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 171962/19515411. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((^x1.x1) b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((^z.z) b))) 7. ==[ beta ]==> (((a a)(a a))(^y.((^z.z) b))) 8. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y) b))) 9. ==[ beta ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 171963/19515624. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171964/19515726. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^a.(^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. ------ 171965/19515939. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 171966/19516617. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^a.(^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. ------ 171967/19516887. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(x1 a))) REDUCED to normal form. ------ 171968/19517670. ------ 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. ------ 171969/19518363. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 171970/19518804. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 171971/19518993. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(a y))) 3. ==[ eta ]==> ((((^x.x)(a a))(a b)) a) 4. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 171972/19519179. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)(^y1.b))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 171973/19519182. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(^x1.z))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 171974/19519353. ------ 1. ==[ start ]==> (((^a.b)(^c.(^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))) REDUCED to normal form. ------ 171975/19520127. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 171976/19520421. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.a)(^x1.(^y1.y1)))(((^z.a)(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.a)(^y.(^z.z)))(((^x1.a)(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (a (((^x1.a)(^y1.(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> (a (((^x.a)(^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (a (a (^x1.x1))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 171977/19520820. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.c)) 3. ==[ beta ]==> (((^y.y) b)(^z.c)) 4. ==[ alpha ]==> (((^x.x) b)(^y.c)) 5. ==[ beta ]==> (b (^y.c)) 6. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 171978/19520946. ------ 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 a)))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 171979/19520982. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^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. ------ 171980/19521027. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.b)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.b)) 3. ==[ beta ]==> (b (^y.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 171981/19521120. ------ 1. ==[ start ]==> ((a (a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 171982/19521147. ------ 1. ==[ start ]==> ((a b)((^a.b)(b a))) 2. ==[ alpha ]==> ((a b)((^x.b)(b a))) 3. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 171983/19521165. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 171984/19521192. ------ 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))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 171985/19521201. ------ 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. ------ 171986/19521228. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 171987/19521300. ------ 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. ------ 171988/19521327. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a (^z.z))) a)) REDUCED to normal form. ------ 171989/19521381. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 171990/19521633. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 171991/19521723. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(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. ------ 171992/19521759. ------ 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)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 171993/19521777. ------ 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 ]==> (((^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)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 171994/19521804. ------ 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. ------ 171995/19521831. ------ 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) 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. ------ 171996/19521840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a)) d)) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 171997/19521885. ------ 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)))((^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. ------ 171998/19521912. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 171999/19522047. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172000/19522074. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) 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. ------ 172001/19522128. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))(b (^z1.z1)))) 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. ------ 172002/19522191. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(^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. ------ 172003/19522218. ------ 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))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 172004/19522245. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 172005/19522272. ------ 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. ------ 172006/19522299. ------ 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)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 172007/19522389. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 172008/19522416. ------ 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. ------ 172009/19522470. ------ 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. ------ 172010/19522596. ------ 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 ]==> (((^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) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172011/19522623. ------ 1. ==[ start ]==> ((((a a) a) a)((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a) a)((b (^x.x)) b)) REDUCED to normal form. ------ 172012/19522821. ------ 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. ------ 172013/19522875. ------ 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))(^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. ------ 172014/19522902. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(a a))(^b.b))) 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))) 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. ------ 172015/19522929. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 172016/19522992. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.b)(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.b)(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 172017/19523073. ------ 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) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b)((^x1.x1) a))) IRREDUCIBLE: cycle. ------ 172018/19523154. ------ 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 (((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 172019/19523181. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a b))) 5. ==[ beta ]==> ((a b)((a a)(a b))) REDUCED to normal form. ------ 172020/19523208. ------ 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)((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. ------ 172021/19523262. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(b a))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(b a))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 172022/19523343. ------ 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 ((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 172023/19523370. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 172024/19523469. ------ 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) 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. ------ 172025/19523496. ------ 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.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(a (a a)))) 8. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(a (a a)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 172026/19523541. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) b)(((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. ------ 172027/19523550. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 172028/19523577. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 172029/19523784. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b (^y.y)) a)) 3. ==[ beta ]==> (((a a) a)((b (^y.y)) a)) 4. ==[ alpha ]==> (((a a) a)((b (^x.x)) a)) REDUCED to normal form. ------ 172030/19523811. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 172031/19523838. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b c)) REDUCED to normal form. ------ 172032/19524063. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(a b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 172033/19524090. ------ 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. ------ 172034/19524189. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a)) b)) 3. ==[ beta ]==> (b ((^y.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 172035/19524288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 172036/19524423. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 172037/19524504. ------ 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. ------ 172038/19524540. ------ 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))(^z.z))) REDUCED to normal form. ------ 172039/19524567. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 172040/19524621. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172041/19524648. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 172042/19524675. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a 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. ------ 172043/19524702. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.b))) REDUCED to normal form. ------ 172044/19524729. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 172045/19524765. ------ 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 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. ------ 172046/19524792. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a (^x.x))(a a))((b a)(b a))) REDUCED to normal form. ------ 172047/19524819. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.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) REDUCED to normal form. ------ 172048/19524846. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.x)) REDUCED to normal form. ------ 172049/19524873. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.z)((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)((^y.y)((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((a a)(a a))) 10. ==[ alpha ]==> ((^x.x)((a a)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 172050/19524927. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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)))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 172051/19524954. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 172052/19525008. ------ 1. ==[ start ]==> ((a (b a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 172053/19525179. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 172054/19525242. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 172055/19525287. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.(^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)))) REDUCED to normal form. ------ 172056/19525314. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)((b a)((^x1.x1) 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. ------ 172057/19525368. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a b)(a b))((a a)((^x.x)(^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. ------ 172058/19525449. ------ 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))((^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 ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 172059/19525557. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 172060/19525575. ------ 1. ==[ start ]==> (((a a)(b a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(a (^x.(a a)))) REDUCED to normal form. ------ 172061/19525602. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b)(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. ------ 172062/19525629. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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. ------ 172063/19525710. ------ 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.(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. ------ 172064/19525737. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.b)((a a) a))) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 172065/19525791. ------ 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))((^y1.y1)(a 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. ------ 172066/19525845. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(b a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 172067/19526178. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(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. ------ 172068/19526232. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(a ((^z.z) b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a ((^z.z) b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(a ((^z.z) b))) 6. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 172069/19526241. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y) a)) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 172070/19526268. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1))) b)) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1))) b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 172071/19526313. ------ 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) a))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 172072/19526322. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(^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. ------ 172073/19526421. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^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. ------ 172074/19526448. ------ 1. ==[ start ]==> ((a (^b.b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 172075/19526493. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(c (^d.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(c (^y.a))) REDUCED to normal form. ------ 172076/19526520. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 172077/19526547. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(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. ------ 172078/19526574. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 172079/19526628. ------ 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) 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. ------ 172080/19526655. ------ 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 (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 172081/19526682. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 172082/19526727. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172083/19526736. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 172084/19526763. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((a b)((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 172085/19527096. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(c ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(c ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(c ((a a)(^y.y)))) 5. ==[ beta ]==> (b (c ((a a)(^y.y)))) 6. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 172086/19527123. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(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. ------ 172087/19527177. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a)(a a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a)(a a))) REDUCED to normal form. ------ 172088/19527213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z)) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172089/19527258. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a b)(a (a a)))) 3. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 172090/19527366. ------ 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)((^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. ------ 172091/19527438. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 172092/19527492. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 172093/19527519. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 172094/19527546. ------ 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)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(a (a a)))) 7. ==[ beta ]==> ((a a)((^y.b)(a (a a)))) 8. ==[ alpha ]==> ((a a)((^x.b)(a (a a)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 172095/19527573. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 172096/19527600. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 172097/19527627. ------ 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)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 172098/19527654. ------ 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)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) a) REDUCED to normal form. ------ 172099/19527708. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(b a)) REDUCED to normal form. ------ 172100/19527933. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(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. ------ 172101/19528041. ------ 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))(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. ------ 172102/19528122. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^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))((^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. ------ 172103/19528149. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 172104/19528203. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (((b a)(b a))((a (^x.x))(a a))) REDUCED to normal form. ------ 172105/19528266. ------ 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))(^z.z))) REDUCED to normal form. ------ 172106/19528293. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 172107/19528347. ------ 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)(^x1.(x1 x1)))) REDUCED to normal form. ------ 172108/19528401. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a))(^x1.a))) REDUCED to normal form. ------ 172109/19528428. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.b))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 172110/19528455. ------ 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.(a a)))) REDUCED to normal form. ------ 172111/19528491. ------ 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. ------ 172112/19528518. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 172113/19528545. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 172114/19528572. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 172115/19528626. ------ 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.(^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. ------ 172116/19528653. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(^y.a))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 172117/19528680. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 172118/19528707. ------ 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.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^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. ------ 172119/19528932. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172120/19529157. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))(^z.b))) 3. ==[ beta ]==> ((b c)((a (^y.y))(^z.b))) 4. ==[ alpha ]==> ((b c)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 172121/19529184. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 172122/19529391. ------ 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 (b (a b))) REDUCED to normal form. ------ 172123/19529427. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 172124/19529499. ------ 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) a))) 3. ==[ beta ]==> ((^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. ------ 172125/19529625. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 172126/19529652. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b)(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 172127/19529679. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.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) REDUCED to normal form. ------ 172128/19529706. ------ 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) 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. ------ 172129/19529733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 172130/19529760. ------ 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. ------ 172131/19529787. ------ 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))((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. ------ 172132/19529814. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 172133/19529841. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 172134/19529895. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^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. ------ 172135/19529922. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> ((b a)((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 172136/19529949. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)(^b.(^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. ------ 172137/19530003. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 172138/19530093. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))((^z.z) 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. ------ 172139/19530174. ------ 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. ------ 172140/19530399. ------ 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 ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 172141/19530498. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b b)(b ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b b)(b ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b b)(b (^y.y))) 10. ==[ alpha ]==> ((b b)(b (^x.x))) REDUCED to normal form. ------ 172142/19530579. ------ 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. ------ 172143/19530588. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z)) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(c c)) REDUCED to normal form. ------ 172144/19530696. ------ 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))(^x2.x2))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 172145/19530723. ------ 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. ------ 172146/19530750. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.a))) REDUCED to normal form. ------ 172147/19530804. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 172148/19530840. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 172149/19530867. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 172150/19530894. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a 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. ------ 172151/19530921. ------ 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))(^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. ------ 172152/19530948. ------ 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))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^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. ------ 172153/19531056. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.(y y)))) REDUCED to normal form. ------ 172154/19531110. ------ 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 y1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(a a))) REDUCED to normal form. ------ 172155/19531137. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(a (^y.y)))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 172156/19531164. ------ 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)) a)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 172157/19531218. ------ 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)(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. ------ 172158/19531236. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(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. ------ 172159/19531245. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.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. ------ 172160/19531641. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 172161/19531668. ------ 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. ------ 172162/19531686. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b b)) 3. ==[ beta ]==> ((a (a (^y.y)))(b b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(b b)) REDUCED to normal form. ------ 172163/19531695. ------ 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. ------ 172164/19531767. ------ 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)))(a (a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 172165/19531803. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^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. ------ 172166/19531830. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 172167/19531848. ------ 1. ==[ start ]==> (((^a.b)(b a))(a b)) 2. ==[ alpha ]==> (((^x.b)(b a))(a b)) 3. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 172168/19531910. ------ 1. ==[ start ]==> (^a.(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (^x.(((x x)(^y.y))(^z.(x x)))) REDUCED to normal form. ------ 172169/19531911. ------ 1. ==[ start ]==> (a (((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (a (((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 172170/19541643. ------ 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))) REDUCED to normal form. ------ 172171/19542735. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a))) a) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 172172/19542741. ------ 1. ==[ start ]==> ((^a.a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^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. ------ 172173/19542969. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 172174/19542993. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a (^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.((^x1.x1)(^z.z))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172175/19543410. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^a.(a (a (^a.a))))) 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))))) REDUCED to normal form. ------ 172176/19543833. ------ 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 ]==> ((^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. ------ 172177/19544118. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3)))))(((^y3.y3)(^z3.z3))(^x4.(^y4.(^z4.z4))))) 5. ==[ beta ]==> ((((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3)))))(((^y3.y3)(^z3.z3))(^x4.(^y4.(^z4.z4))))) 6. ==[ alpha ]==> ((((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2)))))(((^x3.x3)(^y3.y3))(^z3.(^x4.(^y4.y4))))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2)))))(((^x3.x3)(^y3.y3))(^z3.(^x4.(^y4.y4))))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2)))))(((^z2.z2)(^x3.x3))(^y3.(^z3.(^x4.x4))))) 9. ==[ beta ]==> ((^y.(^z.z))(((^z2.z2)(^x3.x3))(^y3.(^z3.(^x4.x4))))) 10. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172178/19544451. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 172179/19545225. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(a a))(^x1.b))(((^z.z)(a a))(^x1.b)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(a a))(^z.b))(((^x1.x1)(a a))(^y1.b)))) 5. ==[ beta ]==> ((((^y.y)(a a))(^z.b))(((^x1.x1)(a a))(^y1.b))) 6. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a))(^x1.b))) 7. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a))(^x1.b))) 8. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.b))) 9. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.b))) 10. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 172180/19546893. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((y y)(y y)))) REDUCED to normal form. ------ 172181/19547205. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (^b.b))) 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. ------ 172182/19547883. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^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))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 172183/19547892. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^a.((^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. ------ 172184/19548411. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 172185/19549410. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (((((a a)(^y.y)) b)(((a a)(^y.y)) b))((((a a)(^y.y)) b)(((a a)(^y.y)) b))) 4. ==[ alpha ]==> (((((a a)(^x.x)) b)(((a a)(^y.y)) b))((((a a)(^z.z)) b)(((a a)(^x1.x1)) b))) REDUCED to normal form. ------ 172186/19550490. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a) d)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a) d)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 172187/19551078. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (((a a)(^x.b))(^y.(y y))) REDUCED to normal form. ------ 172188/19551465. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 172189/19551825. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (b (^x1.(^y1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 172190/19552185. ------ 1. ==[ start ]==> ((((^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) z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((z1 z1) z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((y1 y1) y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((y1 y1) y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((x1 x1) x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172191/19552470. ------ 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))) REDUCED to normal form. ------ 172192/19552473. ------ 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 (^x.(x (^y.y))))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 172193/19552893. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a) b)) 3. ==[ beta ]==> ((((^z.z) a) b)((((^z.z) a) b)(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a) b)((((^y.y) a) b)(^z.z))) 5. ==[ beta ]==> ((a b)((((^y.y) a) b)(^z.z))) 6. ==[ alpha ]==> ((a b)((((^x.x) a) b)(^y.y))) 7. ==[ beta ]==> ((a b)((a b)(^y.y))) 8. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 172194/19553292. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(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)))) REDUCED to normal form. ------ 172195/19553310. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 172196/19553364. ------ 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))) REDUCED to normal form. ------ 172197/19553418. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^a.(^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. ------ 172198/19553454. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(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)) REDUCED to normal form. ------ 172199/19553499. ------ 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))) REDUCED to normal form. ------ 172200/19553562. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 172201/19553574. ------ 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. ------ 172202/19553610. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(a a))((a a)(^a.a)))) 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 a) REDUCED to normal form. ------ 172203/19553637. ------ 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. ------ 172204/19553682. ------ 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. ------ 172205/19553718. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 172206/19553745. ------ 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)((^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. ------ 172207/19553772. ------ 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. ------ 172208/19553799. ------ 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)((^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. ------ 172209/19553826. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.a))((^x1.x1)(^z.z))) 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. ------ 172210/19553844. ------ 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. ------ 172211/19553871. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y)) c)) REDUCED to normal form. ------ 172212/19553907. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 172213/19553934. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 172214/19554240. ------ 1. ==[ start ]==> ((((^a.a) a) b)(a (a (a (^a.a))))) 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. ------ 172215/19554267. ------ 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. ------ 172216/19554294. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 172217/19554321. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 172218/19554348. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 172219/19554375. ------ 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. ------ 172220/19554483. ------ 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 b)((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> ((b b)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 172221/19554618. ------ 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. ------ 172222/19554645. ------ 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. ------ 172223/19554663. ------ 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 ]==> ((^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. ------ 172224/19554816. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 172225/19554843. ------ 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. ------ 172226/19554870. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 8. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 172227/19554897. ------ 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. ------ 172228/19554951. ------ 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. ------ 172229/19554987. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 172230/19555041. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(b (^z.z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 172231/19555203. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 172232/19555284. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 172233/19555455. ------ 1. ==[ start ]==> (((^a.b) a)(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(b (b (^y.y)))) 3. ==[ beta ]==> (b (b (b (^y.y)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 172234/19555617. ------ 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. ------ 172235/19555644. ------ 1. ==[ start ]==> (((a b) a)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 172236/19555671. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.b))((a a)(a b))) REDUCED to normal form. ------ 172237/19555725. ------ 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. ------ 172238/19555752. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z)(b a))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(b a))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 172239/19555779. ------ 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 REDUCED to normal form. ------ 172240/19555806. ------ 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)((^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. ------ 172241/19555824. ------ 1. ==[ start ]==> (((^a.b)(a a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 172242/19555833. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 172243/19555896. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 172244/19555923. ------ 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. ------ 172245/19555950. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) 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. ------ 172246/19555977. ------ 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)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> (a ((a (^y.(^z.z)))(^x1.(x1 x1)))) 8. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 172247/19556004. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 172248/19556031. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 172249/19556058. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 172250/19556067. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(a b))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(a b))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(a b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172251/19556094. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 172252/19556148. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(b a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 7. ==[ beta ]==> ((^y.(^z.z))(b a)) 8. ==[ alpha ]==> ((^x.(^y.y))(b a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172253/19556229. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((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. ------ 172254/19556310. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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 a) REDUCED to normal form. ------ 172255/19556364. ------ 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)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 11. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 12. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172256/19556445. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^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. ------ 172257/19556670. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 172258/19556679. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 172259/19556706. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.y) c)) 3. ==[ beta ]==> (((a a)(a a))((^y.y) c)) 4. ==[ alpha ]==> (((a a)(a a))((^x.x) c)) 5. ==[ beta ]==> (((a a)(a a)) c) REDUCED to normal form. ------ 172260/19556913. ------ 1. ==[ start ]==> (((a b) c)((a (a a))(b a))) REDUCED to normal form. ------ 172261/19556940. ------ 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. ------ 172262/19556967. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^y.y)) b)) REDUCED to normal form. ------ 172263/19556985. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 172264/19557066. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b)(a (^a.a)))) 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. ------ 172265/19557147. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 172266/19557300. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a b))(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 172267/19557327. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 172268/19557381. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 172269/19557408. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) b) b)) 3. ==[ beta ]==> (((a b) a)(((^y.y) b) b)) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b) b)) 5. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 172270/19557579. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (b ((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172271/19557660. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172272/19557723. ------ 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. ------ 172273/19557831. ------ 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)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 172274/19557858. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((a a)((^y.y)(^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. ------ 172275/19557912. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 172276/19557939. ------ 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))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 172277/19557966. ------ 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. ------ 172278/19557993. ------ 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) a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (b a))) REDUCED to normal form. ------ 172279/19558038. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 172280/19558083. ------ 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)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 172281/19558110. ------ 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)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a 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. ------ 172282/19558137. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((b a)(^x.a))) REDUCED to normal form. ------ 172283/19558164. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 172284/19558191. ------ 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)))(((^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. ------ 172285/19558218. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a b)(^x.a))) REDUCED to normal form. ------ 172286/19558245. ------ 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)(^z.b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a 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. ------ 172287/19558272. ------ 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)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^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 (^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(a a))) REDUCED to normal form. ------ 172288/19558335. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172289/19558416. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 172290/19558497. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^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. ------ 172291/19558605. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 172292/19558713. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.a)(^b.b))) 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. ------ 172293/19558722. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a ((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a b)) REDUCED to normal form. ------ 172294/19558749. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 172295/19558803. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 172296/19558830. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(a (a a)))) REDUCED to normal form. ------ 172297/19558857. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a b)(^z.z))) REDUCED to normal form. ------ 172298/19558911. ------ 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))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a b)) REDUCED to normal form. ------ 172299/19559055. ------ 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)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.x1))) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 172300/19559082. ------ 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. ------ 172301/19559109. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 172302/19559136. ------ 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.(z z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a a)(^y.(y y)))) 6. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 172303/19559163. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a b)(^b.(^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. ------ 172304/19559217. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(^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. ------ 172305/19559244. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 172306/19559253. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1)(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. ------ 172307/19559280. ------ 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)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z1.a)((a a)(^x2.x2)))) 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. ------ 172308/19559415. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a))(^b.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. ------ 172309/19559523. ------ 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))(^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. ------ 172310/19559577. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.a)(^c.(^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)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172311/19559586. ------ 1. ==[ start ]==> (((a a)(^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 172312/19559613. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(b (b a))) REDUCED to normal form. ------ 172313/19559694. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172314/19559721. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.b))((a a) a)) REDUCED to normal form. ------ 172315/19559748. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(a (a a)))) REDUCED to normal form. ------ 172316/19559775. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)((^z.z)(^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. ------ 172317/19559802. ------ 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)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a) a)) REDUCED to normal form. ------ 172318/19559856. ------ 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)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a a))) REDUCED to normal form. ------ 172319/19559883. ------ 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)))) REDUCED to normal form. ------ 172320/19559946. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((b a)(^x1.x1))) REDUCED to normal form. ------ 172321/19559973. ------ 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))(^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. ------ 172322/19560000. ------ 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)(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 172323/19560027. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.(z z)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a b)(^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. ------ 172324/19560054. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 172325/19560081. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(^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))) 5. ==[ beta ]==> (((a b)((a a) a))(^y.a)) 6. ==[ alpha ]==> (((a b)((a a) a))(^x.a)) REDUCED to normal form. ------ 172326/19560108. ------ 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))(^x1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (a a))(^x1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 172327/19560135. ------ 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) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 172328/19560216. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((b a) a)) 3. ==[ beta ]==> ((b (a a))((b a) a)) REDUCED to normal form. ------ 172329/19560243. ------ 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. ------ 172330/19560279. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 172331/19560414. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 172332/19560558. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)((^y.y) a))) 3. ==[ beta ]==> ((b b)((a b)((^y.y) a))) 4. ==[ alpha ]==> ((b b)((a b)((^x.x) a))) 5. ==[ beta ]==> ((b b)((a b) a)) REDUCED to normal form. ------ 172333/19560585. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 172334/19560639. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))((a a) a))) REDUCED to normal form. ------ 172335/19560666. ------ 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) a)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(a b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a b))) REDUCED to normal form. ------ 172336/19560684. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c (^y.(a a)))) 3. ==[ beta ]==> (((b a)(b a))(c (^y.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(c (^x.(a a)))) REDUCED to normal form. ------ 172337/19560765. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a 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)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 172338/19560873. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^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. ------ 172339/19560999. