Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 50001/3582141. ------ 1. ==[ start ]==> ((^a.(b a))(^b.(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)))) REDUCED to normal form. ------ 50002/3582846. ------ 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)(^y.y)) b) 4. ==[ alpha ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 50003/3582870. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50004/3582951. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50005/3583185. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50006/3583287. ------ 1. ==[ start ]==> (((a a)(^b.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 50007/3583455. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50008/3583575. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(b y))) 3. ==[ eta ]==> (((^x.x)(a (a a))) b) 4. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 50009/3583680. ------ 1. ==[ start ]==> ((^a.(^b.(^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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50010/3583806. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(b (^c.(^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)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50011/3583818. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^c.((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. ------ 50012/3584331. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> (a (^z.((z z)(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.((x x)(^y.y)))) REDUCED to normal form. ------ 50013/3584751. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(a b)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(a b)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 50014/3585138. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.((((^z.z) a)((^x1.x1)(^y1.y1)))(((^z.z) a)((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> (^x.((((^y.y) a)((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> (^x.((a ((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2))))) 6. ==[ alpha ]==> (^x.((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1))))) 7. ==[ beta ]==> (^x.((a (^z.z))(((^x1.x1) a)((^y1.y1)(^z1.z1))))) 8. ==[ alpha ]==> (^x.((a (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1))))) 9. ==[ beta ]==> (^x.((a (^y.y))(a ((^x1.x1)(^y1.y1))))) 10. ==[ alpha ]==> (^x.((a (^y.y))(a ((^z.z)(^x1.x1))))) 11. ==[ beta ]==> (^x.((a (^y.y))(a (^x1.x1)))) 12. ==[ alpha ]==> (^x.((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 50015/3585213. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 50016/3585345. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.a)((^x1.x1)(^y1.y1)))((^z.a)((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)((^z.z)(^x1.x1)))((^y1.a)((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> (((^y.a)((^z.z)(^x1.x1)))((^y1.a)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((^x.a)((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (a ((^x1.a)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> (a ((^x.a)((^y.y)(^z.z)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50017/3585600. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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. ------ 50018/3585942. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.((a a) a))) 3. ==[ beta ]==> ((((a a) a) a)(^y.((a a) a))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.((a a) a))) REDUCED to normal form. ------ 50019/3586020. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((^z.(z z))(^x1.a))((^z.(z z))(^x1.a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))(^y.a))((^z.(z z))(^x1.a)))(^y1.y1)) 5. ==[ beta ]==> ((((^y.a)(^y.a))((^z.(z z))(^x1.a)))(^y1.y1)) 6. ==[ alpha ]==> ((((^x.a)(^y.a))((^z.(z z))(^x1.a)))(^y1.y1)) 7. ==[ beta ]==> ((a ((^z.(z z))(^x1.a)))(^y1.y1)) 8. ==[ alpha ]==> ((a ((^x.(x x))(^y.a)))(^z.z)) 9. ==[ beta ]==> ((a ((^y.a)(^y.a)))(^z.z)) 10. ==[ alpha ]==> ((a ((^x.a)(^y.a)))(^z.z)) 11. ==[ beta ]==> ((a a)(^z.z)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 50020/3586392. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50021/3586536. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50022/3586671. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50023/3586776. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(a (a a)))) 3. ==[ eta ]==> (b ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 50024/3586779. ------ 1. ==[ start ]==> ((a (b a))(^b.(a (a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(a (a a)))) REDUCED to normal form. ------ 50025/3587148. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 50026/3587220. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.(a (^z.z)))) 3. ==[ beta ]==> (b (^y.(a (^z.z)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 50027/3587229. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.c)) REDUCED to normal form. ------ 50028/3587325. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50029/3587346. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50030/3587400. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 50031/3587427. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(a a))) REDUCED to normal form. ------ 50032/3587454. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^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. ------ 50033/3587481. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 50034/3587511. ------ 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 (^x.x))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 50035/3587538. ------ 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 ]==> (((^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. ------ 50036/3587565. ------ 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. ------ 50037/3587592. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 50038/3587646. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50039/3587682. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b a)(^y.y))) REDUCED to normal form. ------ 50040/3587709. ------ 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)))) REDUCED to normal form. ------ 50041/3587736. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.a))) REDUCED to normal form. ------ 50042/3587772. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 50043/3587790. ------ 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)(((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. ------ 50044/3587826. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^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)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 50045/3587871. ------ 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 (^x.x)) b)(a (^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(a a)))) REDUCED to normal form. ------ 50046/3587952. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a) a)) REDUCED to normal form. ------ 50047/3587979. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 50048/3588015. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 50049/3588042. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 50050/3588096. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 50051/3588186. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)(b ((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.x)(b ((a a)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 50052/3588213. ------ 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. ------ 50053/3588240. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a)(^x1.x1))(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. ------ 50054/3588249. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 50055/3588276. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 50056/3588294. ------ 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 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. ------ 50057/3588321. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 50058/3588447. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 50059/3588456. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50060/3588546. ------ 1. ==[ start ]==> (((a (a a)) b)((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a)) b)((a b)(^x.a))) REDUCED to normal form. ------ 50061/3588573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(y y)))) 5. ==[ beta ]==> (a (((a a) a)(^y.(y y)))) 6. ==[ alpha ]==> (a (((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 50062/3588600. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 50063/3588654. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((a (^x.a))(a (^z.b))) 6. ==[ alpha ]==> ((a (^x.a))(a (^y.b))) REDUCED to normal form. ------ 50064/3588681. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 50065/3588771. ------ 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))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 50066/3588798. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a a)((^y.b)(^z.a))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.a))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 50067/3588852. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.(^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)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 50068/3588915. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(c (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(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. ------ 50069/3588969. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(a ((a a)(^z.z)))) 5. ==[ beta ]==> (a (a ((a a)(^z.z)))) 6. ==[ alpha ]==> (a (a ((a a)(^x.x)))) REDUCED to normal form. ------ 50070/3589005. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a)) b)) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a)) b)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a)) b)) 5. ==[ beta ]==> (b ((^y.(a a)) b)) 6. ==[ alpha ]==> (b ((^x.(a a)) b)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 50071/3589032. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.b) c)) 2. ==[ alpha ]==> ((((a a) a) a)((^x.b) c)) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 50072/3589050. ------ 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. ------ 50073/3589077. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^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. ------ 50074/3589131. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) 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))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((a a) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((a a) a))) 9. ==[ beta ]==> ((a a)(a ((a a) a))) REDUCED to normal form. ------ 50075/3589230. ------ 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. ------ 50076/3589257. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 50077/3589311. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 50078/3589338. ------ 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))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 12. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 13. ==[ beta ]==> ((a (^x.x))(^z.z)) 14. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 50079/3589365. ------ 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) REDUCED to normal form. ------ 50080/3589383. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)((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. ------ 50081/3589392. ------ 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)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 50082/3589590. ------ 1. ==[ start ]==> (((^a.a)(a b))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(c ((a a) a))) 3. ==[ beta ]==> ((a b)(c ((a a) a))) REDUCED to normal form. ------ 50083/3589617. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((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. ------ 50084/3589653. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 50085/3589671. ------ 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 b)(a a))) REDUCED to normal form. ------ 50086/3589680. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.b) b)) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) b) REDUCED to normal form. ------ 50087/3589707. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a) c)) 5. ==[ beta ]==> ((^y.a)((^z.a) c)) 6. ==[ alpha ]==> ((^x.a)((^y.a) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50