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z)) a)) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y)) a)) REDUCED to normal form. ------ 172340/19561026. ------ 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. ------ 172341/19561053. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b) c)) REDUCED to normal form. ------ 172342/19561269. ------ 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 a)) REDUCED to normal form. ------ 172343/19561296. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b) c)) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 172344/19561323. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a) d)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a) d)) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 172345/19561494. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(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 a)) REDUCED to normal form. ------ 172346/19561602. ------ 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 y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172347/19561710. ------ 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))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 172348/19561737. ------ 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.(^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. ------ 172349/19561791. ------ 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))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(x2 x2)))) 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. ------ 172350/19561872. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^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. ------ 172351/19561881. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b (a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b (a b))) REDUCED to normal form. ------ 172352/19561908. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(a (a a))) REDUCED to normal form. ------ 172353/19561989. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1) a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1) a)) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 172354/19562016. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((b (^y.a))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 172355/19562043. ------ 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. ------ 172356/19562133. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b)(^y.y))) REDUCED to normal form. ------ 172357/19562160. ------ 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.(^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. ------ 172358/19562187. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.a)) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.a)) REDUCED to normal form. ------ 172359/19562214. ------ 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 z)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 172360/19562241. ------ 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. ------ 172361/19562268. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 172362/19562295. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 172363/19562322. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b) a)) REDUCED to normal form. ------ 172364/19562655. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> (b (b (^x1.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 172365/19562763. ------ 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) 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. ------ 172366/19562898. ------ 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.(^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)((^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. ------ 172367/19562925. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((^y.(y y))(^z.a)) 6. ==[ alpha ]==> ((^x.(x x))(^y.a)) 7. ==[ beta ]==> ((^y.a)(^y.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 172368/19562979. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 172369/19562988. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(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. ------ 172370/19563015. ------ 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. ------ 172371/19563069. ------ 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. ------ 172372/19563096. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 172373/19563123. ------ 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. ------ 172374/19563303. ------ 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. ------ 172375/19563321. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 172376/19563348. ------ 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. ------ 172377/19563456. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^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. ------ 172378/19563483. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y)) b)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 172379/19563510. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a) c)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a) c)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a) c)) 5. ==[ beta ]==> (((a a)(a a))((^y.a) c)) 6. ==[ alpha ]==> (((a a)(a a))((^x.a) c)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 172380/19563591. ------ 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. ------ 172381/19563618. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) 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. ------ 172382/19563645. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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))) REDUCED to normal form. ------ 172383/19563699. ------ 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. ------ 172384/19563726. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^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. ------ 172385/19563735. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^z.a)(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (a (^x1.x1)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 172386/19564122. ------ 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. ------ 172387/19564140. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (^x1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 172388/19564167. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^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. ------ 172389/19564176. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b b)) REDUCED to normal form. ------ 172390/19564194. ------ 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. ------ 172391/19564248. ------ 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.(^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. ------ 172392/19564284. ------ 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. ------ 172393/19564311. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 172394/19564329. ------ 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. ------ 172395/19564392. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 172396/19575225. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a))) b) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 172397/19575249. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172398/19575330. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172399/19575477. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 172400/19575492. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a (^z.z))) a)) 3. ==[ beta ]==> (^y.((a (a (^z.z))) a)) 4. ==[ alpha ]==> (^x.((a (a (^y.y))) a)) REDUCED to normal form. ------ 172401/19575909. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^b.(^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. ------ 172402/19576185. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a) a)(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. ------ 172403/19576341. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 172404/19576746. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^b.((^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. ------ 172405/19577130. ------ 1. ==[ start ]==> ((^a.(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(b (b (^y.y)))) 3. ==[ beta ]==> ((b (b (^y.y))) b) 4. ==[ alpha ]==> ((b (b (^x.x))) b) REDUCED to normal form. ------ 172406/19577538. ------ 1. ==[ start ]==> (((a a)(a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(b (^y.y)))) REDUCED to normal form. ------ 172407/19577934. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.(b (^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. ------ 172408/19578321. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 172409/19578399. ------ 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) a))) 3. ==[ beta ]==> ((((a (^z.(^x1.x1)))((^y1.y1) a))((a (^z.(^x1.x1)))((^y1.y1) a)))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))((^z.z) a))((a (^x1.(^y1.y1)))((^z1.z1) a)))(^x2.x2)) 5. ==[ beta ]==> ((((a (^x.(^y.y))) a)((a (^x1.(^y1.y1)))((^z1.z1) a)))(^x2.x2)) 6. ==[ alpha ]==> ((((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))((^y1.y1) a)))(^z1.z1)) 7. ==[ beta ]==> ((((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a))(^z1.z1)) 8. ==[ alpha ]==> ((((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a))(^y1.y1)) REDUCED to normal form. ------ 172410/19579392. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.(a a)))) REDUCED to normal form. ------ 172411/19579725. ------ 1. ==[ start ]==> (((a a)(b a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a a)(b a))(^x.b)) REDUCED to normal form. ------ 172412/19580391. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 172413/19581588. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(b a))) 3. ==[ beta ]==> (((a a) b)(^y.(b a))) 4. ==[ alpha ]==> (((a a) b)(^x.(b a))) REDUCED to normal form. ------ 172414/19582911. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 172415/19582989. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 172416/19583577. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.(^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. ------ 172417/19583775. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a b))) REDUCED to normal form. ------ 172418/19584150. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b ((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b ((a a) a))) 3. ==[ eta ]==> ((^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. ------ 172419/19584684. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172420/19584846. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.y1))) REDUCED to normal form. ------ 172421/19584969. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 172422/19585125. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.((^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. ------ 172423/19585809. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.c)) 3. ==[ beta ]==> (((^z.z)(^y.y))(^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. ------ 172424/19585818. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.y))) REDUCED to normal form. ------ 172425/19585980. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 172426/19585998. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 172427/19586061. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 172428/19586091. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 172429/19586127. ------ 1. ==[ start ]==> (((a a) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 172430/19586154. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 172431/19586172. ------ 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. ------ 172432/19586181. ------ 1. ==[ start ]==> (((^a.a) b)((^c.a)(a (^a.(^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) REDUCED to normal form. ------ 172433/19586208. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(^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. ------ 172434/19586235. ------ 1. ==[ start ]==> (((a a) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 172435/19586262. ------ 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 (^x.x)) a) a) REDUCED to normal form. ------ 172436/19586289. ------ 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.(^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. ------ 172437/19586307. ------ 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. ------ 172438/19586316. ------ 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 (^x.x))(^y.y))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (^z.z)))) REDUCED to normal form. ------ 172439/19586334. ------ 1. ==[ start ]==> ((a (^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.a))((a (a (^y.y))) a)) REDUCED to normal form. ------ 172440/19586451. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 172441/19586559. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(a a))(^c.(^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. ------ 172442/19586748. ------ 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)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 172443/19586766. ------ 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 ]==> (((^y.y)(^y.y))((^z.(z (^x1.x1))) 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. ------ 172444/19586919. ------ 1. ==[ start ]==> (((a a)(a (a a)))((b a)((a a) a))) REDUCED to normal form. ------ 172445/19586946. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 172446/19586973. ------ 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.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. ------ 172447/19587000. ------ 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. ------ 172448/19587027. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 172449/19587126. ------ 1. ==[ start ]==> (((a (a a)) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 172450/19587180. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 172451/19587198. ------ 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. ------ 172452/19587252. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 172453/19587288. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.b)(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. ------ 172454/19587495. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (a a))(^b.b))) 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. ------ 172455/19587585. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x) b)((^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 ((^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. ------ 172456/19587630. ------ 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. ------ 172457/19587666. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 172458/19587693. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 172459/19587720. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.(^x1.x1)))(^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. ------ 172460/19587972. ------ 1. ==[ start ]==> ((a (a b))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))(b (b (^x.x)))) REDUCED to normal form. ------ 172461/19588341. ------ 1. ==[ start ]==> (((a b)(^a.a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(c (^y.(a a)))) REDUCED to normal form. ------ 172462/19588377. ------ 1. ==[ start ]==> (((a a)(a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((a a)(b (^x.x)))) REDUCED to normal form. ------ 172463/19588575. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172464/19588602. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 172465/19588737. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 172466/19588746. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 172467/19588773. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.a)(b (^a.a)))) 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)))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 172468/19588791. ------ 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 ]==> (((^y.y)(a a))((b (^z.z)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y)) a)) 5. ==[ beta ]==> ((a a)((b (^y.y)) a)) 6. ==[ alpha ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 172469/19588818. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 172470/19588827. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 172471/19588881. ------ 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 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. ------ 172472/19588935. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 172473/19588962. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 172474/19588989. ------ 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. ------ 172475/19589133. ------ 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)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(b ((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 172476/19589160. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(a (b (^a.a)))) 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. ------ 172477/19589187. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 172478/19589214. ------ 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)))) 5. ==[ beta ]==> (((a a)(a a))(b (a (^y.y)))) 6. ==[ alpha ]==> (((a a)(a a))(b (a (^x.x)))) REDUCED to normal form. ------ 172479/19589241. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 172480/19589556. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 172481/19589574. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 172482/19589610. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172483/19589655. ------ 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.(^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. ------ 172484/19589664. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 172485/19589691. ------ 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 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. ------ 172486/19589718. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 172487/19590231. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(a a))) REDUCED to normal form. ------ 172488/19590276. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.x)(b 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. ------ 172489/19590564. ------ 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. ------ 172490/19590825. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 172491/19590924. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) b) a)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) b) a)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) b) a)) 5. ==[ beta ]==> ((a a)(((^z.z) b) a)) 6. ==[ alpha ]==> ((a a)(((^x.x) b) a)) 7. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 172492/19591122. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^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. ------ 172493/19591230. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.a)(^b.b))) 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. ------ 172494/19591455. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a (a a))(a a))) REDUCED to normal form. ------ 172495/19591482. ------ 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)(^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. ------ 172496/19591509. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.z))(b a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))(b a))) REDUCED to normal form. ------ 172497/19591536. ------ 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. ------ 172498/19591716. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 172499/19591761. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 172500/19591923. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((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. ------ 172501/19592040. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 172502/19592067. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((b a)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((b a)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((b a)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 172503/19592094. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 172504/19592166. ------ 1. ==[ start ]==> (((^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)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) 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. ------ 172505/19592391. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 172506/19592427. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a a)(b a))) 3. ==[ beta ]==> (((a a) b)((a a)(b a))) REDUCED to normal form. ------ 172507/19592787. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^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. ------ 172508/19593030. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^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. ------ 172509/19593273. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 172510/19593282. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 172511/19593336. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 172512/19593381. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^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. ------ 172513/19593390. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))((^z1.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. ------ 172514/19593417. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 172515/19593444. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 172516/19593750. ------ 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. ------ 172517/19593777. ------ 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))(a a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((b (a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 172518/19593804. ------ 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. ------ 172519/19593831. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 172520/19594002. ------ 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. ------ 172521/19594110. ------ 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 (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. ------ 172522/19594146. ------ 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) REDUCED to normal form. ------ 172523/19594173. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^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. ------ 172524/19594218. ------ 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 (^x.x))((a a) a)) REDUCED to normal form. ------ 172525/19594245. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a b) b)) 3. ==[ beta ]==> ((^y.y)((a b) b)) 4. ==[ alpha ]==> ((^x.x)((a b) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 172526/19594281. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 172527/19594308. ------ 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))(^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. ------ 172528/19594389. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 172529/19594416. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 172530/19594614. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 172531/19594992. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b ((a a) a))) 2. ==[ alpha ]==> ((a ((^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. ------ 172532/19595082. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1)) 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. ------ 172533/19595271. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 172534/19595406. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^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. ------ 172535/19595433. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a)) c)) 3. ==[ beta ]==> ((^y.y)((a (a a)) c)) 4. ==[ alpha ]==> ((^x.x)((a (a a)) c)) 5. ==[ beta ]==> ((a (a a)) c) REDUCED to normal form. ------ 172536/19595496. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 172537/19595568. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 172538/19595631. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.(z z)))) REDUCED to normal form. ------ 172539/19595685. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.a))) REDUCED to normal form. ------ 172540/19595712. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 172541/19595739. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 172542/19595793. ------ 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. ------ 172543/19595811. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 172544/19595910. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c ((^y.y) a))) 3. ==[ beta ]==> (((a (a a)) b)(c ((^y.y) a))) 4. ==[ alpha ]==> (((a (a a)) b)(c ((^x.x) a))) 5. ==[ beta ]==> (((a (a a)) b)(c a)) REDUCED to normal form. ------ 172545/19595937. ------ 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. ------ 172546/19595964. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a ((^x.x)(^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. ------ 172547/19595991. ------ 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. ------ 172548/19596018. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(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)(a a))(((^y.y) a)(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) 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. ------ 172549/19596045. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a (^y.y)) a)) REDUCED to normal form. ------ 172550/19596225. ------ 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 ]==> ((a (^y.y))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^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. ------ 172551/19596243. ------ 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 ]==> ((^y.(y (^z.z)))(((^x1.x1) a) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a) b)) 5. ==[ beta ]==> ((((^z.z) a) b)(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a) b)(^y.y)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 172552/19596630. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (^a.(^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. ------ 172553/19596657. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.a))) REDUCED to normal form. ------ 172554/19596675. ------ 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))) REDUCED to normal form. ------ 172555/19596684. ------ 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. ------ 172556/19596702. ------ 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.(^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. ------ 172557/19596756. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a) b)) REDUCED to normal form. ------ 172558/19596792. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(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. ------ 172559/19596819. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 172560/19596837. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(^y.y))) 3. ==[ beta ]==> (b ((a a)(^y.y))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 172561/19596900. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 172562/19607742. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a))) c) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a))) c) REDUCED to normal form. ------ 172563/19607820. ------ 1. ==[ start ]==> ((^a.b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 172564/19607901. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^z.(^x1.x1))((^y1.y1) b))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^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. ------ 172565/19608453. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(z (z (^x1.x1))))) 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. ------ 172566/19608585. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172567/19610043. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (^y.(((a (^z.z))((a a)(a a)))((a (^z.z))((a a)(a a))))) 4. ==[ alpha ]==> (^x.(((a (^y.y))((a a)(a a)))((a (^z.z))((a a)(a a))))) REDUCED to normal form. ------ 172568/19611576. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.((a a)(a a)))) REDUCED to normal form. ------ 172569/19612230. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 172570/19612518. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^x1.(x1 x1))((a a)(^y1.y1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 172571/19613121. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172572/19613250. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^a.(^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. ------ 172573/19613436. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 172574/19613853. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 172575/19614141. ------ 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.(^x2.x2))))) REDUCED to normal form. ------ 172576/19614411. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(y a))) 3. ==[ beta ]==> ((b (a a))(^y.(y a))) 4. ==[ alpha ]==> ((b (a a))(^x.(x a))) REDUCED to normal form. ------ 172577/19615194. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.((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. ------ 172578/19615437. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 172579/19616328. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 172580/19616517. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(a y))) 3. ==[ eta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 172581/19617516. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 172582/19617651. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 172583/19617786. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(^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. ------ 172584/19617894. ------ 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. ------ 172585/19617918. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^z.(z z))(^x1.x1))(((^z.(z z))(^x1.x1))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.(z z))(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(^y.y))(((^z.(z z))(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(z z))(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> ((^y.y)(((^z.(z z))(^x1.x1))(^y1.y1))) 8. ==[ alpha ]==> ((^x.x)(((^y.(y y))(^z.z))(^x1.x1))) 9. ==[ beta ]==> (((^y.(y y))(^z.z))(^x1.x1)) 10. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.z)) 11. ==[ beta ]==> (((^y.y)(^y.y))(^z.z)) 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. ------ 172586/19618344. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.c)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.c)) REDUCED to normal form. ------ 172587/19618506. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 172588/19618587. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 172589/19618635. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (a (((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (a (((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 172590/19618671. ------ 1. ==[ start ]==> ((a b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 172591/19618716. ------ 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. ------ 172592/19618743. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(^a.a))(^b.b))) 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. ------ 172593/19618752. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 172594/19618770. ------ 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. ------ 172595/19618851. ------ 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. ------ 172596/19618887. ------ 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. ------ 172597/19618905. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 172598/19619184. ------ 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. ------ 172599/19619247. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(c (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c (b (^y.y)))) 5. ==[ beta ]==> (c (b (^y.y))) 6. ==[ alpha ]==> (c (b (^x.x))) REDUCED to normal form. ------ 172600/19619301. ------ 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 ]==> (((^y.y)(^y.y))(a (a (a (^z.z))))) 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. ------ 172601/19619310. ------ 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. ------ 172602/19619328. ------ 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. ------ 172603/19619355. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((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. ------ 172604/19619409. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 172605/19619436. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 172606/19619571. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172607/19619598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 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. ------ 172608/19619652. ------ 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) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) 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. ------ 172609/19619706. ------ 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. ------ 172610/19619742. ------ 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)(^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. ------ 172611/19619769. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 172612/19619796. ------ 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. ------ 172613/19619823. ------ 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 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 9. ==[ beta ]==> (b (^y.(y y))) 10. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 172614/19619859. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 172615/19619940. ------ 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. ------ 172616/19619967. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 172617/19620147. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((((a a) a) a)((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x) a)) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 172618/19620201. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a)) c)) REDUCED to normal form. ------ 172619/19620345. ------ 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. ------ 172620/19620372. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 172621/19620426. ------ 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))(^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. ------ 172622/19620453. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 172623/19620480. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.a)(^c.(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. ------ 172624/19620516. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.b)(b (b (^z.z)))) 4. ==[ alpha ]==> ((^x.b)(b (b (^y.y)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 172625/19620597. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(a (^z.z)))) IRREDUCIBLE: cycle. ------ 172626/19620678. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 172627/19620705. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((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))) REDUCED to normal form. ------ 172628/19620732. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 172629/19620786. ------ 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. ------ 172630/19620867. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^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. ------ 172631/19620894. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 172632/19621020. ------ 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) 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 ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172633/19621047. ------ 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)))(a (a 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. ------ 172634/19621065. ------ 1. ==[ start ]==> (((^a.b) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((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. ------ 172635/19621281. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 172636/19621335. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b (^y.y)) a)) REDUCED to normal form. ------ 172637/19621362. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(a a)) b)) REDUCED to normal form. ------ 172638/19621614. ------ 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. ------ 172639/19621641. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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. ------ 172640/19621713. ------ 1. ==[ start ]==> (((^a.b) c)((^d.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 172641/19621812. ------ 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. ------ 172642/19621947. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 172643/19622028. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((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 (^y.y)) b)) REDUCED to normal form. ------ 172644/19622055. ------ 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. ------ 172645/19622091. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 172646/19622145. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172647/19622172. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 172648/19622199. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 172649/19622253. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(^z.b))) REDUCED to normal form. ------ 172650/19622316. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(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 (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 172651/19622343. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(y y))(b a))) 3. ==[ beta ]==> ((a (a b))((^y.(y y))(b a))) 4. ==[ alpha ]==> ((a (a b))((^x.(x x))(b a))) 5. ==[ beta ]==> ((a (a b))((b a)(b a))) REDUCED to normal form. ------ 172652/19622370. ------ 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) REDUCED to normal form. ------ 172653/19622397. ------ 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)))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) 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. ------ 172654/19622424. ------ 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)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 172655/19622451. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.y))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 172656/19622478. ------ 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)(^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. ------ 172657/19622505. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.(^x1.x1)))(^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. ------ 172658/19622811. ------ 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))) 5. ==[ beta ]==> ((b a)(b (a a))) REDUCED to normal form. ------ 172659/19622838. ------ 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)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(a (^z1.z1)))) 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. ------ 172660/19622892. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 172661/19622973. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a) a)(a b))) 3. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 172662/19623081. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 172663/19623099. ------ 1. ==[ start ]==> (((a a)(b a))(b (^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(b (^x.x))) REDUCED to normal form. ------ 172664/19623153. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b)(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 (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. ------ 172665/19623180. ------ 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)))(a (^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. ------ 172666/19623261. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 172667/19623288. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a a) a)((^y.b)((a a) a))) 6. ==[ alpha ]==> (((a a) a)((^x.b)((a a) a))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 172668/19623369. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 172669/19623756. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a)(a a))(b (a (^y.(^z.z))))) 8. ==[ alpha ]==> (((a a)(a a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 172670/19623792. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 172671/19623837. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 172672/19623945. ------ 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) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172673/19623972. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a b))) 5. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 172674/19624071. ------ 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.(^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. ------ 172675/19624098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 172676/19624125. ------ 1. ==[ start ]==> ((((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 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. ------ 172677/19624206. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 172678/19624251. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((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. ------ 172679/19624287. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 172680/19624701. ------ 1. ==[ start ]==> (((^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.x1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 172681/19624764. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 172682/19624782. ------ 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) 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. ------ 172683/19624791. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a)) d)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a)) d)) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 172684/19624890. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 172685/19624989. ------ 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.(^z1.z1))))) REDUCED to normal form. ------ 172686/19625070. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))((^z.z) a))) 7. ==[ beta ]==> ((a a)((^y.(a a))((^z.z) a))) 8. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y) a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 172687/19625097. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 172688/19625124. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 172689/19625151. ------ 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.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^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)(^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. ------ 172690/19625178. ------ 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 y))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a b)(a b))) REDUCED to normal form. ------ 172691/19625232. ------ 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.(^y1.y1))((a a)(^z1.z1)))) 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. ------ 172692/19625259. ------ 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))) 5. ==[ beta ]==> ((b (a a))(b a)) REDUCED to normal form. ------ 172693/19625565. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 172694/19625601. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a)) c)) 3. ==[ beta ]==> ((b b)((^y.(a a)) c)) 4. ==[ alpha ]==> ((b b)((^x.(a a)) c)) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 172695/19625646. ------ 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. ------ 172696/19625673. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 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. ------ 172697/19625727. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)(a b))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)(a b))) 5. ==[ beta ]==> (((b a)(b a))(a (a b))) REDUCED to normal form. ------ 172698/19625817. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 172699/19625871. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.a))) REDUCED to normal form. ------ 172700/19625925. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.y1))) REDUCED to normal form. ------ 172701/19625952. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(^z.a))) REDUCED to normal form. ------ 172702/19625979. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a (^z.b))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a (^y.b))) REDUCED to normal form. ------ 172703/19626015. ------ 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. ------ 172704/19626042. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 172705/19626096. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 172706/19626123. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 172707/19626177. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))(^b.(^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. ------ 172708/19626231. ------ 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)(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 172709/19626456. ------ 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. ------ 172710/19626681. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((b c)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((b c)(a (^y.a))) 6. ==[ alpha ]==> ((b c)(a (^x.a))) REDUCED to normal form. ------ 172711/19626708. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 172712/19626816. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a) c)) 3. ==[ beta ]==> ((a (^y.y))(((a a) a) c)) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a) c)) REDUCED to normal form. ------ 172713/19626915. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c ((a a) a))) 3. ==[ beta ]==> (b (c ((a a) a))) REDUCED to normal form. ------ 172714/19627023. ------ 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 (^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. ------ 172715/19627149. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (^y.b))) REDUCED to normal form. ------ 172716/19627176. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 172717/19627203. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b)(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(a a))) 5. ==[ beta ]==> ((a b)((^y.b)(a a))) 6. ==[ alpha ]==> ((a b)((^x.b)(a a))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 172718/19627257. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 172719/19627284. ------ 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. ------ 172720/19627311. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 172721/19627338. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^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. ------ 172722/19627365. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a b)) REDUCED to normal form. ------ 172723/19627446. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 172724/19627473. ------ 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))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 172725/19627617. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 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. ------ 172726/19627698. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((a (^x1.x1))((^y1.y1)(^z1.z1)))) 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. ------ 172727/19627923. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 172728/19628022. ------ 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. ------ 172729/19628103. ------ 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.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. ------ 172730/19628112. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 172731/19628139. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y)) c)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(c c)) REDUCED to normal form. ------ 172732/19628211. ------ 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))((a a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172733/19628247. ------ 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))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 172734/19628274. ------ 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. ------ 172735/19628328. ------ 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.(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. ------ 172736/19628364. ------ 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. ------ 172737/19628391. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^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)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 172738/19628418. ------ 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.(^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. ------ 172739/19628445. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 172740/19628472. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 172741/19628499. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^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. ------ 172742/19628580. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.a))) REDUCED to normal form. ------ 172743/19628634. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 172744/19628661. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))(a a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))(a a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))(a a))) 5. ==[ beta ]==> ((b (a (a a)))((a a)(a a))) REDUCED to normal form. ------ 172745/19628688. ------ 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 (^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)))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 172746/19628742. ------ 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. ------ 172747/19628760. ------ 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. ------ 172748/19628769. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z)(^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. ------ 172749/19629165. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^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. ------ 172750/19629183. ------ 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. ------ 172751/19629219. ------ 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. ------ 172752/19629237. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b b)) 3. ==[ beta ]==> ((^y.y)(b b)) 4. ==[ alpha ]==> ((^x.x)(b b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 172753/19629291. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 172754/19629327. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^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. ------ 172755/19629354. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 172756/19629372. ------ 1. ==[ start ]==> (((^a.b)(b a))(b a)) 2. ==[ alpha ]==> (((^x.b)(b a))(b a)) 3. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 172757/19629435. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 172758/19629461. ------ 1. ==[ start ]==> (^a.((b a)(^a.b))) 2. ==[ alpha ]==> (^x.((b x)(^y.b))) REDUCED to normal form. ------ 172759/19629462. ------ 1. ==[ start ]==> (a ((b a)(^a.b))) 2. ==[ alpha ]==> (a ((b a)(^x.b))) REDUCED to normal form. ------ 172760/19629717. ------ 1. ==[ start ]==> ((^a.(^b.a))(^b.(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. ------ 172761/19640319. ------ 1. ==[ start ]==> ((^a.a)((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 3. ==[ beta ]==> ((b a)(^y.b)) 4. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 172762/19640346. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 172763/19640373. ------ 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 REDUCED to normal form. ------ 172764/19640409. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172765/19640454. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 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. ------ 172766/19640571. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^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 ]==> (^x.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 172767/19640574. ------ 1. ==[ start ]==> ((a (^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 172768/19640643. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b (^z.z)) c)) 3. ==[ eta ]==> ((^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. ------ 172769/19640814. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 172770/19641006. ------ 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 ]==> (((^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)))) REDUCED to normal form. ------ 172771/19641015. ------ 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. ------ 172772/19641420. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 172773/19641438. ------ 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. ------ 172774/19642029. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 172775/19642596. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c (^z.(a a)))) 3. ==[ beta ]==> (^y.((c (^z.(a a)))(c (^z.(a a))))) 4. ==[ alpha ]==> (^x.((c (^y.(a a)))(c (^z.(a a))))) REDUCED to normal form. ------ 172776/19643031. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.(b (^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. ------ 172777/19643418. ------ 1. ==[ start ]==> (((^a.b) c)(^a.(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. ------ 172778/19643478. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.z) c)) 3. ==[ beta ]==> ((((^z.z) c)((^z.z) c))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) c)((^y.y) c))(^z.z)) 5. ==[ beta ]==> ((c ((^y.y) c))(^z.z)) 6. ==[ alpha ]==> ((c ((^x.x) c))(^y.y)) 7. ==[ beta ]==> ((c c)(^y.y)) 8. ==[ alpha ]==> ((c c)(^x.x)) REDUCED to normal form. ------ 172779/19643769. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 172780/19645164. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.z)) 5. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.z)) 6. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.z)) 7. ==[ beta ]==> ((a a)(^z.z)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 172781/19645497. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^a.((^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. ------ 172782/19645989. ------ 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) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 172783/19646406. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 172784/19646964. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.a))) 3. ==[ beta ]==> ((b (a a))(^y.(^z.a))) 4. ==[ alpha ]==> ((b (a a))(^x.(^y.a))) REDUCED to normal form. ------ 172785/19646988. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((b a) a)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((b a) a)) 3. ==[ beta ]==> ((((b a) a)((b a) a))(((b a) a)((b a) a))) REDUCED to normal form. ------ 172786/19647495. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 172787/19647747. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^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. ------ 172788/19648068. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 172789/19648242. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.(^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. ------ 172790/19648458. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.((^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. ------ 172791/19649925. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 172792/19650048. ------ 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. ------ 172793/19650471. ------ 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. ------ 172794/19650915. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^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. ------ 172795/19651032. ------ 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 ]==> (((^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. ------ 172796/19651077. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^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. ------ 172797/19651140. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(z z))) REDUCED to normal form. ------ 172798/19651179. ------ 1. ==[ start ]==> ((a a)((b a)(^a.b))) 2. ==[ alpha ]==> ((a a)((b a)(^x.b))) REDUCED to normal form. ------ 172799/19651206. ------ 1. ==[ start ]==> ((a (a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 172800/19651233. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 172801/19651242. ------ 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. ------ 172802/19651269. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 172803/19651287. ------ 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. ------ 172804/19651314. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(^a.a))(^b.b))) 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. ------ 172805/19651323. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 172806/19651350. ------ 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)((^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. ------ 172807/19651377. ------ 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. ------ 172808/19651404. ------ 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.(^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. ------ 172809/19651431. ------ 1. ==[ start ]==> ((a (^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (^x.a))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 172810/19651449. ------ 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. ------ 172811/19651476. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 172812/19651503. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a ((^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. ------ 172813/19651674. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 172814/19651845. ------ 1. ==[ start ]==> ((((^a.a) a) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a b)(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a b)(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 172815/19651863. ------ 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 ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 172816/19651872. ------ 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. ------ 172817/19651899. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^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. ------ 172818/19651926. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 172819/19651953. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 172820/19651980. ------ 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. ------ 172821/19652088. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((b b)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((b b)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((b b)((a a)(a a))) REDUCED to normal form. ------ 172822/19652223. ------ 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. ------ 172823/19652250. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> (a ((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> (a ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 172824/19652277. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.(^x1.x1)) 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. ------ 172825/19652295. ------ 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. ------ 172826/19652421. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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)))) REDUCED to normal form. ------ 172827/19652448. ------ 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. ------ 172828/19652475. ------ 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))(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((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))) REDUCED to normal form. ------ 172829/19652502. ------ 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. ------ 172830/19652529. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a 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. ------ 172831/19652592. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172832/19652646. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> (a ((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> (a ((^x.a)((a a)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172833/19652808. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(y y)))) 9. ==[ beta ]==> ((a a)(^y.(y y))) 10. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 172834/19652889. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 172835/19653060. ------ 1. ==[ start ]==> (((^a.b) a)(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 172836/19653222. ------ 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. ------ 172837/19653249. ------ 1. ==[ start ]==> (((a b) a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b) a)((b a)(^y.y))) 4. ==[ alpha ]==> (((a b) a)((b a)(^x.x))) REDUCED to normal form. ------ 172838/19653276. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 172839/19653330. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 172840/19653357. ------ 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. ------ 172841/19653384. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 172842/19653411. ------ 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.(^x1.x1))))) REDUCED to normal form. ------ 172843/19653438. ------ 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)(^x.x))(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. ------ 172844/19653456. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.(a a)))) REDUCED to normal form. ------ 172845/19653528. ------ 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 (^y.y))((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 172846/19653555. ------ 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. ------ 172847/19653582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.a))) 7. ==[ beta ]==> (a (((^y.y) b)(^z.a))) 8. ==[ alpha ]==> (a (((^x.x) b)(^y.a))) 9. ==[ beta ]==> (a (b (^y.a))) 10. ==[ alpha ]==> (a (b (^x.a))) REDUCED to normal form. ------ 172848/19653609. ------ 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)))) REDUCED to normal form. ------ 172849/19653636. ------ 1. ==[ start ]==> (((a b)(a a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 172850/19653672. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(^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 a) REDUCED to normal form. ------ 172851/19653699. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 172852/19653753. ------ 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 REDUCED to normal form. ------ 172853/19653834. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (b ((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172854/19653888. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(b (^z.z)))) 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. ------ 172855/19653969. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(^z1.a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(^z1.a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a))) 9. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 10. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 11. ==[ beta ]==> ((^y.y)(^z.a)) 12. ==[ alpha ]==> ((^x.x)(^y.a)) 13. ==[ beta ]==> (^y.a) 14. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 172856/19654050. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 172857/19654275. ------ 1. ==[ start ]==> (((^a.b) c)(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(a (b (^y.y)))) 3. ==[ beta ]==> (b (a (b (^y.y)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 172858/19654338. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y) c)) 3. ==[ beta ]==> ((a ((a a)(^x.x))) c) REDUCED to normal form. ------ 172859/19654518. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b) c)((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b) c)((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (((a b) c)((a a)(^y.y))) 6. ==[ alpha ]==> (((a b) c)((a a)(^x.x))) REDUCED to normal form. ------ 172860/19654545. ------ 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. ------ 172861/19654572. ------ 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 (^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. ------ 172862/19654617. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(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. ------ 172863/19654626. ------ 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. ------ 172864/19654851. ------ 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.(a a)))) REDUCED to normal form. ------ 172865/19654932. ------ 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.(^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. ------ 172866/19654959. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 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)) REDUCED to normal form. ------ 172867/19655013. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(a a)) a)) 3. ==[ beta ]==> (((a b) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 172868/19655040. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 172869/19655184. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(^x1.b))) 5. ==[ beta ]==> (b ((^z.b)(^x1.b))) 6. ==[ alpha ]==> (b ((^x.b)(^y.b))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 172870/19655328. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b ((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b b)) REDUCED to normal form. ------ 172871/19655436. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((b a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((b a) a)) REDUCED to normal form. ------ 172872/19655463. ------ 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))(a (a a)))) REDUCED to normal form. ------ 172873/19655517. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 172874/19655544. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a) a)(a b))) REDUCED to normal form. ------ 172875/19655571. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.a))((^z.z)(a a))) 8. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a a))) 9. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 172876/19655598. ------ 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))((a a)(^x1.x1)))) REDUCED to normal form. ------ 172877/19655715. ------ 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))) 7. ==[ beta ]==> ((a (a a))(b (^y.y))) 8. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 172878/19655742. ------ 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)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 172879/19655769. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((b 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. ------ 172880/19655796. ------ 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))(^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. ------ 172881/19655823. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(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. ------ 172882/19655850. ------ 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. ------ 172883/19655877. ------ 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)(^z.b))) REDUCED to normal form. ------ 172884/19655940. ------ 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 y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172885/19656021. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((a a)((^z.z)((^x1.x1) 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. ------ 172886/19656237. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 172887/19656264. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^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. ------ 172888/19656318. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 172889/19656327. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 172890/19656354. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(a ((^z.z) b))) 5. ==[ beta ]==> ((^y.b)(a ((^z.z) b))) 6. ==[ alpha ]==> ((^x.b)(a ((^y.y) b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 172891/19656408. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 172892/19656435. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 172893/19656462. ------ 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)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(a (a a)))) REDUCED to normal form. ------ 172894/19656516. ------ 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 a) a))) REDUCED to normal form. ------ 172895/19656687. ------ 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))) REDUCED to normal form. ------ 172896/19656714. ------ 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. ------ 172897/19656741. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 172898/19656768. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(^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. ------ 172899/19656849. ------ 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 b)(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.b))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.b))) 7. ==[ beta ]==> ((a b)(^y.b)) 8. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 172900/19656858. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 172901/19656885. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(z1 z1))((^x2.x2)(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. ------ 172902/19657020. ------ 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)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 172903/19657182. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))(^b.(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. ------ 172904/19657209. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.a)(^c.(^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 172905/19657263. ------ 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)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 172906/19657299. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(a a))) 5. ==[ beta ]==> ((^y.(a a))((b a)(a a))) 6. ==[ alpha ]==> ((^x.(a a))((b a)(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172907/19657326. ------ 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))(a (^z.z)))) REDUCED to normal form. ------ 172908/19657353. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a b)(^x.a))((a a) a)) REDUCED to normal form. ------ 172909/19657380. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(a (a a)))) REDUCED to normal form. ------ 172910/19657407. ------ 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)(^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. ------ 172911/19657461. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(a b))) REDUCED to normal form. ------ 172912/19657488. ------ 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 (^x.x))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((b (^x.x))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 172913/19657578. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((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. ------ 172914/19657605. ------ 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))(^z.(^x1.x1)))) REDUCED to normal form. ------ 172915/19657632. ------ 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)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.a))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.a))) 9. ==[ beta ]==> ((a a)((a a)(^y.a))) 10. ==[ alpha ]==> ((a a)((a a)(^x.a))) REDUCED to normal form. ------ 172916/19657659. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a b)(^x.(x x)))) REDUCED to normal form. ------ 172917/19657686. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 172918/19657740. ------ 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))(^y.b))) REDUCED to normal form. ------ 172919/19657848. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((b a) a)) REDUCED to normal form. ------ 172920/19657884. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^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 ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172921/19658019. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^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. ------ 172922/19658163. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> ((b b)((a a)(a (^y.y)))) 6. ==[ alpha ]==> ((b b)((a a)(a (^x.x)))) REDUCED to normal form. ------ 172923/19658190. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a b)((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a b) a)) REDUCED to normal form. ------ 172924/19658244. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^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))(^y.y))((^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))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 172925/19658271. ------ 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 a))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))((a a) a))) REDUCED to normal form. ------ 172926/19658352. ------ 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. ------ 172927/19658577. ------ 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. ------ 172928/19658604. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((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. ------ 172929/19658631. ------ 1. ==[ start ]==> ((((^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)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 172930/19658658. ------ 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. ------ 172931/19658685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b) c)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b) c)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b) c)) 5. ==[ beta ]==> (((a a)(^y.y))((a b) c)) 6. ==[ alpha ]==> (((a a)(^x.x))((a b) c)) REDUCED to normal form. ------ 172932/19658874. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.(^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. ------ 172933/19658901. ------ 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 a)) REDUCED to normal form. ------ 172934/19658928. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b) c)) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 172935/19659099. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 172936/19659207. ------ 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.(^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. ------ 172937/19659315. ------ 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 (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 172938/19659342. ------ 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)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 172939/19659477. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 172940/19659486. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c ((a a) a))) REDUCED to normal form. ------ 172941/19659513. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b (a b))) 3. ==[ beta ]==> (((a a)(^y.b))(b (a b))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (a b))) REDUCED to normal form. ------ 172942/19659594. ------ 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)(a (^x1.x1)))) REDUCED to normal form. ------ 172943/19659621. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((b (^x.a))((^z.z) a)) 8. ==[ alpha ]==> ((b (^x.a))((^y.y) a)) 9. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 172944/19659648. ------ 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. ------ 172945/19659765. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b)(^z.z))) 3. ==[ beta ]==> ((a ((^y.y) b))((a b)(^z.z))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b)(^y.y))) 5. ==[ beta ]==> ((a b)((a b)(^y.y))) 6. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 172946/19659792. ------ 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.(^x1.x1)))) REDUCED to normal form. ------ 172947/19659819. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 172948/19659846. ------ 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. ------ 172949/19659873. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) 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. ------ 172950/19659900. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 172951/19659927. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)(^y.b))) REDUCED to normal form. ------ 172952/19659981. ------ 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. ------ 172953/19660008. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z)) c)) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y)) c)) 7. ==[ beta ]==> ((b a)((^y.y) c)) 8. ==[ alpha ]==> ((b a)((^x.x) c)) 9. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 172954/19660260. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 172955/19660368. ------ 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))(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. ------ 172956/19660530. ------ 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.(^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. ------ 172957/19660584. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(^z.(z z)))) 7. ==[ beta ]==> ((b b)((^y.a)(^z.(z z)))) 8. ==[ alpha ]==> ((b b)((^x.a)(^y.(y y)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 172958/19660593. ------ 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. ------ 172959/19660620. ------ 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))))(b ((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b ((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 172960/19660674. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 172961/19660701. ------ 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. ------ 172962/19660728. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a ((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 172963/19660773. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172964/19660782. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.y1))) REDUCED to normal form. ------ 172965/19660908. ------ 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. ------ 172966/19660926. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) 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. ------ 172967/19660953. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^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. ------ 172968/19660980. ------ 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. ------ 172969/19661007. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a) c)) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a) c)) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a) c)) 5. ==[ beta ]==> (((a (a a)) b)(a c)) REDUCED to normal form. ------ 172970/19661088. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z)) 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. ------ 172971/19661115. ------ 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 z)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y)) b)) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y)) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x)) b)) 7. ==[ beta ]==> (((a a)(a a))(b b)) REDUCED to normal form. ------ 172972/19661142. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 172973/19661223. ------ 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. ------ 172974/19661250. ------ 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.(^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. ------ 172975/19661304. ------ 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. ------ 172976/19661331. ------ 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. ------ 172977/19661340. ------ 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 ]==> (((^z.(z z))(^x1.x1))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.z)) 7. ==[ beta ]==> (((^y.y)(^y.y))(^z.z)) 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. ------ 172978/19661727. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(a a))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a a))) 5. ==[ beta ]==> (b ((a (^y.y))(a a))) 6. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 172979/19661745. ------ 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 ]==> (((^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. ------ 172980/19661754. ------ 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. ------ 172981/19661772. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 172982/19661799. ------ 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))(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. ------ 172983/19661853. ------ 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)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 172984/19661889. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 172985/19661916. ------ 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. ------ 172986/19661934. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^a.(^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. ------ 172987/19661997. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (a a))) REDUCED to normal form. ------ 172988/19662288. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 172989/19672908. ------ 1. ==[ start ]==> ((^a.(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 172990/19673151. ------ 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. ------ 172991/19673154. ------ 1. ==[ start ]==> ((a (^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 172992/19673595. ------ 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. ------ 172993/19673844. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a b)((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. ------ 172994/19674027. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 172995/19674432. ------ 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)(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 172996/19674789. ------ 1. ==[ start ]==> ((^a.(a b))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((c ((a a)(a a))) b) REDUCED to normal form. ------ 172997/19675620. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 172998/19675998. ------ 1. ==[ start ]==> (((^a.b) c)(^b.(^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. ------ 172999/19676007. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 173000/19676058. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((((^z.z) b)(a (^x1.x1)))(((^z.z) b)(a (^x1.x1))))(^y.y)) 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 (^x.x)))(b (a (^z.z))))(^x1.x1)) 8. ==[ alpha ]==> (((b (a (^x.x)))(b (a (^y.y))))(^z.z)) REDUCED to normal form. ------ 173001/19677744. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 173002/19678077. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^b.(^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. ------ 173003/19678383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(^y.(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 173004/19680597. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 173005/19680648. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)(a (^z.z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173006/19681038. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 173007/19682208. ------ 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))) REDUCED to normal form. ------ 173008/19682532. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^c.a))) 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. ------ 173009/19682628. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 173010/19682811. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.((^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. ------ 173011/19683045. ------ 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. ------ 173012/19683495. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.c)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.c)) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.c)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.c)) REDUCED to normal form. ------ 173013/19683504. ------ 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. ------ 173014/19683612. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^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. ------ 173015/19683657. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.b)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.y)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173016/19683720. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 173017/19683777. ------ 1. ==[ start ]==> ((a (^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 173018/19683804. ------ 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 ]==> ((^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. ------ 173019/19683840. ------ 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)))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 173020/19683867. ------ 1. ==[ start ]==> (((^a.a) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.b)(b a))) 3. ==[ beta ]==> (b ((^y.b)(b a))) 4. ==[ alpha ]==> (b ((^x.b)(b a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 173021/19683912. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 173022/19683921. ------ 1. ==[ start ]==> (((a a) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 173023/19683948. ------ 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 (^x.x)) a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 173024/19683975. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 173025/19684002. ------ 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 (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 173026/19684020. ------ 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. ------ 173027/19684056. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a (^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173028/19684101. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z)) c)) 3. ==[ beta ]==> ((^y.a)((b (^z.z)) c)) 4. ==[ alpha ]==> ((^x.a)((b (^y.y)) c)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 173029/19684137. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 173030/19684164. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.b)(^b.(^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. ------ 173031/19684191. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 173032/19684353. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 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. ------ 173033/19684461. ------ 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. ------ 173034/19684479. ------ 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. ------ 173035/19684605. ------ 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. ------ 173036/19684632. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((b a)((a a) a))) REDUCED to normal form. ------ 173037/19684659. ------ 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))(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. ------ 173038/19684686. ------ 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. ------ 173039/19684713. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 173040/19684893. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 173041/19684938. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 173042/19685181. ------ 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))(^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. ------ 173043/19685235. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (a (((^z.z) a)(^x1.(a a)))) 6. ==[ alpha ]==> (a (((^x.x) a)(^y.(a a)))) 7. ==[ beta ]==> (a (a (^y.(a a)))) 8. ==[ alpha ]==> (a (a (^x.(a a)))) REDUCED to normal form. ------ 173044/19685271. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(b (^z.z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173045/19685298. ------ 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)((^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. ------ 173046/19685316. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)((a 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. ------ 173047/19685343. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1)) 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. ------ 173048/19685406. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.(z z))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(y y))) REDUCED to normal form. ------ 173049/19685433. ------ 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.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173050/19685649. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 173051/19685658. ------ 1. ==[ start ]==> ((a (a b))(c ((a a)(a a)))) REDUCED to normal form. ------ 173052/19686063. ------ 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)))) REDUCED to normal form. ------ 173053/19686090. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a a)(b (^y.y)))) REDUCED to normal form. ------ 173054/19686216. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 173055/19686261. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173056/19686288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 173057/19686342. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^y1.(^z1.z1)))) 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. ------ 173058/19686423. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 173059/19686432. ------ 1. ==[ start ]==> (((a b) b)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) b)((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 173060/19686459. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 173061/19686486. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(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. ------ 173062/19686504. ------ 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 (^z.z)) 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. ------ 173063/19686558. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b) c)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b) c)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b) c)) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b) c)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) c)) 9. ==[ beta ]==> ((^y.y)(((^z.z) b) c)) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 11. ==[ beta ]==> (((^y.y) b) c) 12. ==[ alpha ]==> (((^x.x) b) c) 13. ==[ beta ]==> (b c) REDUCED to normal form. ------ 173064/19686567. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 173065/19686594. ------ 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)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 9. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173066/19686648. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(^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. ------ 173067/19686675. ------ 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. ------ 173068/19686846. ------ 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. ------ 173069/19686864. ------ 1. ==[ start ]==> (((^a.b) c)((^a.a)(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 173070/19686873. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 173071/19686900. ------ 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. ------ 173072/19686927. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b)(a (^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. ------ 173073/19687215. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (^z.(a a)))) REDUCED to normal form. ------ 173074/19687260. ------ 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))(^y.y))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 173075/19687296. ------ 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)(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. ------ 173076/19687323. ------ 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) 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. ------ 173077/19687341. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((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. ------ 173078/19687404. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 173079/19687917. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 173080/19687962. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a)) a)) 3. ==[ beta ]==> ((b a)((^y.(a a)) a)) 4. ==[ alpha ]==> ((b a)((^x.(a a)) a)) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 173081/19687989. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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) 7. ==[ beta ]==> b REDUCED to normal form. ------ 173082/19688250. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 173083/19688277. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a) b)) REDUCED to normal form. ------ 173084/19688511. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 173085/19688610. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a a)(^z.z))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.(a 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. ------ 173086/19688691. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 173087/19688835. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^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. ------ 173088/19688916. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 173089/19688943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.a)(^b.b))) 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. ------ 173090/19688988. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1))) 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. ------ 173091/19689141. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(a b))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 173092/19689168. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a (a a))(a a))) REDUCED to normal form. ------ 173093/19689195. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 173094/19689222. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(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. ------ 173095/19689249. ------ 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 (^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. ------ 173096/19689402. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173097/19689447. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^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. ------ 173098/19689474. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z1.(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. ------ 173099/19689609. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a) b)) 3. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 173100/19689726. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 173101/19689753. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 173102/19689780. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 173103/19689807. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 173104/19689933. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 173105/19690113. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 173106/19690140. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(b a))) REDUCED to normal form. ------ 173107/19690473. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((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. ------ 173108/19690941. ------ 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. ------ 173109/19691022. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 173110/19691067. ------ 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)(^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. ------ 173111/19691076. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 173112/19691103. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 173113/19691130. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 173114/19691436. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b ((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (a a))) REDUCED to normal form. ------ 173115/19691463. ------ 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)))) REDUCED to normal form. ------ 173116/19691490. ------ 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))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a)(a a))) REDUCED to normal form. ------ 173117/19691517. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 173118/19691796. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173119/19691832. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b c)(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b c)((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b c)((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b c)((^y.y)(^z.z))) 10. ==[ alpha ]==> ((b c)((^x.x)(^y.y))) 11. ==[ beta ]==> ((b c)(^y.y)) 12. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 173120/19691859. ------ 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) REDUCED to normal form. ------ 173121/19691904. ------ 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)))) REDUCED to normal form. ------ 173122/19691931. ------ 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)(((^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. ------ 173123/19691967. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^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. ------ 173124/19692075. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 173125/19692102. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 173126/19692174. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b) b)) 3. ==[ beta ]==> ((^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. ------ 173127/19692300. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 173128/19692327. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(a b))) REDUCED to normal form. ------ 173129/19692768. ------ 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) 9. ==[ beta ]==> a REDUCED to normal form. ------ 173130/19692957. ------ 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.(^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. ------ 173131/19693074. ------ 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))) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 173132/19693092. ------ 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 ]==> (((^y.(^z.z)) a)(((a a) a) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((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. ------ 173133/19693119. ------ 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)(((^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 ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 173134/19693182. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 173135/19693209. ------ 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.(^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. ------ 173136/19693254. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a) a)) 3. ==[ beta ]==> (b ((^z.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 173137/19693371. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) REDUCED to normal form. ------ 173138/19693398. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.a))) REDUCED to normal form. ------ 173139/19693425. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(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. ------ 173140/19693479. ------ 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) 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. ------ 173141/19693497. ------ 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 x1)))) REDUCED to normal form. ------ 173142/19693650. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (a (a a)))) REDUCED to normal form. ------ 173143/19693677. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 173144/19693704. ------ 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. ------ 173145/19693731. ------ 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 (^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. ------ 173146/19693785. ------ 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. ------ 173147/19693911. ------ 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. ------ 173148/19693929. ------ 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. ------ 173149/19694316. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (^z.z))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.z))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.y))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 173150/19694334. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^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. ------ 173151/19694343. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (^y.(^z.z)))) REDUCED to normal form. ------ 173152/19694370. ------ 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. ------ 173153/19694388. ------ 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)) REDUCED to normal form. ------ 173154/19694442. ------ 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)) REDUCED to normal form. ------ 173155/19694478. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^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 ]==> ((^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. ------ 173156/19694505. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 173157/19694523. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y) b)) 3. ==[ beta ]==> (b ((^y.y) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 173158/19694586. ------ 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))) 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. ------ 173159/19694630. ------ 1. ==[ start ]==> (^a.((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))((x x) x))) 3. ==[ beta ]==> (^x.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 173160/19694631. ------ 1. ==[ start ]==> (a ((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 173161/19701303. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(y a))) 3. ==[ beta ]==> (((^y.(y a))(^y.(y a)))((^y.(y a))(^y.(y a)))) 4. ==[ alpha ]==> (((^x.(x a))(^y.(y a)))((^z.(z a))(^x1.(x1 a)))) 5. ==[ beta ]==> (((^y.(y a)) a)((^z.(z a))(^x1.(x1 a)))) 6. ==[ alpha ]==> (((^x.(x a)) a)((^y.(y a))(^z.(z a)))) 7. ==[ beta ]==> ((a a)((^y.(y a))(^z.(z a)))) 8. ==[ alpha ]==> ((a a)((^x.(x a))(^y.(y 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. ------ 173162/19704786. ------ 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. ------ 173163/19705500. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a)) a) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a)) 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. ------ 173164/19705506. ------ 1. ==[ start ]==> ((^a.a)((^a.(^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. ------ 173165/19705560. ------ 1. ==[ start ]==> ((^a.b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 173166/19705779. ------ 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. ------ 173167/19706100. ------ 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. ------ 173168/19706220. ------ 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. ------ 173169/19706325. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173170/19706883. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.b)((a a)(^z.z)))((^y.b)((a a)(^z.z))))((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.b)((a a)(^y.y)))((^z.b)((a a)(^x1.x1))))((^y1.b)((a a)(^z1.z1)))) 5. ==[ beta ]==> ((b ((^z.b)((a a)(^x1.x1))))((^y1.b)((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.b)((a a)(^y.y))))((^z.b)((a a)(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^z.b)((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.b)((a a)(^y.y)))) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 173171/19707396. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.a)(^z.(a a))) b) 4. ==[ alpha ]==> (((^x.a)(^y.(a a))) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 173172/19707783. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (^y.((((^z.z) a)((^x1.x1) b))(((^z.z) a)((^x1.x1) b)))) 4. ==[ alpha ]==> (^x.((((^y.y) a)((^z.z) b))(((^x1.x1) a)((^y1.y1) b)))) 5. ==[ beta ]==> (^x.((a ((^z.z) b))(((^x1.x1) a)((^y1.y1) b)))) 6. ==[ alpha ]==> (^x.((a ((^y.y) b))(((^z.z) a)((^x1.x1) b)))) 7. ==[ beta ]==> (^x.((a b)(((^z.z) a)((^x1.x1) b)))) 8. ==[ alpha ]==> (^x.((a b)(((^y.y) a)((^z.z) b)))) 9. ==[ beta ]==> (^x.((a b)(a ((^z.z) b)))) 10. ==[ alpha ]==> (^x.((a b)(a ((^y.y) b)))) 11. ==[ beta ]==> (^x.((a b)(a b))) REDUCED to normal form. ------ 173173/19708227. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 173174/19709343. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^b.((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. ------ 173175/19709421. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ eta ]==> (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. ------ 173176/19709703. ------ 1. ==[ start ]==> (((^a.a)(b a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.((y y)(y y)))) 3. ==[ beta ]==> ((b a)(^y.((y y)(y y)))) 4. ==[ alpha ]==> ((b a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 173177/19709970. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(b a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 173178/19710258. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^x1.(^y1.y1))((^z1.z1)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^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. ------ 173179/19710861. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173180/19711017. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 173181/19711176. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)((a a) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 173182/19711908. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^a.(^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. ------ 173183/19712175. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.y)(b a))) 3. ==[ beta ]==> ((((^y.y)(b a))((^y.y)(b a)))(((^y.y)(b a))((^y.y)(b a)))) 4. ==[ alpha ]==> ((((^x.x)(b a))((^y.y)(b a)))(((^z.z)(b a))((^x1.x1)(b a)))) 5. ==[ beta ]==> (((b a)((^y.y)(b a)))(((^z.z)(b a))((^x1.x1)(b a)))) 6. ==[ alpha ]==> (((b a)((^x.x)(b a)))(((^y.y)(b a))((^z.z)(b a)))) 7. ==[ beta ]==> (((b a)(b a))(((^y.y)(b a))((^z.z)(b a)))) 8. ==[ alpha ]==> (((b a)(b a))(((^x.x)(b a))((^y.y)(b a)))) 9. ==[ beta ]==> (((b a)(b a))((b a)((^y.y)(b a)))) 10. ==[ alpha ]==> (((b a)(b a))((b a)((^x.x)(b a)))) 11. ==[ beta ]==> (((b a)(b a))((b a)(b a))) REDUCED to normal form. ------ 173184/19712178. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(x a))) REDUCED to normal form. ------ 173185/19712457. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^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. ------ 173186/19712700. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 173187/19712961. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 173188/19713204. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.(^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. ------ 173189/19713429. ------ 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 (^x.(a a))) REDUCED to normal form. ------ 173190/19714095. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 173191/19714416. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^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. ------ 173192/19714995. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((z z) z))) 3. ==[ beta ]==> (b (^z.((z z) z))) 4. ==[ alpha ]==> (b (^x.((x x) x))) REDUCED to normal form. ------ 173193/19715283. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.((^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. ------ 173194/19715418. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 173195/19715553. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^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. ------ 173196/19715658. ------ 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. ------ 173197/19715661. ------ 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. ------ 173198/19716111. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.c)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.c)) REDUCED to normal form. ------ 173199/19716219. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.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. ------ 173200/19716264. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a a))) 3. ==[ beta ]==> (b (^y.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 173201/19716327. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 173202/19716372. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.a)) 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. ------ 173203/19716384. ------ 1. ==[ start ]==> ((a a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 173204/19716402. ------ 1. ==[ start ]==> (((^a.a) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x) a)((b a)(^y.b))) 3. ==[ beta ]==> (a ((b a)(^y.b))) 4. ==[ alpha ]==> (a ((b a)(^x.b))) REDUCED to normal form. ------ 173205/19716429. ------ 1. ==[ start ]==> (((a a) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 173206/19716438. ------ 1. ==[ start ]==> ((a b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 173207/19716492. ------ 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. ------ 173208/19716510. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 173209/19716537. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(^a.a))(^b.b))) 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. ------ 173210/19716654. ------ 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. ------ 173211/19716672. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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. ------ 173212/19716681. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^x1.x1)(^z.z))) 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. ------ 173213/19716897. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) 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. ------ 173214/19716978. ------ 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. ------ 173215/19717068. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b ((^z.(^x1.x1)) 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. ------ 173216/19717095. ------ 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. ------ 173217/19717104. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 173218/19717122. ------ 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)(((^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. ------ 173219/19717176. ------ 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))((^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. ------ 173220/19717203. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 173221/19717338. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173222/19717365. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 173223/19717419. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^y1.y1) 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. ------ 173224/19717473. ------ 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. ------ 173225/19717500. ------ 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. ------ 173226/19717536. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(^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. ------ 173227/19717563. ------ 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. ------ 173228/19717590. ------ 1. ==[ start ]==> ((((^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.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 173229/19717626. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 173230/19717653. ------ 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. ------ 173231/19717734. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 173232/19717761. ------ 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. ------ 173233/19717968. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1)) b)) REDUCED to normal form. ------ 173234/19718139. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(a a))(^y1.(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. ------ 173235/19718166. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.b)(^c.(^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. ------ 173236/19718220. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 173237/19718247. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^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. ------ 173238/19718274. ------ 1. ==[ start ]==> ((a (a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 173239/19718283. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((^y.b)(c ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.b)(c ((a a)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 173240/19718364. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(a a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(a a))) IRREDUCIBLE: cycle. ------ 173241/19718445. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 173242/19718472. ------ 1. ==[ start ]==> (((^a.a)(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)((b a)((^y.y)(^z.z)))) 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. ------ 173243/19718499. ------ 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)(^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. ------ 173244/19718553. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a b)(a a))) REDUCED to normal form. ------ 173245/19718634. ------ 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))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 173246/19718661. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(a b)) REDUCED to normal form. ------ 173247/19718679. ------ 1. ==[ start ]==> (((a a)(a b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(c (^x.(a a)))) REDUCED to normal form. ------ 173248/19718814. ------ 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) 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. ------ 173249/19718832. ------ 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 ((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 173250/19718841. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 173251/19719048. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a b) b)(a (^y.y))) 4. ==[ alpha ]==> (((a b) b)(a (^x.x))) REDUCED to normal form. ------ 173252/19719129. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b (^z.z)) a)) REDUCED to normal form. ------ 173253/19719183. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 173254/19719327. ------ 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)(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. ------ 173255/19719354. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 173256/19719408. ------ 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))(^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. ------ 173257/19719435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (a a))((^y.a)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.a)(^y.y))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 173258/19719579. ------ 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) 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. ------ 173259/19719714. ------ 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) 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. ------ 173260/19719795. ------ 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)(^x.x))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 173261/19719822. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((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. ------ 173262/19719912. ------ 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)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173263/19719939. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 173264/19719966. ------ 1. ==[ start ]==> (((a b)(^b.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 173265/19719993. ------ 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)))(((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. ------ 173266/19720056. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.b)(a b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 173267/19720110. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 173268/19720137. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(x x))(b a))) 3. ==[ beta ]==> (((a (a a))((a a) a))((b a)(b a))) REDUCED to normal form. ------ 173269/19720164. ------ 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 (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 11. ==[ beta ]==> a REDUCED to normal form. ------ 173270/19720191. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 173271/19720218. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (((a b) a)((a a)(a a))) REDUCED to normal form. ------ 173272/19720272. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b)(^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. ------ 173273/19720299. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 173274/19720578. ------ 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. ------ 173275/19720605. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) 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. ------ 173276/19720641. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1))) c)) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 173277/19720659. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b))((b a)((^y.y) a))) 4. ==[ alpha ]==> (((a b)(a b))((b a)((^x.x) a))) 5. ==[ beta ]==> (((a b)(a b))((b a) a)) REDUCED to normal form. ------ 173278/19720740. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 173279/19720848. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (b a))) REDUCED to normal form. ------ 173280/19720866. ------ 1. ==[ start ]==> (((a a)(b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173281/19720893. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 173282/19720947. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(a a))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 173283/19720974. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 173284/19721028. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 173285/19721055. ------ 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.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)((^y.(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 173286/19721082. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 173287/19721127. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 173288/19721136. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^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. ------ 173289/19721604. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 173290/19721613. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 173291/19721667. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 173292/19721712. ------ 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)(^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. ------ 173293/19721739. ------ 1. ==[ start ]==> ((a (^b.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 173294/19721865. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(b (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173295/19721892. ------ 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. ------ 173296/19721919. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 173297/19722018. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((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. ------ 173298/19722027. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 173299/19722054. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a b)((^y.a)((a a) a))) 4. ==[ alpha ]==> ((a b)((^x.a)((a a) a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 173300/19722468. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(b (b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(b (b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(b (b a))) REDUCED to normal form. ------ 173301/19722504. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1))) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173302/19722549. ------ 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))(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. ------ 173303/19722558. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 173304/19722657. ------ 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)(^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. ------ 173305/19722729. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 173306/19722783. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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. ------ 173307/19722864. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(a b))(a a)) REDUCED to normal form. ------ 173308/19722891. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(a (a a)))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 173309/19722945. ------ 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. ------ 173310/19722999. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 173311/19723026. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 173312/19723053. ------ 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. ------ 173313/19723332. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 173314/19723368. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z)) b)) 3. ==[ beta ]==> ((b b)((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((b b)((^x.(^y.y)) b)) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 173315/19723395. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a)) c)) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 173316/19723413. ------ 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) a))) 3. ==[ beta ]==> (((a a)(a a))((a b)((^y.y) a))) 4. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x) a))) 5. ==[ beta ]==> (((a a)(a a))((a b) a)) REDUCED to normal form. ------ 173317/19723440. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((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. ------ 173318/19723494. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (a a))((a a) a))) 3. ==[ beta ]==> (((b a)(b a))((a (a a))((a a) a))) REDUCED to normal form. ------ 173319/19723575. ------ 1. ==[ start ]==> (((^a.b)(a b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 173320/19723638. ------ 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.(^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. ------ 173321/19723692. ------ 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)(^x1.(x1 x1)))) REDUCED to normal form. ------ 173322/19723719. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 173323/19723782. ------ 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. ------ 173324/19723809. ------ 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))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 173325/19723836. ------ 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)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((a a)(^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. ------ 173326/19723863. ------ 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))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 173327/19723890. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 173328/19723917. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b)(^b.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. ------ 173329/19723944. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 173330/19723971. ------ 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.(^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. ------ 173331/19724052. ------ 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.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^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. ------ 173332/19724079. ------ 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 (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 173333/19724223. ------ 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 (a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (a a))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173334/19724304. ------ 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)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 173335/19724448. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((b c)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 173336/19724475. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) 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. ------ 173337/19724583. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b) b)) 3. ==[ beta ]==> ((a (^y.y))((a b) b)) 4. ==[ alpha ]==> ((a (^x.x))((a b) b)) REDUCED to normal form. ------ 173338/19724790. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((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. ------ 173339/19724799. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 173340/19724826. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a) c)) 3. ==[ beta ]==> ((b (^y.a))((^z.a) c)) 4. ==[ alpha ]==> ((b (^x.a))((^y.a) c)) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 173341/19724916. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c (^y.a))) REDUCED to normal form. ------ 173342/19724943. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (^y.b))) REDUCED to normal form. ------ 173343/19724970. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a (^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 173344/19724997. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b)(a a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 173345/19725024. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.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) REDUCED to normal form. ------ 173346/19725051. ------ 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. ------ 173347/19725078. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (((a b)(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 173348/19725105. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a 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. ------ 173349/19725132. ------ 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)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 173350/19725186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 173351/19725213. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 173352/19725240. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(^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. ------ 173353/19725294. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 173354/19725384. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 173355/19725465. ------ 1. ==[ start ]==> (((^a.b)(^c.(^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. ------ 173356/19725870. ------ 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. ------ 173357/19725879. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 173358/19725906. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 173359/19725933. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(c c)) REDUCED to normal form. ------ 173360/19725978. ------ 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. ------ 173361/19726041. ------ 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))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 173362/19726095. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 173363/19726131. ------ 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. ------ 173364/19726158. ------ 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. ------ 173365/19726185. ------ 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))(^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. ------ 173366/19726212. ------ 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.(^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. ------ 173367/19726239. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 173368/19726266. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 173369/19726293. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 173370/19726401. ------ 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 (^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.(x1 x1)))) REDUCED to normal form. ------ 173371/19726428. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a (^b.(^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. ------ 173372/19726455. ------ 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 y))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))(a a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(a a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a a)(a a))) REDUCED to normal form. ------ 173373/19726509. ------ 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) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 173374/19726527. ------ 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 (^y.y))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 173375/19726536. ------ 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. ------ 173376/19726932. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.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. ------ 173377/19726950. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((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. ------ 173378/19726959. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^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. ------ 173379/19726977. ------ 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. ------ 173380/19727094. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 173381/19727121. ------ 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)) 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. ------ 173382/19727139. ------ 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. ------ 173383/19727202. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a) a)) REDUCED to normal form. ------ 173384/19727247. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 173385/19738125. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a)) b) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a)) 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. ------ 173386/19738149. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173387/19738167. ------ 1. ==[ start ]==> ((^a.(a a))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(x x))((b a)(^y.b))) 3. ==[ beta ]==> (((b a)(^y.b))((b a)(^y.b))) 4. ==[ alpha ]==> (((b a)(^x.b))((b a)(^y.b))) REDUCED to normal form. ------ 173388/19738194. ------ 1. ==[ start ]==> ((^a.b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 173389/19738230. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 173390/19738275. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^z.(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 173391/19738392. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^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 ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173392/19738464. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.(^x1.x1)) a) b)) 3. ==[ eta ]==> ((^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. ------ 173393/19738854. ------ 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. ------ 173394/19738863. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 173395/19739517. ------ 1. ==[ start ]==> ((^a.((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 173396/19739691. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((a 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. ------ 173397/19740624. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((b a)(^z.(^x1.x1)))((b a)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((b a)(^y.(^z.z)))((b a)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((b a)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((b a)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 173398/19740879. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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))) REDUCED to normal form. ------ 173399/19741239. ------ 1. ==[ start ]==> (((^a.b) c)(^d.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(^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. ------ 173400/19741617. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 173401/19741977. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 173402/19742055. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z))) c)) 3. ==[ eta ]==> (b ((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 173403/19742337. ------ 1. ==[ start ]==> (((^a.a)(b a))(^b.(^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. ------ 173404/19742892. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((((^x1.x1)(^y1.y1))(^z1.(a a)))(^y.(^z.z))) 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. ------ 173405/19743810. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 173406/19744263. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y (^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173407/19745343. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 173408/19745889. ------ 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. ------ 173409/19746306. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a 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 ]==> (^x.(a a)) REDUCED to normal form. ------ 173410/19747467. ------ 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)) REDUCED to normal form. ------ 173411/19747629. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(^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. ------ 173412/19747638. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((z z) z))) REDUCED to normal form. ------ 173413/19747773. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 173414/19747869. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 173415/19747917. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 173416/19748292. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^z.(z z)))(((a a)(^z.(z z)))(^y.y))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.(y y)))(^z.z))) REDUCED to normal form. ------ 173417/19748304. ------ 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. ------ 173418/19748691. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.(^y.y)) a) b)(^x1.x1)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) 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. ------ 173419/19748763. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 173420/19748817. ------ 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)))) REDUCED to normal form. ------ 173421/19748880. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(x1 (^y1.y1)))) REDUCED to normal form. ------ 173422/19748961. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.b)) REDUCED to normal form. ------ 173423/19749006. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a 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. ------ 173424/19749036. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 173425/19749054. ------ 1. ==[ start ]==> ((a (a a))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (a a))((b a)(^x.b))) REDUCED to normal form. ------ 173426/19749081. ------ 1. ==[ start ]==> ((a b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 173427/19749117. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 173428/19749162. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 173429/19749198. ------ 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)((^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. ------ 173430/19749225. ------ 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. ------ 173431/19749252. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 173432/19749279. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 173433/19749297. ------ 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. ------ 173434/19749324. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a (^y.y))) a)) REDUCED to normal form. ------ 173435/19749351. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a ((^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. ------ 173436/19749441. ------ 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. ------ 173437/19749630. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 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. ------ 173438/19749657. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 173439/19749693. ------ 1. ==[ start ]==> ((((^a.a) a) b)(c (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(c (b (^y.y)))) 3. ==[ beta ]==> ((a b)(c (b (^y.y)))) 4. ==[ alpha ]==> ((a b)(c (b (^x.x)))) REDUCED to normal form. ------ 173440/19749720. ------ 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. ------ 173441/19749738. ------ 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. ------ 173442/19749747. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 173443/19749774. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 173444/19749801. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 173445/19749828. ------ 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. ------ 173446/19749936. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 173447/19750071. ------ 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. ------ 173448/19750098. ------ 1. ==[ start ]==> ((((^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 a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (a (((^y.y) 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. ------ 173449/19750125. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 173450/19750152. ------ 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.(^x1.x1)) a))) 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. ------ 173451/19750269. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 173452/19750296. ------ 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. ------ 173453/19750323. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) a))((b a)(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.a))) 5. ==[ beta ]==> ((a a)((b a)(^y.a))) 6. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 173454/19750350. ------ 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))(^z.b))) REDUCED to normal form. ------ 173455/19750377. ------ 1. ==[ start ]==> ((((^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))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 8. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 173456/19750404. ------ 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. ------ 173457/19750440. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^y1.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. ------ 173458/19750494. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> (a ((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> (a ((^x.(x x))((^y.y) b))) 7. ==[ beta ]==> (a (((^y.y) b)((^y.y) b))) 8. ==[ alpha ]==> (a (((^x.x) b)((^y.y) b))) 9. ==[ beta ]==> (a (b ((^y.y) b))) 10. ==[ alpha ]==> (a (b ((^x.x) b))) 11. ==[ beta ]==> (a (b b)) REDUCED to normal form. ------ 173459/19750575. ------ 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)((^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. ------ 173460/19750926. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 173461/19751070. ------ 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. ------ 173462/19751097. ------ 1. ==[ start ]==> (((a b) a)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 173463/19751124. ------ 1. ==[ start ]==> (((a a)(^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b))((b a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))((b a)(^y.y))) REDUCED to normal form. ------ 173464/19751178. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 173465/19751205. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a b)(a a))) REDUCED to normal form. ------ 173466/19751232. ------ 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. ------ 173467/19751259. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 173468/19751286. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 173469/19751403. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 173470/19751430. ------ 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. ------ 173471/19751457. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b (^z.a))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 173472/19751484. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 173473/19751511. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 173474/19751547. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 173475/19751601. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.b)((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 173476/19751682. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 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. ------ 173477/19751736. ------ 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))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 173478/19751763. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 173479/19752123. ------ 1. ==[ start ]==> (((^a.b) c)(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 173480/19752366. ------ 1. ==[ start ]==> (((a b) c)(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) c)(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b) c)(((a a) a)(a a))) REDUCED to normal form. ------ 173481/19752393. ------ 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. ------ 173482/19752420. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (a a))(b a))) REDUCED to normal form. ------ 173483/19752474. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a (^z.z)) b)) REDUCED to normal form. ------ 173484/19752501. ------ 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. ------ 173485/19752600. ------ 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) 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. ------ 173486/19752699. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a b)(^y.b))) REDUCED to normal form. ------ 173487/19752726. ------ 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 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. ------ 173488/19752753. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(^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)))) 7. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 173489/19752807. ------ 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)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 173490/19752834. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 173491/19752861. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a a)(^c.(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. ------ 173492/19752888. ------ 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)) REDUCED to normal form. ------ 173493/19752915. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b b)) REDUCED to normal form. ------ 173494/19752942. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 173495/19753032. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 173496/19753113. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(^a.a))(^c.(^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. ------ 173497/19753176. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 173498/19753221. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((b a)(^y.(a a))) 6. ==[ alpha ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 173499/19753284. ------ 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)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 173500/19753311. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((b a) a)) REDUCED to normal form. ------ 173501/19753365. ------ 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)(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. ------ 173502/19753392. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)((a a) a))) REDUCED to normal form. ------ 173503/19753419. ------ 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. ------ 173504/19753446. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 173505/19753590. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) 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. ------ 173506/19753617. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 173507/19753644. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 173508/19753671. ------ 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))(^y.(y y)))) REDUCED to normal form. ------ 173509/19753698. ------ 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))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) 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) a)(((^y.y)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(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. ------ 173510/19753725. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 173511/19753779. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(a a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 173512/19753788. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173513/19753869. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 173514/19753950. ------ 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)))(^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. ------ 173515/19754058. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 173516/19754112. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 173517/19754175. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(c (b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(c (b a))) REDUCED to normal form. ------ 173518/19754202. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.b)(b (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.b)(b (a (^y.(^z.z))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 173519/19754256. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 173520/19754283. ------ 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)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 173521/19754310. ------ 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. ------ 173522/19754364. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a b)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b)(^x1.x1))) REDUCED to normal form. ------ 173523/19754562. ------ 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)))(^y1.y1))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 173524/19754589. ------ 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. ------ 173525/19754616. ------ 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 a)(^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))) REDUCED to normal form. ------ 173526/19754670. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 173527/19754697. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a 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. ------ 173528/19754706. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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 REDUCED to normal form. ------ 173529/19754733. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(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. ------ 173530/19754868. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 173531/19754976. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.b)(^b.(^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. ------ 173532/19755030. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173533/19755057. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 173534/19755147. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(a a))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.(a a))(a (a (^y.(^z.z))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173535/19755174. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a)(a a))) REDUCED to normal form. ------ 173536/19755201. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 173537/19755228. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 173538/19755255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(a (a a)))) REDUCED to normal form. ------ 173539/19755309. ------ 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)(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) a)) REDUCED to normal form. ------ 173540/19755336. ------ 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))) REDUCED to normal form. ------ 173541/19755453. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((b a)(^y.y))) REDUCED to normal form. ------ 173542/19755480. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^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)))) REDUCED to normal form. ------ 173543/19755507. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(a a))(^b.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. ------ 173544/19755534. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 173545/19755561. ------ 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.(^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. ------ 173546/19755642. ------ 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) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 173547/19755669. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (^a.a))(^c.(^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. ------ 173548/19755867. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a))(^c.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. ------ 173549/19756011. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a)(^y.y))(a a))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 173550/19756038. ------ 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)))) 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. ------ 173551/19756092. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 173552/19756119. ------ 1. ==[ start ]==> ((((^a.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))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 10. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 173553/19756200. ------ 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.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a (^y.y))(a a))) REDUCED to normal form. ------ 173554/19756218. ------ 1. ==[ start ]==> (((^a.b)(a b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(b (^y.(^z.z)))) 3. ==[ beta ]==> (b (b (^y.(^z.z)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 173555/19756227. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 173556/19756326. ------ 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) 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. ------ 173557/19756425. ------ 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. ------ 173558/19756452. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^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)))) REDUCED to normal form. ------ 173559/19756506. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 173560/19756533. ------ 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. ------ 173561/19756560. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b) c)) 3. ==[ beta ]==> ((((a a) a)(a a))((a b) c)) REDUCED to normal form. ------ 173562/19756776. ------ 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 a)) REDUCED to normal form. ------ 173563/19756947. ------ 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 (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 173564/19757163. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^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. ------ 173565/19757190. ------ 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)((^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. ------ 173566/19757244. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 173567/19757325. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 173568/19757361. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))(c ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(c ((a a) a))) REDUCED to normal form. ------ 173569/19757442. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b)(a a))) REDUCED to normal form. ------ 173570/19757469. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.a))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 173571/19757496. ------ 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. ------ 173572/19757640. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b)(^z.z))) REDUCED to normal form. ------ 173573/19757667. ------ 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.(^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. ------ 173574/19757694. ------ 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. ------ 173575/19757721. ------ 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 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. ------ 173576/19757748. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^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. ------ 173577/19757829. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b) a)) REDUCED to normal form. ------ 173578/19757856. ------ 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. ------ 173579/19758108. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (^x1.(x1 x1)))) 3. ==[ beta ]==> (b (d (^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (d (^x.(x x)))) REDUCED to normal form. ------ 173580/19758216. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.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. ------ 173581/19758351. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 173582/19758378. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^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. ------ 173583/19758432. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(^z.a))) 7. ==[ beta ]==> ((b b)((^y.(y y))(^z.a))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(^y.a))) 9. ==[ beta ]==> ((b b)((^y.a)(^y.a))) 10. ==[ alpha ]==> ((b b)((^x.a)(^y.a))) 11. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 173584/19758513. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 173585/19758522. ------ 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. ------ 173586/19758549. ------ 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)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 173587/19758576. ------ 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 (^z.z)))) REDUCED to normal form. ------ 173588/19758630. ------ 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. ------ 173589/19758657. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 173590/19758756. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 173591/19758774. ------ 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)))) 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. ------ 173592/19758801. ------ 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)))) REDUCED to normal form. ------ 173593/19758828. ------ 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)(^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. ------ 173594/19758855. ------ 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. ------ 173595/19758963. ------ 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.(^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)(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. ------ 173596/19758990. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(b b)) REDUCED to normal form. ------ 173597/19759098. ------ 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. ------ 173598/19759152. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(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))) REDUCED to normal form. ------ 173599/19759179. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.(y y)))) REDUCED to normal form. ------ 173600/19759188. ------ 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. ------ 173601/19759575. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 173602/19759602. ------ 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. ------ 173603/19759620. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (^a.(^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. ------ 173604/19759629. ------ 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. ------ 173605/19759647. ------ 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)(a (^y1.a))) 4. ==[ alpha ]==> ((^x.x)(a (^y.a))) 5. ==[ beta ]==> (a (^y.a)) 6. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 173606/19759701. ------ 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. ------ 173607/19759737. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(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. ------ 173608/19759764. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a (^x1.x1)))) REDUCED to normal form. ------ 173609/19759782. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (^y.y))) 3. ==[ beta ]==> (b (b (^y.y))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 173610/19759845. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a b)) REDUCED to normal form. ------ 173611/19759890. ------ 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))(a (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173612/19771092. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(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. ------ 173613/19771524. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 173614/19771620. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a)) d)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173615/19771746. ------ 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.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. ------ 173616/19771956. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^a.(^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. ------ 173617/19773540. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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. ------ 173618/19773549. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 173619/19773936. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 173620/19773960. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((((a 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 a)))(^x.x)) REDUCED to normal form. ------ 173621/19776924. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^b.(^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. ------ 173622/19777203. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(b a))) 3. ==[ beta ]==> ((a (b a))(^y.(b a))) 4. ==[ alpha ]==> ((a (b a))(^x.(b a))) REDUCED to normal form. ------ 173623/19778526. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 173624/19778550. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173625/19779390. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(a b))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(a b))) 5. ==[ beta ]==> ((a b)(^y.(a b))) 6. ==[ alpha ]==> ((a b)(^x.(a b))) REDUCED to normal form. ------ 173626/19780299. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 173627/19780461. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 173628/19780530. ------ 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 (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 173629/19780740. ------ 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.((^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. ------ 173630/19780848. ------ 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. ------ 173631/19781352. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^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. ------ 173632/19781424. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 173633/19781541. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 173634/19781622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a a))) REDUCED to normal form. ------ 173635/19781667. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.a)) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173636/19781715. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 173637/19781733. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((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. ------ 173638/19781760. ------ 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. ------ 173639/19781796. ------ 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)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 173640/19781823. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 173641/19781841. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 173642/19781850. ------ 1. ==[ start ]==> (((a a) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 173643/19781868. ------ 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)(((^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. ------ 173644/19781877. ------ 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 (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 173645/19781904. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 173646/19781931. ------ 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 (^x.x))(^y.y)) a) REDUCED to normal form. ------ 173647/19781985. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 173648/19782030. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 173649/19782057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 173650/19782120. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 173651/19782417. ------ 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)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 173652/19782435. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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 ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 173653/19782516. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) d)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 173654/19782534. ------ 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. ------ 173655/19782561. ------ 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)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) 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 (^x.x)) a)((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 173656/19782588. ------ 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. ------ 173657/19782615. ------ 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. ------ 173658/19782642. ------ 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.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 173659/19782795. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 173660/19782849. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.a))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 173661/19782867. ------ 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)(^y1.y1))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a)(^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. ------ 173662/19783164. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (a a))(^b.b))) 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. ------ 173663/19783200. ------ 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) REDUCED to normal form. ------ 173664/19783227. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 173665/19783272. ------ 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) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 173666/19783335. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 173667/19783362. ------ 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)(^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. ------ 173668/19783389. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.(^x1.x1)))(^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. ------ 173669/19783578. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.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. ------ 173670/19783992. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)((^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. ------ 173671/19784019. ------ 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)))) REDUCED to normal form. ------ 173672/19784046. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 173673/19784145. ------ 1. ==[ start ]==> (((^a.b) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) 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)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 173674/19784190. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((b a)(^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173675/19784217. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((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. ------ 173676/19784271. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(^y1.(a a)))) 5. ==[ beta ]==> ((^y.y)((a b)(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 7. ==[ beta ]==> ((a b)(^y.(a a))) 8. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 173677/19784352. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173678/19784361. ------ 1. ==[ start ]==> (((a b) b)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) b)((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) b)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 173679/19784388. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a) a)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)((^x.a)((^y.y) b))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 173680/19784415. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((a 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. ------ 173681/19784442. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.z))) REDUCED to normal form. ------ 173682/19784487. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a)) b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a)) b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a)) b)) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a)) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a)) b)) 9. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 10. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 11. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 173683/19784496. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 173684/19784523. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.a))) 7. ==[ beta ]==> (((^y.y)(^z.a))((^y.y)(^z.a))) 8. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.a))) 9. ==[ beta ]==> ((^y.a)((^z.z)(^x1.a))) 10. ==[ alpha ]==> ((^x.a)((^y.y)(^z.a))) 11. ==[ beta ]==> a REDUCED to normal form. ------ 173685/19784550. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 173686/19784793. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 173687/19784802. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(b ((a a)(a a)))) REDUCED to normal form. ------ 173688/19784829. ------ 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. ------ 173689/19784856. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 173690/19784892. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 173691/19785144. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(c (^z.z))) REDUCED to normal form. ------ 173692/19785171. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(b (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.b))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.(a a)))) REDUCED to normal form. ------ 173693/19785225. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173694/19785252. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b)(a (^a.a)))) 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. ------ 173695/19785270. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((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. ------ 173696/19785279. ------ 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) a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 173697/19785846. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 173698/19785972. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 173699/19786179. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a a)(b a))(a (b a))) REDUCED to normal form. ------ 173700/19786206. ------ 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.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 173701/19786233. ------ 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. ------ 173702/19786458. ------ 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)(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173703/19786539. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 173704/19786620. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 173705/19786737. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 173706/19786872. ------ 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))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 173707/19786917. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> (b ((^x1.x1) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 173708/19787070. ------ 1. ==[ start ]==> (((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) a))) REDUCED to normal form. ------ 173709/19787097. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(a b))) 5. ==[ beta ]==> (((a (^x.x))(b a))(a b)) REDUCED to normal form. ------ 173710/19787124. ------ 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. ------ 173711/19787151. ------ 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. ------ 173712/19787178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.z))(b a))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))(b a))) 5. ==[ beta ]==> ((a b)((a (^y.y))(b a))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(b a))) REDUCED to normal form. ------ 173713/19787205. ------ 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. ------ 173714/19787331. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^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. ------ 173715/19787376. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((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. ------ 173716/19787403. ------ 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))(^y2.b))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(^x2.x2))(^y2.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. ------ 173717/19787538. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 173718/19787655. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 173719/19787682. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)(^z.a))) 3. ==[ beta ]==> ((b a)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 173720/19787709. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 173721/19787736. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.(a a))(^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 173722/19787817. ------ 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)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 173723/19788042. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a) b)(a ((^x.x)(a a)))) 7. ==[ beta ]==> (((a a) b)(a (a a))) REDUCED to normal form. ------ 173724/19788069. ------ 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 (^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 173725/19788096. ------ 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. ------ 173726/19788402. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((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. ------ 173727/19788726. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a)) c)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a)) c)) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 173728/19788870. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(c (^y.(a a)))) REDUCED to normal form. ------ 173729/19788897. ------ 1. ==[ start ]==> (((a b)(^a.b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 173730/19788951. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(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. ------ 173731/19788996. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((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. ------ 173732/19789005. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 173733/19789032. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 173734/19789059. ------ 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.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. ------ 173735/19789392. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(b (a a))) REDUCED to normal form. ------ 173736/19789419. ------ 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. ------ 173737/19789446. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((a (b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 173738/19789725. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a) a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173739/19789761. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 173740/19789788. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.y))) 9. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 10. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 173741/19789833. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 173742/19789860. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a 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. ------ 173743/19789896. ------ 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))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 173744/19789914. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b) b)) REDUCED to normal form. ------ 173745/19789923. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 173746/19790004. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 173747/19790031. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(^c.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. ------ 173748/19790103. ------ 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. ------ 173749/19790229. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 173750/19790256. ------ 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. ------ 173751/19790283. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(a b))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(a b))) 5. ==[ beta ]==> ((a b)((a a)(a b))) REDUCED to normal form. ------ 173752/19790697. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.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. ------ 173753/19790778. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1)) d)) 3. ==[ beta ]==> (b ((^x1.(x1 x1)) d)) 4. ==[ alpha ]==> (b ((^x.(x x)) d)) 5. ==[ beta ]==> (b (d d)) REDUCED to normal form. ------ 173754/19790886. ------ 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)(^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. ------ 173755/19791003. ------ 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) 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. ------ 173756/19791048. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((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. ------ 173757/19791102. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a)) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a)) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a)) c)) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a)) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a)) c)) 7. ==[ beta ]==> ((b b)((a (a a)) c)) REDUCED to normal form. ------ 173758/19791111. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 173759/19791138. ------ 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)(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173760/19791192. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 173761/19791300. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.(y1 y1)))) REDUCED to normal form. ------ 173762/19791327. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 173763/19791354. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.a))) REDUCED to normal form. ------ 173764/19791408. ------ 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 (^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. ------ 173765/19791426. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.a))) REDUCED to normal form. ------ 173766/19791579. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c ((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(c a)) REDUCED to normal form. ------ 173767/19791606. ------ 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. ------ 173768/19791633. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a ((^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. ------ 173769/19791660. ------ 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. ------ 173770/19791714. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1)) a)) REDUCED to normal form. ------ 173771/19791741. ------ 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. ------ 173772/19791840. ------ 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) 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. ------ 173773/19791858. ------ 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 ]==> ((^y.(y (^z.z)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^z.(z z)))(^y.y)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 173774/19792245. ------ 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))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 173775/19792263. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^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. ------ 173776/19792290. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^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. ------ 173777/19792299. ------ 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. ------ 173778/19792371. ------ 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)))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 173779/19792407. ------ 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 ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173780/19792434. ------ 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.(^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. ------ 173781/19792452. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^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. ------ 173782/19792515. ------ 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. ------ 173783/19792560. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a 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. ------ 173784/19792586. ------ 1. ==[ start ]==> (^a.((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^x.((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173785/19792587. ------ 1. ==[ start ]==> (a ((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (a ((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (a ((^y.y)(^z.z))) 4. ==[ alpha ]==> (a ((^x.x)(^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 173786/19803489. ------ 1. ==[ start ]==> ((^a.a)((^b.b)((^a.a)(^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. ------ 173787/19803516. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^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))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 173788/19803624. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((^z.b)(b a))(^y.y)) 4. ==[ alpha ]==> (((^x.b)(b a))(^y.y)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 173789/19803780. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^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. ------ 173790/19803789. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 173791/19803813. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a (^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173792/19804230. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^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. ------ 173793/19804308. ------ 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) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 173794/19804866. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.(a a))((^z.z)(a a)))((^y.(a a))((^z.z)(a a))))((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((^x.(a a))((^y.y)(a a)))((^z.(a a))((^x1.x1)(a a))))((^y1.(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a a)((^z.(a a))((^x1.x1)(a a))))((^y1.(a a))((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))((^y.y)(a a))))((^z.(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^z.(a a))((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))((^y.y)(a a)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 173795/19805379. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((^y.(y y))(^z.z)) b) 4. ==[ alpha ]==> (((^x.(x x))(^y.y)) b) 5. ==[ beta ]==> (((^y.y)(^y.y)) 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. ------ 173796/19805472. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(x x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.x1))) IRREDUCIBLE: cycle. ------ 173797/19805766. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.(((a (a a))(a (^z.(^x1.x1))))((a (a a))(a (^z.(^x1.x1)))))) 4. ==[ alpha ]==> (^x.(((a (a a))(a (^y.(^z.z))))((a (a a))(a (^x1.(^y1.y1)))))) REDUCED to normal form. ------ 173798/19805973. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.(^y1.y1)))(a (a a)))((^z.(^x1.(^y1.y1)))(a (a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1)))(a (a a)))((^y1.(^z1.(^x2.x2)))(a (a a))))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(a (a a)))((^y1.(^z1.(^x2.x2)))(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. ------ 173799/19806237. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 173800/19807353. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 173801/19807404. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(^z.(^x1.x1)))) 3. ==[ eta ]==> (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. ------ 173802/19807713. ------ 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 x1)(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.((x1 x1)(x1 x1)))) 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. ------ 173803/19807953. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 173804/19808055. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 173805/19808712. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^a.((^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. ------ 173806/19808844. ------ 1. ==[ start ]==> ((^a.(^b.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173807/19809027. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.(^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. ------ 173808/19809159. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 173809/19809918. ------ 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.(^y1.y1))))) REDUCED to normal form. ------ 173810/19810158. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x 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))))(((^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))))(((^x2.(^y2.y2))((a a)(^z2.z2)))((^x3.(^y3.y3))((a a)(^z3.z3))))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1))))(((^x2.(^y2.y2))((a a)(^z2.z2)))((^x3.(^y3.y3))((a a)(^z3.z3))))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a)(^x1.x1))))(((^y1.(^z1.z1))((a a)(^x2.x2)))((^y2.(^z2.z2))((a a)(^x3.x3))))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))(((^y1.(^z1.z1))((a a)(^x2.x2)))((^y2.(^z2.z2))((a a)(^x3.x3))))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.(^y1.y1))((a a)(^z1.z1)))((^x2.(^y2.y2))((a a)(^z2.z2))))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))((a a)(^z1.z1)))((^x2.(^y2.y2))((a a)(^z2.z2))))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2))))) 11. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 12. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 15. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 16. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173811/19810971. ------ 1. ==[ start ]==> (((a (a a))(b a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 173812/19811214. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 173813/19811898. ------ 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)(x1 x1)))) 3. ==[ beta ]==> ((^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. ------ 173814/19812105. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 173815/19812294. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(a z))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 173816/19812399. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173817/19812492. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(z b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(z 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. ------ 173818/19813293. ------ 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)(^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. ------ 173819/19813428. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 173820/19813563. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(^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. ------ 173821/19813641. ------ 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) a))) 3. ==[ beta ]==> (((^z.(^x1.x1))((^y1.y1) a))(((^z.(^x1.x1))((^y1.y1) a))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.(^y1.y1))((^z1.z1) a))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))((^z1.z1) a))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1) a))(^y1.y1))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) a))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^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. ------ 173822/19814040. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) 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. ------ 173823/19814058. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^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 ]==> (((^z.z)(^y.y))(^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. ------ 173824/19814247. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(y (^z.z)))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 173825/19814310. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 173826/19814355. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(x1 x1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173827/19814394. ------ 1. ==[ start ]==> ((a a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 173828/19814421. ------ 1. ==[ start ]==> ((a (a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 173829/19814439. ------ 1. ==[ start ]==> (((a a) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((a a) a)((b a)(^x.b))) REDUCED to normal form. ------ 173830/19814466. ------ 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. ------ 173831/19814493. ------ 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. ------ 173832/19814502. ------ 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. ------ 173833/19814529. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(b a))) 3. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 173834/19814547. ------ 1. ==[ start ]==> (((a a) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173835/19814574. ------ 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 (^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. ------ 173836/19814664. ------ 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. ------ 173837/19814682. ------ 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. ------ 173838/19814691. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(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. ------ 173839/19814718. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a (^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)((^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. ------ 173840/19814763. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x)) b)((b (^y.y)) c)) REDUCED to normal form. ------ 173841/19814934. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 173842/19815105. ------ 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. ------ 173843/19815132. ------ 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 (^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. ------ 173844/19815141. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z (^x1.x1))) 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. ------ 173845/19815186. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 173846/19815213. ------ 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) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 173847/19815348. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173848/19815375. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^x1.x1)))) 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. ------ 173849/19815429. ------ 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)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 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. ------ 173850/19815483. ------ 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. ------ 173851/19815510. ------ 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. ------ 173852/19815573. ------ 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. ------ 173853/19815600. ------ 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))) REDUCED to normal form. ------ 173854/19815663. ------ 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. ------ 173855/19815690. ------ 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.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 173856/19815771. ------ 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. ------ 173857/19815897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 7. ==[ beta ]==> (b (a (^y.(a a)))) 8. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 173858/19815978. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 173859/19816005. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b (^z.z)) b)) 3. ==[ beta ]==> ((a (^y.(y y)))((b (^z.z)) b)) 4. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y)) b)) REDUCED to normal form. ------ 173860/19816032. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a)(a a)) c)) REDUCED to normal form. ------ 173861/19816176. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 173862/19816203. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 173863/19816257. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 173864/19816284. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^y.y))) 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. ------ 173865/19816374. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a ((^z.(^x1.x1)) a))) IRREDUCIBLE: cycle. ------ 173866/19816437. ------ 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. ------ 173867/19816455. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 173868/19816482. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 173869/19816509. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 173870/19816563. ------ 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))(a b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(a a))(a b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(a b))) REDUCED to normal form. ------ 173871/19816644. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^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. ------ 173872/19816671. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 173873/19816842. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)(((^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. ------ 173874/19816851. ------ 1. ==[ start ]==> (((a b)(a a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.y) 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. ------ 173875/19816878. ------ 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 (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. ------ 173876/19817058. ------ 1. ==[ start ]==> (((a b) b)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173877/19817085. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) 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. ------ 173878/19817112. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 173879/19817193. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a)) b)) REDUCED to normal form. ------ 173880/19817220. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b) c)) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) b) c)) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) b) c)) 7. ==[ beta ]==> ((((^y.y) b) c)(((^y.y) b) c)) 8. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) b) c)) 9. ==[ beta ]==> ((b c)(((^y.y) b) c)) 10. ==[ alpha ]==> ((b c)(((^x.x) b) c)) 11. ==[ beta ]==> ((b c)(b c)) REDUCED to normal form. ------ 173881/19817337. ------ 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)(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. ------ 173882/19817364. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) b) REDUCED to normal form. ------ 173883/19817445. ------ 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))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 10. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 173884/19817472. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 173885/19817499. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 173886/19817589. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 173887/19817724. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 173888/19817805. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^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. ------ 173889/19817832. ------ 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 (^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. ------ 173890/19817886. ------ 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. ------ 173891/19817922. ------ 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))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173892/19817949. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 173893/19817976. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 173894/19818003. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.(z z)))) REDUCED to normal form. ------ 173895/19818030. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 173896/19818066. ------ 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 a)) REDUCED to normal form. ------ 173897/19818093. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.b)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(a b))) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 173898/19818120. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 173899/19818147. ------ 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. ------ 173900/19818174. ------ 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)))((^y1.(y1 y1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(b a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(b a))) 7. ==[ beta ]==> ((^y.y)((^z.(z z))(b a))) 8. ==[ alpha ]==> ((^x.x)((^y.(y y))(b a))) 9. ==[ beta ]==> ((^y.(y y))(b a)) 10. ==[ alpha ]==> ((^x.(x x))(b a)) 11. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 173901/19818201. ------ 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) REDUCED to normal form. ------ 173902/19818228. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 173903/19818255. ------ 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 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. ------ 173904/19818309. ------ 1. ==[ start ]==> ((a (b a))((^b.b)(^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. ------ 173905/19818588. ------ 1. ==[ start ]==> (((^a.a)(b a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(b a))(b ((^y.y) b))) 3. ==[ beta ]==> ((b a)(b ((^y.y) b))) 4. ==[ alpha ]==> ((b a)(b ((^x.x) b))) 5. ==[ beta ]==> ((b a)(b b)) REDUCED to normal form. ------ 173906/19818615. ------ 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. ------ 173907/19818651. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z) b)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 173908/19818669. ------ 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)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 173909/19818678. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 173910/19818750. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^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)))) 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. ------ 173911/19818858. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))((a a)(^x1.x1)))) REDUCED to normal form. ------ 173912/19818930. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b (^z.z))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b (^z.z))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 173913/19818957. ------ 1. ==[ start ]==> (((a (a a))(a b))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 173914/19818984. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.b)(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. ------ 173915/19819011. ------ 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 (^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. ------ 173916/19819092. ------ 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.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 173917/19819137. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 173918/19819614. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(a ((^x1.x1) b))) 3. ==[ beta ]==> (b (a ((^x1.x1) b))) 4. ==[ alpha ]==> (b (a ((^x.x) b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 173919/19819623. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 173920/19819650. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 173921/19819722. ------ 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)(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. ------ 173922/19819749. ------ 1. ==[ start ]==> ((a (^b.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))((a b)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 173923/19819875. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c (^z.a))) 3. ==[ beta ]==> (((^y.y)(a b))(c (^z.a))) 4. ==[ alpha ]==> (((^x.x)(a b))(c (^y.a))) 5. ==[ beta ]==> ((a b)(c (^y.a))) 6. ==[ alpha ]==> ((a b)(c (^x.a))) REDUCED to normal form. ------ 173924/19819902. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 173925/19819929. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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. ------ 173926/19819956. ------ 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.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 173927/19820028. ------ 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))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173928/19820037. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 173929/19820064. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 173930/19820541. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.(^x1.x1))) 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. ------ 173931/19820559. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a)(a a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 173932/19820568. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a) b)) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 173933/19820595. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 173934/19820667. ------ 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)(^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. ------ 173935/19820820. ------ 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.(^x1.x1))))) REDUCED to normal form. ------ 173936/19820874. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))(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. ------ 173937/19820901. ------ 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) a))) 3. ==[ beta ]==> (((a b)((a a) a))(a a)) REDUCED to normal form. ------ 173938/19820928. ------ 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)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 173939/19821009. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(a b))) REDUCED to normal form. ------ 173940/19821036. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 173941/19821063. ------ 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. ------ 173942/19821342. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 173943/19821423. ------ 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)))) 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. ------ 173944/19821450. ------ 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) a))) 3. ==[ beta ]==> ((^y.y)((a b)((^x1.x1) 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. ------ 173945/19821504. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((b a)(b a))(^y.y)) 10. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 173946/19821585. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 173947/19821648. ------ 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))(^y1.y1))) REDUCED to normal form. ------ 173948/19821702. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)(^x1.a))) REDUCED to normal form. ------ 173949/19821729. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 173950/19821756. ------ 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)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^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. ------ 173951/19821792. ------ 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. ------ 173952/19821819. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(a b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(a b))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 173953/19821846. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 173954/19821873. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.x)((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. ------ 173955/19821927. ------ 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.(^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. ------ 173956/19821954. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.a))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 173957/19822008. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 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. ------ 173958/19822062. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 173959/19822089. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 173960/19822233. ------ 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)(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173961/19822314. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 173962/19822458. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b c)((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> ((b c)((^x.x)(^y.(y y)))) 7. ==[ beta ]==> ((b c)(^y.(y y))) 8. ==[ alpha ]==> ((b c)(^x.(x x))) REDUCED to normal form. ------ 173963/19822485. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 173964/19822593. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^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. ------ 173965/19822620. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b) b)) REDUCED to normal form. ------ 173966/19822800. ------ 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. ------ 173967/19822809. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 173968/19822836. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b) b)) 3. ==[ beta ]==> ((b (^y.a))((^z.b) b)) 4. ==[ alpha ]==> ((b (^x.a))((^y.b) b)) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 173969/19822980. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (^z.b))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (^z.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.b))) 5. ==[ beta ]==> ((a b)(b (^y.b))) 6. ==[ alpha ]==> ((a b)(b (^x.b))) REDUCED to normal form. ------ 173970/19823007. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.(a a)))) REDUCED to normal form. ------ 173971/19823034. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b)(a a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b)(a a))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 173972/19823088. ------ 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) 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))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 173973/19823115. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (((a a)(a b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 173974/19823142. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 173975/19823196. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a b)) REDUCED to normal form. ------ 173976/19823223. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b)(^z.z))) 5. ==[ beta ]==> ((b a)((^y.b)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.y))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 173977/19823304. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 173978/19823394. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(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. ------ 173979/19823475. ------ 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) a))) 3. ==[ beta ]==> (b ((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x) a))) 5. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 173980/19823700. ------ 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)))) REDUCED to normal form. ------ 173981/19823808. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a)) c)) REDUCED to normal form. ------ 173982/19823880. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 173983/19823916. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a) a)) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 173984/19823943. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 173985/19823988. ------ 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) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 173986/19824105. ------ 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. ------ 173987/19824141. ------ 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) 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. ------ 173988/19824168. ------ 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. ------ 173989/19824195. ------ 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. ------ 173990/19824222. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^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)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 173991/19824249. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 173992/19824276. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 173993/19824303. ------ 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))(^x1.(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. ------ 173994/19824330. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^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. ------ 173995/19824438. ------ 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. ------ 173996/19824465. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) 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. ------ 173997/19824519. ------ 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)(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)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 173998/19824537. ------ 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 (^y.y))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 173999/19824546. ------ 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) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 174000/19824942. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a) c)) 3. ==[ beta ]==> (((^y.y) b)((a a) c)) 4. ==[ alpha ]==> (((^x.x) b)((a a) c)) 5. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 174001/19824960. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(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. ------ 174002/19824969. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 174003/19824987. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(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))) REDUCED to normal form. ------ 174004/19824996. ------ 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. ------ 174005/19825014. ------ 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. ------ 174006/19825068. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b b)) REDUCED to normal form. ------ 174007/19825104. ------ 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) REDUCED to normal form. ------ 174008/19825131. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 174009/19825149. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (a (^y.y)))) 3. ==[ beta ]==> (b (a (a (^y.y)))) 4. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 174010/19825212. ------ 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. ------ 174011/19825257. ------ 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))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174012/19825292. ------ 1. ==[ start ]==> (^a.(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^x.(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (^x.(b (^y.(^z.z)))) REDUCED to normal form. ------ 174013/19825293. ------ 1. ==[ start ]==> (a (((^a.a) b)(^b.(^a.a)))) 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. ------ 174014/19836198. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a))) a) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z))) a) 3. ==[ beta ]==> ((b (^y.(^z.z))) a) 4. ==[ alpha ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 174015/19836204. ------ 1. ==[ start ]==> ((^a.a)(((^a.a) b)(^b.(^a.a)))) 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. ------ 174016/19836213. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174017/19836258. ------ 1. ==[ start ]==> ((^a.b)((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.b)((b a)(^y.b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 174018/19836456. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (^x.((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 174019/19836528. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (a (^z.z))) a)) 3. ==[ eta ]==> ((^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. ------ 174020/19836945. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.(^a.(a (^a.a))))) 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)))) REDUCED to normal form. ------ 174021/19836954. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 174022/19837359. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.a))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.a))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 174023/19837377. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^a.(^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. ------ 174024/19837581. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((((^y.y)(a a))(^z.(a a)))(((^y.y)(a a))(^z.(a a))))(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(a a))))(((^y1.y1)(a a))(^z1.(a a)))) 5. ==[ beta ]==> ((((a a)(^y.(a a)))(((^z.z)(a a))(^x1.(a a))))(((^y1.y1)(a a))(^z1.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.(a a)))(((^y.y)(a a))(^z.(a a))))(((^x1.x1)(a a))(^y1.(a a)))) 7. ==[ beta ]==> ((((a a)(^x.(a a)))((a a)(^z.(a a))))(((^x1.x1)(a a))(^y1.(a a)))) 8. ==[ alpha ]==> ((((a a)(^x.(a a)))((a a)(^y.(a a))))(((^z.z)(a a))(^x1.(a a)))) 9. ==[ beta ]==> ((((a a)(^x.(a a)))((a a)(^y.(a a))))((a a)(^x1.(a a)))) 10. ==[ alpha ]==> ((((a a)(^x.(a a)))((a a)(^y.(a a))))((a a)(^z.(a a)))) REDUCED to normal form. ------ 174025/19837782. ------ 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.(^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. ------ 174026/19837914. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 174027/19838688. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.(^x1.x1)))(^y1.(y1 y1)))((a (^z.(^x1.x1)))(^y1.(y1 y1))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2))))) 5. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) REDUCED to normal form. ------ 174028/19840119. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b) b)) 3. ==[ eta ]==> (b (((^y.y) b) b)) 4. ==[ alpha ]==> (b (((^x.x) b) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 174029/19840428. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 174030/19840956. ------ 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 ]==> ((((a a) a)(^x1.b))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 174031/19841427. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^b.(^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. ------ 174032/19841436. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^a.((^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. ------ 174033/19841874. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 174034/19842048. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^b.(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. ------ 174035/19842354. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 174036/19842912. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^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. ------ 174037/19843191. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(b y))) 3. ==[ eta ]==> ((((^x.x) b) b) b) 4. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 174038/19843686. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 174039/19843953. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174040/19844613. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a 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. ------ 174041/19844622. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(x1 x1))) REDUCED to normal form. ------ 174042/19845207. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.z))) 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. ------ 174043/19845396. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.(^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. ------ 174044/19845558. ------ 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)) REDUCED to normal form. ------ 174045/19845702. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 174046/19845729. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((z z) z))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((z z) z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((y y) y))) REDUCED to normal form. ------ 174047/19845864. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 174048/19845933. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 174049/19846356. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^z.z))(^x1.a))(((a (^z.z))(^x1.a))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a (^z.z))(^x1.a))(^y1.y1))) REDUCED to normal form. ------ 174050/19846773. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(^b.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. ------ 174051/19846782. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 174052/19846917. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.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. ------ 174053/19846962. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(^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. ------ 174054/19847070. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a 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. ------ 174055/19847106. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.a)) 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. ------ 174056/19847118. ------ 1. ==[ start ]==> ((a a)(((^a.a) b)(^b.(^a.a)))) 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. ------ 174057/19847127. ------ 1. ==[ start ]==> ((a (^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 174058/19847154. ------ 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 ]==> ((^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. ------ 174059/19847172. ------ 1. ==[ start ]==> ((a b)((b a)(^a.b))) 2. ==[ alpha ]==> ((a b)((b a)(^x.b))) REDUCED to normal form. ------ 174060/19847262. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 174061/19847316. ------ 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. ------ 174062/19847343. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 174063/19847370. ------ 1. ==[ start ]==> ((a (^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 174064/19847415. ------ 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. ------ 174065/19847442. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((^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. ------ 174066/19847451. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a (^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. ------ 174067/19847559. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 174068/19847748. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(^a.a))(^b.b))) 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)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174069/19847838. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 174070/19847856. ------ 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 ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 174071/19847865. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (a (a (^z.z))))) REDUCED to normal form. ------ 174072/19847892. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 174073/19847919. ------ 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. ------ 174074/19848027. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b a)((a a) a))) 3. ==[ beta ]==> ((b b)((b a)((a a) a))) REDUCED to normal form. ------ 174075/19848162. ------ 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. ------ 174076/19848189. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.x) a)((a (a 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. ------ 174077/19848216. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 174078/19848243. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 174079/19848270. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.a))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.a))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 174080/19848288. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 174081/19848360. ------ 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)(^y.y))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 174082/19848387. ------ 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. ------ 174083/19848414. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.(^a.a)))(^b.(^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)))) REDUCED to normal form. ------ 174084/19848441. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b a)(^y.a))) REDUCED to normal form. ------ 174085/19848468. ------ 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))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((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))) REDUCED to normal form. ------ 174086/19848495. ------ 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. ------ 174087/19848531. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 174088/19848585. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 174089/19848666. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a 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. ------ 174090/19848693. ------ 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.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.(^x2.x2)) 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. ------ 174091/19848828. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 174092/19849017. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 174093/19849161. ------ 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. ------ 174094/19849188. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> (((a b) a)(b ((^y.y) a))) 4. ==[ alpha ]==> (((a b) a)(b ((^x.x) a))) 5. ==[ beta ]==> (((a b) a)(b a)) REDUCED to normal form. ------ 174095/19849215. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 174096/19849269. ------ 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)(^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. ------ 174097/19849296. ------ 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))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)(a b))) REDUCED to normal form. ------ 174098/19849323. ------ 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.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.a)((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.a)((a b)((^y.y)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 174099/19849350. ------ 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. ------ 174100/19849377. ------ 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)(^x.x))((^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. ------ 174101/19849521. ------ 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))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.z))) 7. ==[ beta ]==> (a ((b (^y.y))(^z.z))) 8. ==[ alpha ]==> (a ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 174102/19849548. ------ 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. ------ 174103/19849575. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) b)(^y.a))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.a))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.a))) REDUCED to normal form. ------ 174104/19849602. ------ 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)))(^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. ------ 174105/19849611. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174106/19849692. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a b))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 7. ==[ beta ]==> ((^y.(a a))(a b)) 8. ==[ alpha ]==> ((^x.(a a))(a b)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174107/19849773. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174108/19849827. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.a)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.a)((^y.y) b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 174109/19849854. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 174110/19849989. ------ 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)))(^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. ------ 174111/19850214. ------ 1. ==[ start ]==> (((^a.b) c)(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)(c ((^y.y) b))) 3. ==[ beta ]==> (b (c ((^y.y) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 174112/19850457. ------ 1. ==[ start ]==> (((a b) c)((a b)(a b))) REDUCED to normal form. ------ 174113/19850484. ------ 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. ------ 174114/19850511. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((a 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. ------ 174115/19850565. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 174116/19850592. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.b))((a (^y.y)) b)) REDUCED to normal form. ------ 174117/19850610. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(b (^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(b (^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.(a a)))) REDUCED to normal form. ------ 174118/19850691. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b)(a (^a.a)))) 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. ------ 174119/19850817. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a b)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a b)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a b)(^y.b))) REDUCED to normal form. ------ 174120/19850844. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a 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. ------ 174121/19850925. ------ 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.(^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. ------ 174122/19850952. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 174123/19851006. ------ 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. ------ 174124/19851033. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b) b)) 3. ==[ beta ]==> ((a (b a))(b b)) REDUCED to normal form. ------ 174125/19851123. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174126/19851204. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 174127/19851312. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 174128/19851375. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(a a))) 5. ==[ beta ]==> ((a (^x.(a a)))(b (a a))) REDUCED to normal form. ------ 174129/19851402. ------ 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)))(a (^x1.x1)))) REDUCED to normal form. ------ 174130/19851456. ------ 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. ------ 174131/19851483. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)((^y.y)(^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. ------ 174132/19851510. ------ 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. ------ 174133/19851537. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^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. ------ 174134/19851708. ------ 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. ------ 174135/19851735. ------ 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.(^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. ------ 174136/19851762. ------ 1. ==[ start ]==> (((a b)(a (a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 174137/19851789. ------ 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. ------ 174138/19851816. ------ 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)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 174139/19851870. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(^z.b))) REDUCED to normal form. ------ 174140/19851960. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(b a))) 5. ==[ beta ]==> ((a a)((^z.a)(b a))) 6. ==[ alpha ]==> ((a a)((^x.a)(b a))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 174141/19852041. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 174142/19852149. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 174143/19852176. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 174144/19852203. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 174145/19852293. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(c (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(c (b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(c (b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(c (b a))) 5. ==[ beta ]==> ((^y.b)(c (b a))) 6. ==[ alpha ]==> ((^x.b)(c (b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 174146/19852338. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.a)(^b.b))) 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. ------ 174147/19852347. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 174148/19852374. ------ 1. ==[ start ]==> ((((^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 a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 174149/19852401. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a)(a (^z.z)))) REDUCED to normal form. ------ 174150/19852455. ------ 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)))(^z.z))((a a)(a (a a)))) REDUCED to normal form. ------ 174151/19852680. ------ 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)))(^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. ------ 174152/19852707. ------ 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. ------ 174153/19852761. ------ 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))(^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. ------ 174154/19852788. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 174155/19852797. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.b)((^a.a)(^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. ------ 174156/19852959. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.a)(a (^a.(^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. ------ 174157/19853067. ------ 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))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174158/19853121. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 174159/19853148. ------ 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))(^x2.b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.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. ------ 174160/19853202. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.a)(^c.(^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)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 174161/19853238. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(b (b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(b (b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (b a))) 5. ==[ beta ]==> ((^y.(a a))(b (b a))) 6. ==[ alpha ]==> ((^x.(a a))(b (b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174162/19853265. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 174163/19853292. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(a a))) REDUCED to normal form. ------ 174164/19853319. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 174165/19853346. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a) a)) REDUCED to normal form. ------ 174166/19853400. ------ 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)(^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. ------ 174167/19853427. ------ 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. ------ 174168/19853571. ------ 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)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)(^z.z))) 5. ==[ beta ]==> (((^y.y)(a a))((b a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((b a)(^y.y))) 7. ==[ beta ]==> ((a a)((b a)(^y.y))) 8. ==[ alpha ]==> ((a a)((b a)(^x.x))) REDUCED to normal form. ------ 174169/19853598. ------ 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))(^y.(^z.z)))) REDUCED to normal form. ------ 174170/19853625. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(a a))(^b.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. ------ 174171/19853652. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 174172/19853679. ------ 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. ------ 174173/19853733. ------ 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))(^x1.b))) REDUCED to normal form. ------ 174174/19853760. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) 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. ------ 174175/19853823. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^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. ------ 174176/19853958. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a)(^b.(^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. ------ 174177/19854066. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(^a.a))(^c.(^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. ------ 174178/19854102. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(a (b a))) 3. ==[ beta ]==> ((b b)(a (b a))) REDUCED to normal form. ------ 174179/19854129. ------ 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))) REDUCED to normal form. ------ 174180/19854183. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a b) a)) REDUCED to normal form. ------ 174181/19854210. ------ 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) a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 174182/19854291. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a (a b))) REDUCED to normal form. ------ 174183/19854309. ------ 1. ==[ start ]==> (((^a.b)(a b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 174184/19854318. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))((a (^y.y))(a a))) REDUCED to normal form. ------ 174185/19854417. ------ 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))(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. ------ 174186/19854543. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)(^z.b))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (^z.b))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.b))) REDUCED to normal form. ------ 174187/19854570. ------ 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 (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 174188/19854597. ------ 1. ==[ start ]==> (((a (a a))(b a))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 174189/19854624. ------ 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)(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z)) a)) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 174190/19854651. ------ 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. ------ 174191/19854678. ------ 1. ==[ start ]==> (((a b)(a b))((a b) c)) REDUCED to normal form. ------ 174192/19854867. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 174193/19855038. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c (^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c (^z.b))) 3. ==[ beta ]==> (b (c (^z.b))) 4. ==[ alpha ]==> (b (c (^x.b))) REDUCED to normal form. ------ 174194/19855146. ------ 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)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174195/19855254. ------ 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) REDUCED to normal form. ------ 174196/19855281. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a 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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174197/19855335. ------ 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))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 174198/19855416. ------ 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))(^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. ------ 174199/19855524. ------ 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.(a a)))) 3. ==[ beta ]==> ((^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. ------ 174200/19855533. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (a a))) REDUCED to normal form. ------ 174201/19855560. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b)(a a))) 3. ==[ beta ]==> ((b (^y.a))((a b)(a a))) 4. ==[ alpha ]==> ((b (^x.a))((a b)(a a))) REDUCED to normal form. ------ 174202/19855587. ------ 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. ------ 174203/19855758. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b)(^z.z))) 3. ==[ beta ]==> (((^y.y)(b a))((a b)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 174204/19855785. ------ 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. ------ 174205/19855812. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.a))) 7. ==[ beta ]==> (((a b)(a a))(^y.a)) 8. ==[ alpha ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 174206/19855839. ------ 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 y)))) 3. ==[ beta ]==> (((a a)(a b))((a (a a))(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a b))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 174207/19855866. ------ 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) 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. ------ 174208/19855920. ------ 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. ------ 174209/19855947. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b) a)) 3. ==[ beta ]==> ((b ((^y.y) a))((a b) a)) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b) a)) 5. ==[ beta ]==> ((b a)((a b) a)) REDUCED to normal form. ------ 174210/19855974. ------ 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. ------ 174211/19856118. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.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. ------ 174212/19856307. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 174213/19856442. ------ 1. ==[ start ]==> (((^a.a)((^a.(^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)((^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. ------ 174214/19856469. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.x1)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((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. ------ 174215/19856523. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 174216/19856604. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^a.a))(^b.(^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. ------ 174217/19856613. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((^z.z)(^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. ------ 174218/19856640. ------ 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. ------ 174219/19856667. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 174220/19856721. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 174221/19856748. ------ 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. ------ 174222/19856775. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 174223/19856847. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 174224/19856865. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^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. ------ 174225/19856892. ------ 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))(^x1.(x1 x1)))) REDUCED to normal form. ------ 174226/19856919. ------ 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. ------ 174227/19856946. ------ 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)) b)(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^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. ------ 174228/19856973. ------ 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. ------ 174229/19857000. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a) c)) 3. ==[ beta ]==> ((((a a) a)(b a))(a c)) REDUCED to normal form. ------ 174230/19857081. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z)) 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. ------ 174231/19857135. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a) c)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 174232/19857243. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 174233/19857270. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 174234/19857279. ------ 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 ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((^z.(^x1.x1))((^y1.y1) a))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^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. ------ 174235/19857666. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (a (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(b (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(b (a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 174236/19857684. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^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. ------ 174237/19857693. ------ 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. ------ 174238/19857720. ------ 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. ------ 174239/19857738. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (^a.(^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. ------ 174240/19857792. ------ 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))(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. ------ 174241/19857828. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(a c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a c)) 5. ==[ beta ]==> ((^y.y)(a c)) 6. ==[ alpha ]==> ((^x.x)(a c)) 7. ==[ beta ]==> (a c) REDUCED to normal form. ------ 174242/19857855. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 174243/19857873. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(^a.(^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. ------ 174244/19857936. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b a)) REDUCED to normal form. ------ 174245/19857981. ------ 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. ------ 174246/19858017. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 174247/19861188. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^z.(b (^x1.x1)))(^z.(b (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> (((^x.(b (^y.y)))(^z.(b (^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((b (^y.y))(^y1.y1)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 174248/19865778. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174249/19868931. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a))) b) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z))) b) 3. ==[ beta ]==> ((b (^y.(^z.z))) b) 4. ==[ alpha ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 174250/19868955. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174251/19869036. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 174252/19869696. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 174253/19869891. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(^x1.x1))(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. ------ 174254/19870128. ------ 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. ------ 174255/19870533. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^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)))(^x1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 174256/19872105. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(a (b (^z.z)))) 3. ==[ beta ]==> (((a (b (^z.z)))(a (b (^z.z))))(^y.y)) 4. ==[ alpha ]==> (((a (b (^x.x)))(a (b (^y.y))))(^z.z)) REDUCED to normal form. ------ 174257/19872108. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 174258/19873512. ------ 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))(^x.b)) REDUCED to normal form. ------ 174259/19874178. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 174260/19874484. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^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))))) REDUCED to normal form. ------ 174261/19874790. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.(^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. ------ 174262/19875096. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 174263/19875654. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^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. ------ 174264/19876695. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174265/19876698. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 174266/19877148. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.((^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. ------ 174267/19877364. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 174268/19878300. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^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. ------ 174269/19878471. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(^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. ------ 174270/19878675. ------ 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. ------ 174271/19878912. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.((^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. ------ 174272/19879524. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.a))) REDUCED to normal form. ------ 174273/19879659. ------ 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))) REDUCED to normal form. ------ 174274/19879704. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.b)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.b)) 3. ==[ beta ]==> (b (^y.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 174275/19879767. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 174276/19879848. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^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))) REDUCED to normal form. ------ 174277/19879878. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 174278/19879887. ------ 1. ==[ start ]==> (((^a.a) a)((^b.b)((^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)))) 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. ------ 174279/19879914. ------ 1. ==[ start ]==> (((a a) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 174280/19879932. ------ 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. ------ 174281/19879959. ------ 1. ==[ start ]==> ((a (^a.(^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. ------ 174282/19879968. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(^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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174283/19879995. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 174284/19880022. ------ 1. ==[ start ]==> (((a a) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((a a) b)((^x.b)(b a))) 3. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 174285/19880040. ------ 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)(((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. ------ 174286/19880067. ------ 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. ------ 174287/19880076. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 174288/19880103. ------ 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 (^x.x))(^y.y))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 174289/19880157. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 174290/19880202. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((^y.a)((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((^x.a)((a (a (^y.y))) a)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 174291/19880229. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^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. ------ 174292/19880292. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 174293/19880319. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 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. ------ 174294/19880535. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 174295/19880616. ------ 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))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 174296/19880706. ------ 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. ------ 174297/19880733. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (a (a a)))) REDUCED to normal form. ------ 174298/19880760. ------ 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.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. ------ 174299/19880787. ------ 1. ==[ start ]==> (((a (a a))(a a))((b a)((a a) a))) REDUCED to normal form. ------ 174300/19880814. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 174301/19881048. ------ 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. ------ 174302/19881282. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 174303/19881336. ------ 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))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (a (((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 174304/19881372. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (b ((^y.(y y))((^z.z) b))) 6. ==[ alpha ]==> (b ((^x.(x x))((^y.y) b))) 7. ==[ beta ]==> (b (((^y.y) b)((^y.y) b))) 8. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b))) 9. ==[ beta ]==> (b (b ((^y.y) b))) 10. ==[ alpha ]==> (b (b ((^x.x) b))) 11. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 174305/19881399. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 174306/19881453. ------ 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.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 174307/19881498. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b (^z.z)) b)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b (^z.z)) b)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z)) b)) 5. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z)) b)) 6. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y)) b)) 7. ==[ beta ]==> ((a a)((b (^y.y)) b)) 8. ==[ alpha ]==> ((a a)((b (^x.x)) b)) REDUCED to normal form. ------ 174308/19881561. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(z z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 174309/19881750. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 174310/19881930. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 174311/19882164. ------ 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. ------ 174312/19882191. ------ 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)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(a ((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(a b)) REDUCED to normal form. ------ 174313/19882218. ------ 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.x1))((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 174314/19882245. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(b (^x.x)))) REDUCED to normal form. ------ 174315/19882317. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^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. ------ 174316/19882362. ------ 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)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174317/19882389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 174318/19882443. ------ 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))(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 9. ==[ beta ]==> ((a a)(^y.b)) 10. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 174319/19882533. ------ 1. ==[ start ]==> (((a b) b)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 174320/19882560. ------ 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 (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 174321/19882578. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.x1))) 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))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 174322/19882587. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 174323/19882605. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((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. ------ 174324/19882614. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))((a 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. ------ 174325/19882659. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1)) a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b (^y1.y1)) a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1)) a)) 7. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1)) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) a)) 9. ==[ beta ]==> ((^y.y)((b (^z.z)) a)) 10. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 11. ==[ beta ]==> ((b (^y.y)) a) 12. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 174326/19882722. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.a)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.a)) REDUCED to normal form. ------ 174327/19882749. ------ 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)))(^z1.(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. ------ 174328/19882965. ------ 1. ==[ start ]==> (((^a.b) c)((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 174329/19882974. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(c ((^y.y) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(c b)) REDUCED to normal form. ------ 174330/19883001. ------ 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. ------ 174331/19883028. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 174332/19883064. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(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. ------ 174333/19883343. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(c (^z.z))) 3. ==[ beta ]==> ((a (^y.b))(c (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(c (^y.y))) REDUCED to normal form. ------ 174334/19883442. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^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. ------ 174335/19883451. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b)(a (^a.a)))) 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. ------ 174336/19883478. ------ 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) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) 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. ------ 174337/19884144. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y) b)) 3. ==[ beta ]==> (((a b)(a b))((^y.y) b)) 4. ==[ alpha ]==> (((a b)(a b))((^x.x) b)) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 174338/19884351. ------ 1. ==[ start ]==> (((a a)(b a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 174339/19884378. ------ 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) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (b a))) REDUCED to normal form. ------ 174340/19884405. ------ 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.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y)(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 (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. ------ 174341/19884432. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))((a a)((^x.x) b))) 3. ==[ beta ]==> (((a (a a))(a b))((a a) b)) REDUCED to normal form. ------ 174342/19884612. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 174343/19884630. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 174344/19884792. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 174345/19884909. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 174346/19884936. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 174347/19885017. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 174348/19885098. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.a)(^b.b))) 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. ------ 174349/19885242. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b)(^z.z))) REDUCED to normal form. ------ 174350/19885269. ------ 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. ------ 174351/19885296. ------ 1. ==[ start ]==> ((((^a.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))(a b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(a b))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(a b))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 174352/19885323. ------ 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))((^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. ------ 174353/19885350. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((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. ------ 174354/19885377. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(b a))) REDUCED to normal form. ------ 174355/19885404. ------ 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 (^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. ------ 174356/19885503. ------ 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) 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. ------ 174357/19885548. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)(^b.(^a.a)))) 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. ------ 174358/19885710. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 174359/19885827. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 174360/19885854. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 174361/19885881. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 174362/19885908. ------ 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))(^x2.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. ------ 174363/19886016. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 174364/19886034. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)((a 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 (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 174365/19886214. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (a a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (a a))(a b))) 3. ==[ beta ]==> (((a a) b)((a (a a))(a b))) REDUCED to normal form. ------ 174366/19886241. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 174367/19886268. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b 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)))) REDUCED to normal form. ------ 174368/19886295. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(b a))) REDUCED to normal form. ------ 174369/19886925. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 174370/19887069. ------ 1. ==[ start ]==> (((a b)(^a.b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(c (^y.(a a)))) REDUCED to normal form. ------ 174371/19887168. ------ 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.(^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. ------ 174372/19887177. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 174373/19887204. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 174374/19887564. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c (a b))) 3. ==[ beta ]==> ((b (a (^y.y)))(c (a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c (a b))) REDUCED to normal form. ------ 174375/19887591. ------ 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)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(b (a a))) REDUCED to normal form. ------ 174376/19887618. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 174377/19887897. ------ 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.(^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. ------ 174378/19887933. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((b c)((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((b c)((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 174379/19887960. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 174380/19888005. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)(^c.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 (^x.x))(a (^z.a))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.a))) REDUCED to normal form. ------ 174381/19888032. ------ 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 (^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. ------ 174382/19888068. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^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))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 174383/19888086. ------ 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)(a a)) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a a)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a) a)) REDUCED to normal form. ------ 174384/19888095. ------ 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 a)) REDUCED to normal form. ------ 174385/19888176. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 174386/19888203. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 174387/19888284. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(a a))) REDUCED to normal form. ------ 174388/19888401. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 174389/19888428. ------ 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) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.y))) REDUCED to normal form. ------ 174390/19888455. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^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))) REDUCED to normal form. ------ 174391/19888482. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(a b))) REDUCED to normal form. ------ 174392/19888950. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (b ((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174393/19889175. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(a (a a)))) 5. ==[ beta ]==> (a ((^y.a)(a (a a)))) 6. ==[ alpha ]==> (a ((^x.a)(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174394/19889193. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((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. ------ 174395/19889220. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.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. ------ 174396/19889274. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1)) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z)) b)) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z)) b)) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y)) b)) 9. ==[ beta ]==> ((b b)((^y.y) b)) 10. ==[ alpha ]==> ((b b)((^x.x) b)) 11. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 174397/19889283. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^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. ------ 174398/19889310. ------ 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))))((^z1.(z1 z1))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 174399/19889364. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^a.a))(^b.(^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. ------ 174400/19889391. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 174401/19889499. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (^z.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (^y.(y y)))) REDUCED to normal form. ------ 174402/19889526. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 174403/19889580. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 174404/19889598. ------ 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. ------ 174405/19889643. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c d)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c d)) REDUCED to normal form. ------ 174406/19889778. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c ((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(c a)) REDUCED to normal form. ------ 174407/19889805. ------ 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. ------ 174408/19889832. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a ((^y.y)(^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. ------ 174409/19889886. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(a (^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. ------ 174410/19889913. ------ 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) a))) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((b (a (a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 174411/19889940. ------ 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. ------ 174412/19890012. ------ 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 ]==> ((a (^y.y))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 174413/19890030. ------ 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 ]==> ((^y.(y (^z.z)))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (((a (^z.z))(^x1.a))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 174414/19890417. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(^a.(^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. ------ 174415/19890444. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)(^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. ------ 174416/19890462. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^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. ------ 174417/19890489. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^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. ------ 174418/19890543. ------ 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))) REDUCED to normal form. ------ 174419/19890579. ------ 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. ------ 174420/19890606. ------ 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))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 174421/19890624. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((a a) b)) 3. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 174422/19890687. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 174423/19890732. ------ 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)) 4. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174424/19890768. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x) 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))) REDUCED to normal form. ------ 174425/19891113. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(a (a (^x1.x1))))) 3. ==[ eta ]==> ((^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. ------ 174426/19898538. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.(^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. ------ 174427/19901691. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a))) c) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z))) c) 3. ==[ beta ]==> ((b (^y.(^z.z))) c) 4. ==[ alpha ]==> ((b (^x.(^y.y))) c) REDUCED to normal form. ------ 174428/19901742. ------ 1. ==[ start ]==> ((^a.(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^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)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 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. ------ 174429/19901769. ------ 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 REDUCED to normal form. ------ 174430/19901850. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^z.(a a))((a a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((^x.(a a))((a a)(^y.y)))(^z.z)) 5. ==[ beta ]==> ((a a)(^z.z)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 174431/19902039. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(a (a (^x1.x1))))) 3. ==[ eta ]==> ((^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. ------ 174432/19902042. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^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. ------ 174433/19902534. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 174434/19903605. ------ 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 ]==> (((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1)))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 174435/19903992. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.((((^z.z)(^x1.x1))(b a))(((^z.z)(^x1.x1))(b a)))) 4. ==[ alpha ]==> (^x.((((^y.y)(^z.z))(b a))(((^x1.x1)(^y1.y1))(b a)))) 5. ==[ beta ]==> (^x.(((^z.z)(b a))(((^x1.x1)(^y1.y1))(b a)))) 6. ==[ alpha ]==> (^x.(((^y.y)(b a))(((^z.z)(^x1.x1))(b a)))) 7. ==[ beta ]==> (^x.((b a)(((^z.z)(^x1.x1))(b a)))) 8. ==[ alpha ]==> (^x.((b a)(((^y.y)(^z.z))(b a)))) 9. ==[ beta ]==> (^x.((b a)((^z.z)(b a)))) 10. ==[ alpha ]==> (^x.((b a)((^y.y)(b a)))) 11. ==[ beta ]==> (^x.((b a)(b a))) REDUCED to normal form. ------ 174436/19904199. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.x1) a))((^z.z)((^x1.x1) a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.z) a))((^x1.x1)((^y1.y1) a)))) 5. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.x1) a))) 8. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z) a))) 9. ==[ beta ]==> (a ((^y.y)((^z.z) a))) 10. ==[ alpha ]==> (a ((^x.x)((^y.y) a))) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174437/19905606. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 174438/19905630. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))(^z.z))) 3. ==[ eta ]==> (b ((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 174439/19906179. ------ 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))((^x2.x2)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 174440/19906467. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.b)((a a) a))) 3. ==[ beta ]==> (((^x1.b)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 174441/19907070. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174442/19907280. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^a.(^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. ------ 174443/19907385. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 174444/19907883. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^a.(a (^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))))) REDUCED to normal form. ------ 174445/19908171. ------ 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.(^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. ------ 174446/19908384. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.a)((^z.z)(a a)))((^y.a)((^z.z)(a a))))(((^y.a)((^z.z)(a a)))((^y.a)((^z.z)(a a))))) 4. ==[ alpha ]==> ((((^x.a)((^y.y)(a a)))((^z.a)((^x1.x1)(a a))))(((^y1.a)((^z1.z1)(a a)))((^x2.a)((^y2.y2)(a a))))) 5. ==[ beta ]==> ((a ((^z.a)((^x1.x1)(a a))))(((^y1.a)((^z1.z1)(a a)))((^x2.a)((^y2.y2)(a a))))) 6. ==[ alpha ]==> ((a ((^x.a)((^y.y)(a a))))(((^z.a)((^x1.x1)(a a)))((^y1.a)((^z1.z1)(a a))))) 7. ==[ beta ]==> ((a a)(((^z.a)((^x1.x1)(a a)))((^y1.a)((^z1.z1)(a a))))) 8. ==[ alpha ]==> ((a a)(((^x.a)((^y.y)(a a)))((^z.a)((^x1.x1)(a a))))) 9. ==[ beta ]==> ((a a)(a ((^z.a)((^x1.x1)(a a))))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)((^y.y)(a a))))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 174447/19909224. ------ 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)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 174448/19909464. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174449/19909467. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 174450/19909917. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^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. ------ 174451/19910358. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 174452/19910547. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) b)((^y.y) a)) a) 4. ==[ beta ]==> ((b ((^y.y) a)) a) 5. ==[ alpha ]==> ((b ((^x.x) a)) a) 6. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 174453/19910625. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.a))) 3. ==[ eta ]==> ((^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. ------ 174454/19910907. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.((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. ------ 174455/19911546. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.((^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. ------ 174456/19911681. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 174457/19911867. ------ 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 ]==> (((^z.a)(a (^x1.x1)))(((^z.a)(a (^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((^x.a)(a (^y.y)))(((^z.a)(a (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (a (((^z.a)(a (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (a (((^x.a)(a (^y.y)))(^z.z))) 7. ==[ beta ]==> (a (a (^z.z))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 174458/19912311. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.x)(a (a (^y.y))))(^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. ------ 174459/19912428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(^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. ------ 174460/19912536. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 174461/19912581. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.b)) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174462/19912617. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.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. ------ 174463/19912665. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a) b)(^b.(^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)))) 5. ==[ beta ]==> (a (b (^y.(^z.z)))) 6. ==[ alpha ]==> (a (b (^x.(^y.y)))) REDUCED to normal form. ------ 174464/19912674. ------ 1. ==[ start ]==> ((a (a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 174465/19912701. ------ 1. ==[ start ]==> ((a b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 174466/19912719. ------ 1. ==[ start ]==> (((a a)(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 174467/19912746. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 174468/19912782. ------ 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)))) 3. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 174469/19912827. ------ 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))))) REDUCED to normal form. ------ 174470/19912854. ------ 1. ==[ start ]==> (((a a)(^a.(^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. ------ 174471/19912917. ------ 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. ------ 174472/19912944. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 174473/19912971. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^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. ------ 174474/19913016. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 174475/19913043. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b (^a.a)) 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)) REDUCED to normal form. ------ 174476/19913214. ------ 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. ------ 174477/19913385. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(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. ------ 174478/19913421. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^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)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 174479/19913439. ------ 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 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. ------ 174480/19913466. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 174481/19913601. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174482/19913628. ------ 1. ==[ start ]==> (((^a.(^a.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)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1)(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. ------ 174483/19913682. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 174484/19913736. ------ 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. ------ 174485/19913763. ------ 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. ------ 174486/19913817. ------ 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.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)((^z.(^x1.x1)) a))) 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. ------ 174487/19913853. ------ 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 ]==> (((^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)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174488/19913943. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) 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)))) 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. ------ 174489/19913970. ------ 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.(^z.(^x1.x1)))((^y1.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. ------ 174490/19914150. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (a a))(^b.b))) 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. ------ 174491/19914258. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 174492/19914285. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((b (^y.y)) b)) REDUCED to normal form. ------ 174493/19914375. ------ 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. ------ 174494/19914456. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 174495/19914483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^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. ------ 174496/19914537. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 174497/19914627. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b (b (^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(b (b (^z.z)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b (b (^z.z)))) IRREDUCIBLE: cycle. ------ 174498/19914708. ------ 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 a))(a (^z.z)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 174499/19914717. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b) a)((^x.(a a)) c)) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 174500/19914735. ------ 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)(b ((^y.y) a))) 6. ==[ alpha ]==> ((a b)(b ((^x.x) a))) 7. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 174501/19914762. ------ 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.(^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. ------ 174502/19914816. ------ 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)(^y.y))((a a) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 174503/19914897. ------ 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. ------ 174504/19914924. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(b a))) 5. ==[ beta ]==> ((a (^x.(a a)))(b a)) REDUCED to normal form. ------ 174505/19915095. ------ 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. ------ 174506/19915104. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 174507/19915131. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 174508/19915338. ------ 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. ------ 174509/19915365. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) 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. ------ 174510/19915392. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 174511/19915446. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 174512/19915473. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a)) b)) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a)) b)) 7. ==[ beta ]==> ((((a a)(a a)) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 174513/19915500. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b c)) REDUCED to normal form. ------ 174514/19915617. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 174515/19915644. ------ 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. ------ 174516/19915725. ------ 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))(^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. ------ 174517/19915752. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 174518/19915842. ------ 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))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 174519/19915977. ------ 1. ==[ start ]==> (((^a.b)(^b.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. ------ 174520/19916058. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^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))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^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. ------ 174521/19916085. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(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. ------ 174522/19916139. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a (^x.x)) b)) REDUCED to normal form. ------ 174523/19916202. ------ 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))(^y.y))) REDUCED to normal form. ------ 174524/19916229. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 174525/19916256. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 174526/19916283. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b a)(^z.(z z)))) REDUCED to normal form. ------ 174527/19916346. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 174528/19916373. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.b)(a b))) 3. ==[ beta ]==> ((a (a b))((^y.b)(a b))) 4. ==[ alpha ]==> ((a (a b))((^x.b)(a b))) 5. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 174529/19916427. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 9. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 10. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174530/19916454. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(x x))(b a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((b a)(b a))) REDUCED to normal form. ------ 174531/19916481. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.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) REDUCED to normal form. ------ 174532/19916508. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 174533/19916535. ------ 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)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(a a))) REDUCED to normal form. ------ 174534/19916562. ------ 1. ==[ start ]==> ((a (b a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.y))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 174535/19916841. ------ 1. ==[ start ]==> (((^a.a)(b a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> ((b a)(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((b a)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 174536/19916868. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(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)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 174537/19916904. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a)) a)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a)) a)) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 174538/19916922. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b)(a a))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b)(a a))) 5. ==[ beta ]==> (((a b)(a b))(b (a a))) REDUCED to normal form. ------ 174539/19916931. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y) b)) 3. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 174540/19917003. ------ 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))(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. ------ 174541/19917111. ------ 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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a a))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 174542/19917210. ------ 1. ==[ start ]==> (((a (a a))(a b))(b (^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))(b (^x.x))) REDUCED to normal form. ------ 174543/19917264. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 174544/19917291. ------ 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)))(a (^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. ------ 174545/19917390. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 174546/19917399. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)((a a) a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 174547/19917867. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.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. ------ 174548/19917903. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z) a)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 174549/19917930. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1))) b)) 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. ------ 174550/19917975. ------ 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 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. ------ 174551/19918002. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 174552/19918182. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^y.y))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 174553/19918209. ------ 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. ------ 174554/19918236. ------ 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.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 174555/19918281. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174556/19918317. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 174557/19918812. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 174558/19918821. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 174559/19918920. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^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. ------ 174560/19919046. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a))(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 174561/19919100. ------ 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. ------ 174562/19919154. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(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. ------ 174563/19919181. ------ 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) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 174564/19919208. ------ 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 (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 174565/19919262. ------ 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.(^y1.y1))((a a) 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. ------ 174566/19919289. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))(a b))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))(a b))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))(a b))) 5. ==[ beta ]==> ((b (a a))((a b)(a b))) REDUCED to normal form. ------ 174567/19919316. ------ 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. ------ 174568/19919595. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c ((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174569/19919676. ------ 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.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))) REDUCED to normal form. ------ 174570/19919703. ------ 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))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(a (^y1.y1)))) 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. ------ 174571/19919712. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 174572/19919757. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((b a)(b a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 174573/19919838. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y) a)(a b))) 3. ==[ beta ]==> (b (((^y.y) a)(a b))) 4. ==[ alpha ]==> (b (((^x.x) a)(a b))) 5. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 174574/19919955. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 174575/19919982. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 174576/19920009. ------ 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)(^y.(y y)))) REDUCED to normal form. ------ 174577/19920045. ------ 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. ------ 174578/19920072. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))((a a) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 174579/19920099. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.a)(a b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.a)(a b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(a b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 174580/19920126. ------ 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)(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 174581/19920153. ------ 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 a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^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. ------ 174582/19920207. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 174583/19920234. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b)(^b.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. ------ 174584/19920342. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.b))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 174585/19920369. ------ 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.(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. ------ 174586/19920396. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 174587/19920486. ------ 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) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a)((^x2.x2) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174588/19920567. ------ 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. ------ 174589/19920711. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)(^b.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. ------ 174590/19920738. ------ 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))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^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. ------ 174591/19920846. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((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. ------ 174592/19920873. ------ 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. ------ 174593/19921053. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a 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. ------ 174594/19921089. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(a a)) a)) 3. ==[ beta ]==> ((b (^y.a))((^z.(a a)) a)) 4. ==[ alpha ]==> ((b (^x.a))((^y.(a a)) a)) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 174595/19921116. ------ 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. ------ 174596/19921233. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c (^z.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(c (^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c (^y.a))) 5. ==[ beta ]==> ((a b)(c (^y.a))) 6. ==[ alpha ]==> ((a b)(c (^x.a))) REDUCED to normal form. ------ 174597/19921260. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.b))) REDUCED to normal form. ------ 174598/19921287. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b 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. ------ 174599/19921314. ------ 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. ------ 174600/19921341. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.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) REDUCED to normal form. ------ 174601/19921368. ------ 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) a))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 174602/19921395. ------ 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 y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 174603/19921449. ------ 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 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. ------ 174604/19921476. ------ 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))) 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. ------ 174605/19921503. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 174606/19921557. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 174607/19921647. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^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. ------ 174608/19921728. ------ 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))(a (^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(a (^z1.z1)))) 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. ------ 174609/19921836. ------ 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. ------ 174610/19921953. ------ 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)))) 7. ==[ beta ]==> (a (a (^y.(y y)))) 8. ==[ alpha ]==> (a (a (^x.(x x)))) REDUCED to normal form. ------ 174611/19922061. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^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. ------ 174612/19922133. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (a (a a)))) 3. ==[ beta ]==> (b (c (a (a a)))) REDUCED to normal form. ------ 174613/19922196. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 174614/19922241. ------ 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 (^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. ------ 174615/19922250. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c c)) REDUCED to normal form. ------ 174616/19922358. ------ 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)(^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. ------ 174617/19922394. ------ 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 (^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. ------ 174618/19922421. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 174619/19922448. ------ 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. ------ 174620/19922475. ------ 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. ------ 174621/19922502. ------ 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)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 174622/19922529. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 174623/19922556. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 174624/19922583. ------ 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.(y1 y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(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)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 174625/19922610. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 174626/19922691. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (^y.a))) 3. ==[ beta ]==> ((b (a (a a)))(c (^y.a))) 4. ==[ alpha ]==> ((b (a (a a)))(c (^x.a))) REDUCED to normal form. ------ 174627/19922718. ------ 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)))) 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. ------ 174628/19922772. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(a a))) 5. ==[ beta ]==> ((a a)((^y.(y y))(a a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(a a))) 7. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 174629/19922790. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(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. ------ 174630/19922799. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.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. ------ 174631/19923195. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) 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)) REDUCED to normal form. ------ 174632/19923213. ------ 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 ]==> (((^z.z)(^y.y))(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. ------ 174633/19923240. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(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. ------ 174634/19923249. ------ 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. ------ 174635/19923267. ------ 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 (^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. ------ 174636/19923357. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(^a.(^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. ------ 174637/19923384. ------ 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)) REDUCED to normal form. ------ 174638/19923402. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (a a))) 3. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 174639/19923465. ------ 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. ------ 174640/19923510. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 174641/19923546. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a) 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)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 174642/19923572. ------ 1. ==[ start ]==> (^a.(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (^x.(((x x)(x x))(^y.(y y)))) REDUCED to normal form. ------ 174643/19923573. ------ 1. ==[ start ]==> (a (((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (a (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 174644/19934505. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a))) a) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 174645/19934511. ------ 1. ==[ start ]==> ((^a.a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 174646/19934538. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^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)))) 5. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(b (^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 174647/19934565. ------ 1. ==[ start ]==> ((^a.b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 174648/19934763. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (^y.((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (^x.((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (^x.(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 174649/19934835. ------ 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. ------ 174650/19934847. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^b.(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. ------ 174651/19935288. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(a (a (^a.a))))) 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))))) REDUCED to normal form. ------ 174652/19935888. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (((((a a)(^y.y))(^z.b))(((a a)(^y.y))(^z.b)))(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (((((a a)(^x.x))(^y.b))(((a a)(^z.z))(^x1.b)))(((a a)(^y1.y1))(^z1.b))) REDUCED to normal form. ------ 174653/19936221. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 174654/19936995. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((((^z.z) b)(^x1.a))(((^z.z) b)(^x1.a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) b)(^z.a))(((^x1.x1) b)(^y1.a)))) 5. ==[ beta ]==> ((((^y.y) b)(^z.a))(((^x1.x1) b)(^y1.a))) 6. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) b)(^x1.a))) 7. ==[ beta ]==> ((b (^y.a))(((^z.z) b)(^x1.a))) 8. ==[ alpha ]==> ((b (^x.a))(((^y.y) b)(^z.a))) 9. ==[ beta ]==> ((b (^x.a))(b (^z.a))) 10. ==[ alpha ]==> ((b (^x.a))(b (^y.a))) REDUCED to normal form. ------ 174655/19937304. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (^y1.y1)))) 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))) REDUCED to normal form. ------ 174656/19938042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174657/19938426. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(a a)) a)) 3. ==[ eta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 174658/19938771. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 174659/19939263. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a b)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 174660/19939437. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (b (^x1.x1)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174661/19939770. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 174662/19940181. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 174663/19940679. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^b.(^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. ------ 174664/19940688. ------ 1. ==[ start ]==> (((a b)(^c.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 174665/19941180. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((((^y.y) a)(^z.(a a)))(((^y.y) a)(^z.(a a))))((((^y.y) a)(^z.(a a)))(((^y.y) a)(^z.(a a))))) 4. ==[ alpha ]==> (((((^x.x) a)(^y.(a a)))(((^z.z) a)(^x1.(a a))))((((^y1.y1) a)(^z1.(a a)))(((^x2.x2) a)(^y2.(a a))))) 5. ==[ beta ]==> (((a (^y.(a a)))(((^z.z) a)(^x1.(a a))))((((^y1.y1) a)(^z1.(a a)))(((^x2.x2) a)(^y2.(a a))))) 6. ==[ alpha ]==> (((a (^x.(a a)))(((^y.y) a)(^z.(a a))))((((^x1.x1) a)(^y1.(a a)))(((^z1.z1) a)(^x2.(a a))))) 7. ==[ beta ]==> (((a (^x.(a a)))(a (^z.(a a))))((((^x1.x1) a)(^y1.(a a)))(((^z1.z1) a)(^x2.(a a))))) 8. ==[ alpha ]==> (((a (^x.(a a)))(a (^y.(a a))))((((^z.z) a)(^x1.(a a)))(((^y1.y1) a)(^z1.(a a))))) 9. ==[ beta ]==> (((a (^x.(a a)))(a (^y.(a a))))((a (^x1.(a a)))(((^y1.y1) a)(^z1.(a a))))) 10. ==[ alpha ]==> (((a (^x.(a a)))(a (^y.(a a))))((a (^z.(a a)))(((^x1.x1) a)(^y1.(a a))))) 11. ==[ beta ]==> (((a (^x.(a a)))(a (^y.(a a))))((a (^z.(a a)))(a (^y1.(a a))))) 12. ==[ alpha ]==> (((a (^x.(a a)))(a (^y.(a a))))((a (^z.(a a)))(a (^x1.(a a))))) REDUCED to normal form. ------ 174666/19941525. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(b x))) 3. ==[ eta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 174667/19941768. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 174668/19942731. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(a a))) REDUCED to normal form. ------ 174669/19942956. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((b (^y.a))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b (^x.a))(^y.(y y))) REDUCED to normal form. ------ 174670/19943343. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.b))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.b))) 5. ==[ beta ]==> ((b a)(^y.(^z.b))) 6. ==[ alpha ]==> ((b a)(^x.(^y.b))) REDUCED to normal form. ------ 174671/19944063. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((z z) z))) REDUCED to normal form. ------ 174672/19944240. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 174673/19944342. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 174674/19944663. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^z.z) a)(^x1.(^y1.y1)))((((^z.z) a)(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((((^x1.x1) a)(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((((^x1.x1) a)(^y1.(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((((^z.z) a)(^x1.(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (^x1.(^y1.y1)))(^z1.z1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 174675/19945107. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(^b.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. ------ 174676/19945116. ------ 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. ------ 174677/19945188. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.y))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.x))) REDUCED to normal form. ------ 174678/19945332. ------ 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. ------ 174679/19945377. ------ 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. ------ 174680/19945413. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(x1 x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 174681/19945440. ------ 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. ------ 174682/19945452. ------ 1. ==[ start ]==> ((a a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 174683/19945479. ------ 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. ------ 174684/19945488. ------ 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 ]==> ((^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. ------ 174685/19945506. ------ 1. ==[ start ]==> ((a b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 174686/19945515. ------ 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. ------ 174687/19945560. ------ 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. ------ 174688/19945596. ------ 1. ==[ start ]==> (((^a.a)(^a.(^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. ------ 174689/19945623. ------ 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)((^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. ------ 174690/19945677. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 174691/19945704. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 174692/19945776. ------ 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. ------ 174693/19945785. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.a)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 174694/19945812. ------ 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)))(^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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174695/19946082. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 174696/19946199. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(b (^z.z))) REDUCED to normal form. ------ 174697/19946226. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a (a (a (^a.a))))) 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. ------ 174698/19946253. ------ 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. ------ 174699/19946361. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b b)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b b)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b b)((a (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> ((b b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 174700/19946496. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a) a)(b a))) REDUCED to normal form. ------ 174701/19946523. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 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. ------ 174702/19946550. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 174703/19946577. ------ 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) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 174704/19946604. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 174705/19946631. ------ 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.(^x1.x1)) a))) 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. ------ 174706/19946694. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 174707/19946721. ------ 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. ------ 174708/19946748. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 174709/19946775. ------ 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)))) REDUCED to normal form. ------ 174710/19946802. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((b a)(^y.a))) 5. ==[ beta ]==> ((a a)((b a)(^y.a))) 6. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 174711/19946829. ------ 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. ------ 174712/19946865. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 174713/19946919. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(b a))) 5. ==[ beta ]==> (a ((^z.a)(b a))) 6. ==[ alpha ]==> (a ((^x.a)(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174714/19947000. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a 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. ------ 174715/19947027. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(b (^x2.x2)))) 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. ------ 174716/19947162. ------ 1. ==[ start ]==> ((a (^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.b))(^z.(z z))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(y y))) REDUCED to normal form. ------ 174717/19947351. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 174718/19947495. ------ 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. ------ 174719/19947522. ------ 1. ==[ start ]==> (((a b) a)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 174720/19947549. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.b))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(b ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.b))(b a)) REDUCED to normal form. ------ 174721/19947603. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((b a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 174722/19947630. ------ 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)(^y.y))((a a) a))) REDUCED to normal form. ------ 174723/19947657. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(a b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 174724/19947684. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^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. ------ 174725/19947711. ------ 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. ------ 174726/19947882. ------ 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))) REDUCED to normal form. ------ 174727/19947909. ------ 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. ------ 174728/19947936. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(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. ------ 174729/19947945. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174730/19947972. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 174731/19948026. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(^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) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174732/19948107. ------ 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) REDUCED to normal form. ------ 174733/19948161. ------ 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 z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)((^y.(y y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 174734/19948188. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) 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. ------ 174735/19948242. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(b (^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(b (^x1.x1)))) 9. ==[ beta ]==> ((^y.y)((^z.z)(b (^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)((^y.y)(b (^z.z)))) 11. ==[ beta ]==> ((^y.y)(b (^z.z))) 12. ==[ alpha ]==> ((^x.x)(b (^y.y))) 13. ==[ beta ]==> (b (^y.y)) 14. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174736/19948323. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^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. ------ 174737/19948548. ------ 1. ==[ start ]==> (((^a.b) c)(d (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(d (a (^y.(^z.z))))) 3. ==[ beta ]==> (b (d (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (d (a (^x.(^y.y))))) REDUCED to normal form. ------ 174738/19948791. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(a a))((a a) a))) 3. ==[ beta ]==> (((a b) c)((a a)((a a) a))) REDUCED to normal form. ------ 174739/19948818. ------ 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. ------ 174740/19948845. ------ 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. ------ 174741/19948899. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (a a))(b a))) REDUCED to normal form. ------ 174742/19948926. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.b))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.b))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 174743/19948980. ------ 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. ------ 174744/19949025. ------ 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))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 174745/19949124. ------ 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)))) REDUCED to normal form. ------ 174746/19949178. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a b)(^y.b))) 3. ==[ beta ]==> ((a (a b))((a b)(^y.b))) 4. ==[ alpha ]==> ((a (a b))((a b)(^x.b))) REDUCED to normal form. ------ 174747/19949205. ------ 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. ------ 174748/19949286. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) a)(^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. ------ 174749/19949313. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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. ------ 174750/19949367. ------ 1. ==[ start ]==> ((a (b a))(((a a)(a a)) a)) REDUCED to normal form. ------ 174751/19949538. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (b ((^z.b)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 174752/19949646. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b a)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b a)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 174753/19949673. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 174754/19949709. ------ 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. ------ 174755/19949736. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(b (a a))) REDUCED to normal form. ------ 174756/19949790. ------ 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) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 174757/19949817. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 174758/19949844. ------ 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)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a 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. ------ 174759/19949871. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^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. ------ 174760/19950069. ------ 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. ------ 174761/19950096. ------ 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)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 174762/19950123. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((b a)(^z.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((b 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. ------ 174763/19950150. ------ 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))(^x1.(x1 x1)))) REDUCED to normal form. ------ 174764/19950204. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.a))) REDUCED to normal form. ------ 174765/19950213. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)((a a) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 174766/19950294. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^z.(z z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 174767/19950375. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 174768/19950510. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(a a))(^b.(^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. ------ 174769/19950537. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 174770/19950591. ------ 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.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(a a)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 174771/19950672. ------ 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))(^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. ------ 174772/19950681. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 174773/19950708. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(a ((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a b)) REDUCED to normal form. ------ 174774/19950735. ------ 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))) REDUCED to normal form. ------ 174775/19950789. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 174776/19951041. ------ 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))) REDUCED to normal form. ------ 174777/19951095. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 174778/19951122. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(y y)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(x x)))) REDUCED to normal form. ------ 174779/19951131. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 174780/19951158. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.b)((^x2.x2)(^y2.y2)))) 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. ------ 174781/19951293. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^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. ------ 174782/19951455. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 174783/19951536. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 174784/19951572. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c ((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(c ((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.(a a))(c ((a a)(^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174785/19951599. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(b (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(b (b a))) REDUCED to normal form. ------ 174786/19951617. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 174787/19951626. ------ 1. ==[ start ]==> (((a b)(^c.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 174788/19951653. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a)(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(a a))) REDUCED to normal form. ------ 174789/19951680. ------ 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))(a (^x1.x1)))) REDUCED to normal form. ------ 174790/19951734. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(a (a a)))) REDUCED to normal form. ------ 174791/19951761. ------ 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. ------ 174792/19951932. ------ 1. ==[ start ]==> ((((a a) a)(a b))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((b a)(^x.x))) REDUCED to normal form. ------ 174793/19951959. ------ 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))(^y.(^z.z)))) REDUCED to normal form. ------ 174794/19951986. ------ 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)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 174795/19952013. ------ 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.(y y)))) REDUCED to normal form. ------ 174796/19952094. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (a a))(^y.b))) 3. ==[ beta ]==> ((b (a a))((a (a a))(^y.b))) 4. ==[ alpha ]==> ((b (a a))((a (a a))(^x.b))) REDUCED to normal form. ------ 174797/19952121. ------ 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. ------ 174798/19952157. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174799/19952292. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 174800/19952400. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 174801/19952436. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b ((a a)(^y.y)))) 3. ==[ beta ]==> ((b b)(b ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b b)(b ((a a)(^x.x)))) REDUCED to normal form. ------ 174802/19952463. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(a (b a))) REDUCED to normal form. ------ 174803/19952517. ------ 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))(a (^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. ------ 174804/19952544. ------ 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) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a b) a)) REDUCED to normal form. ------ 174805/19952625. ------ 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. ------ 174806/19952652. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((a b)(^x.b))(a (a b))) REDUCED to normal form. ------ 174807/19952706. ------ 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)(^x1.x1)))) REDUCED to normal form. ------ 174808/19952850. ------ 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. ------ 174809/19952877. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(^y.a))) REDUCED to normal form. ------ 174810/19952904. ------ 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)(^y1.b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (^x1.b))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.b))) REDUCED to normal form. ------ 174811/19952931. ------ 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. ------ 174812/19952985. ------ 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)(a a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 174813/19953012. ------ 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. ------ 174814/19953039. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b) c)) 3. ==[ beta ]==> (((a a)((a a) a))((a b) c)) REDUCED to normal form. ------ 174815/19953480. ------ 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))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(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. ------ 174816/19953588. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b (^x.x))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> ((b (^x.x))(^z.z)) 12. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 174817/19953615. ------ 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 REDUCED to normal form. ------ 174818/19953669. ------ 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)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(a a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 174819/19953750. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a 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. ------ 174820/19953858. ------ 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))(^z1.b))) 3. ==[ beta ]==> ((^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. ------ 174821/19953867. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (a b))) REDUCED to normal form. ------ 174822/19953894. ------ 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 ]==> ((b (^y.a))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.a))(a (a a))) REDUCED to normal form. ------ 174823/19953921. ------ 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. ------ 174824/19954119. ------ 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. ------ 174825/19954146. ------ 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.(^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. ------ 174826/19954173. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.a))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.a))) 7. ==[ beta ]==> (((a a)(a b))(^y.a)) 8. ==[ alpha ]==> (((a a)(a b))(^x.a)) REDUCED to normal form. ------ 174827/19954200. ------ 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 y)))) REDUCED to normal form. ------ 174828/19954281. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a a)(^z.b))) 3. ==[ beta ]==> ((b ((^y.y) a))((a a)(^z.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a a)(^y.b))) 5. ==[ beta ]==> ((b a)((a a)(^y.b))) 6. ==[ alpha ]==> ((b a)((a a)(^x.b))) REDUCED to normal form. ------ 174829/19954308. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b) a)) REDUCED to normal form. ------ 174830/19954452. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))(^c.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. ------ 174831/19954641. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^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. ------ 174832/19954776. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^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. ------ 174833/19954803. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 174834/19954857. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(^z.z))) 7. ==[ beta ]==> ((b b)((^y.a)(^z.z))) 8. ==[ alpha ]==> ((b b)((^x.a)(^y.y))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 174835/19954938. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^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. ------ 174836/19954947. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (a (a a)))) REDUCED to normal form. ------ 174837/19954974. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.y))) REDUCED to normal form. ------ 174838/19955001. ------ 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. ------ 174839/19955055. ------ 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))(a (^y1.y1)))) REDUCED to normal form. ------ 174840/19955082. ------ 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) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 174841/19955109. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 174842/19955181. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 174843/19955199. ------ 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)))) 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. ------ 174844/19955226. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.a))) REDUCED to normal form. ------ 174845/19955253. ------ 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.(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. ------ 174846/19955280. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((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. ------ 174847/19955307. ------ 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)(^z1.z1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1)) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1)) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1)) a)) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 174848/19955334. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a)) b)) REDUCED to normal form. ------ 174849/19955361. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a c)) REDUCED to normal form. ------ 174850/19955469. ------ 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 y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(b b)) REDUCED to normal form. ------ 174851/19955496. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a) c)) 3. ==[ beta ]==> ((b (a (a a)))((^y.a) c)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a) c)) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 174852/19955577. ------ 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. ------ 174853/19955604. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(^a.(^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. ------ 174854/19955613. ------ 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 ]==> (((^z.a)(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(a (^y.y)))(^z.z)) 7. ==[ beta ]==> (a (^z.z)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 174855/19956000. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (a a))) 3. ==[ beta ]==> (((^y.y) b)(c (a a))) 4. ==[ alpha ]==> (((^x.x) b)(c (a a))) 5. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 174856/19956018. ------ 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.(^x2.x2)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^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. ------ 174857/19956027. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (a (^y.y)))) REDUCED to normal form. ------ 174858/19956045. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)(^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. ------ 174859/19956054. ------ 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. ------ 174860/19956126. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a (^y.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.a))) REDUCED to normal form. ------ 174861/19956162. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(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. ------ 174862/19956207. ------ 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174863/19956270. ------ 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. ------ 174864/19956315. ------ 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. ------ 174865/19956351. ------ 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. ------ 174866/19956378. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 174867/19967319. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a))) b) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x))) b) REDUCED to normal form. ------ 174868/19967343. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174869/19967424. ------ 1. ==[ start ]==> ((^a.(^a.(^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. ------ 174870/19967586. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (^y.((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (^x.((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 174871/19967670. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 174872/19968111. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^b.(^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. ------ 174873/19968279. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b 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. ------ 174874/19968543. ------ 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 ]==> ((^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. ------ 174875/19968948. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 174876/19970136. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 174877/19970493. ------ 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 ]==> (((b ((a a)(a a)))(b ((a a)(a a))))(^y.y)) 4. ==[ alpha ]==> (((b ((a a)(a a)))(b ((a a)(a a))))(^x.x)) REDUCED to normal form. ------ 174878/19971594. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^b.(^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. ------ 174879/19972260. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (b (^x1.(^y1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 174880/19972593. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 174881/19972689. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174882/19973511. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 174883/19975083. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174884/19975563. ------ 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))))(^x1.(a a))) REDUCED to normal form. ------ 174885/19975779. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.(^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. ------ 174886/19975977. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(a b))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(a b))) 5. ==[ beta ]==> ((b a)(^y.(a b))) 6. ==[ alpha ]==> ((b a)(^x.(a b))) REDUCED to normal form. ------ 174887/19976886. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.a))) REDUCED to normal form. ------ 174888/19977063. ------ 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))) REDUCED to normal form. ------ 174889/19977939. ------ 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. ------ 174890/19978011. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.c)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.c)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.c)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.c)) REDUCED to normal form. ------ 174891/19978074. ------ 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)))) REDUCED to normal form. ------ 174892/19978236. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^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. ------ 174893/19978263. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 174894/19978293. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 174895/19978320. ------ 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. ------ 174896/19978329. ------ 1. ==[ start ]==> (((a a) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 174897/19978356. ------ 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. ------ 174898/19978374. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 174899/19978437. ------ 1. ==[ start ]==> (((a a) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 174900/19978464. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(b a))) 3. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 174901/19978482. ------ 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. ------ 174902/19978509. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a)(^a.a))(^b.b))) 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. ------ 174903/19978518. ------ 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 (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 174904/19978536. ------ 1. ==[ start ]==> ((a (^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 174905/19978572. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 174906/19978617. ------ 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. ------ 174907/19978644. ------ 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 (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) REDUCED to normal form. ------ 174908/19978653. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)((^x1.x1)(^z.z))) 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. ------ 174909/19978698. ------ 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. ------ 174910/19978761. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.b)(^b.(^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. ------ 174911/19978869. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 174912/19978950. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(^a.a))(^b.b))) 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))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 174913/19979058. ------ 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)))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 174914/19979076. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(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))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 174915/19979121. ------ 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. ------ 174916/19979148. ------ 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) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 174917/19979175. ------ 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 (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 174918/19979202. ------ 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. ------ 174919/19979229. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 174920/19979436. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 174921/19979490. ------ 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 ]==> ((^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. ------ 174922/19979697. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 174923/19979787. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 174924/19979814. ------ 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)(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a) a)(b ((^y.y) b))) 6. ==[ alpha ]==> ((((a a) a) a)(b ((^x.x) b))) 7. ==[ beta ]==> ((((a a) a) a)(b b)) REDUCED to normal form. ------ 174925/19979868. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(b (^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. ------ 174926/19979895. ------ 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.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 174927/19979913. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) a)) 8. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) a)) 9. ==[ beta ]==> ((a a)((^y.y) a)) 10. ==[ alpha ]==> ((a a)((^x.x) a)) 11. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 174928/19980165. ------ 1. ==[ start ]==> (((^a.b) a)((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.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. ------ 174929/19980372. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a)) c)) 3. ==[ beta ]==> ((a b)((^y.(a a)) c)) 4. ==[ alpha ]==> ((a b)((^x.(a a)) c)) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 174930/19980579. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(b a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(b a))) 5. ==[ beta ]==> (((a a)(a b))(b a)) REDUCED to normal form. ------ 174931/19980606. ------ 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.(^z.z))))) REDUCED to normal form. ------ 174932/19980633. ------ 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)((^y1.y1) b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(a ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 174933/19980660. ------ 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)(a a)))) REDUCED to normal form. ------ 174934/19980687. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(b (^z.z)))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(b (^y.y)))) 7. ==[ beta ]==> (a ((a a)(b (^y.y)))) 8. ==[ alpha ]==> (a ((a a)(b (^x.x)))) REDUCED to normal form. ------ 174935/19980777. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 174936/19980804. ------ 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)))(^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. ------ 174937/19980858. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 174938/19980939. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 174939/19980948. ------ 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) REDUCED to normal form. ------ 174940/19980975. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 174941/19980993. ------ 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))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^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. ------ 174942/19981002. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 174943/19981020. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 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. ------ 174944/19981029. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 174945/19981083. ------ 1. ==[ start ]==> (((a (a a))(^b.(^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. ------ 174946/19981137. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 174947/19981155. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^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. ------ 174948/19981164. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 174949/19981191. ------ 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. ------ 174950/19981380. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (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. ------ 174951/19981443. ------ 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. ------ 174952/19981812. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b (^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 174953/19981857. ------ 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 a))(^z.z))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 174954/19981866. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 174955/19981893. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b)(a (^a.a)))) 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. ------ 174956/19981920. ------ 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) a))) 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. ------ 174957/19982433. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(^a.a))(^c.(^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. ------ 174958/19982541. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 174959/19982559. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a)) a)) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a)) a)) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 174960/19982766. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(b a))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(b a))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(b a))((^y.y)(a a))) 6. ==[ alpha ]==> (((a a)(b a))((^x.x)(a a))) 7. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 174961/19982793. ------ 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 a))((a a)(^z.z)))) REDUCED to normal form. ------ 174962/19982820. ------ 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) a)(b a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 174963/19982847. ------ 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 (^y.(^z.z))))) REDUCED to normal form. ------ 174964/19982874. ------ 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. ------ 174965/19983027. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 174966/19983045. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 174967/19983126. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 174968/19983207. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 174969/19983351. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 174970/19983432. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^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. ------ 174971/19983459. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 174972/19983513. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^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. ------ 174973/19983540. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.a)(^b.b))) 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. ------ 174974/19983639. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) d)) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 174975/19983657. ------ 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. ------ 174976/19983684. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a b)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((a b)(^y.y))) REDUCED to normal form. ------ 174977/19983711. ------ 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. ------ 174978/19983738. ------ 1. ==[ start ]==> (((a (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))(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. ------ 174979/19983765. ------ 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))((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (a a))((^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. ------ 174980/19983792. ------ 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. ------ 174981/19983819. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.z))(b a))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.z))(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 174982/19983846. ------ 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. ------ 174983/19983963. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(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. ------ 174984/19983990. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z1.(^x2.x2)))) 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. ------ 174985/19984125. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.a))(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((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. ------ 174986/19984242. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 174987/19984269. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 174988/19984296. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 174989/19984404. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.a)(^c.(^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. ------ 174990/19984458. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 174991/19984629. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a) b)((^y.y)((a a) a))) 6. ==[ alpha ]==> (((a a) b)((^x.x)((a a) a))) 7. ==[ beta ]==> (((a a) b)((a a) a)) REDUCED to normal form. ------ 174992/19984656. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))(a b))) REDUCED to normal form. ------ 174993/19984683. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) 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. ------ 174994/19984710. ------ 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 (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 174995/19984737. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a a)(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a a)(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(b a))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(b a))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(b a))) 7. ==[ beta ]==> ((a a)((a a)(b a))) REDUCED to normal form. ------ 174996/19984989. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (^a.a))(^c.(^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))) REDUCED to normal form. ------ 174997/19985268. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(^a.a))(^c.(^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. ------ 174998/19985340. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) 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. ------ 174999/19985538. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 175000/19985583. ------ 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))(^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.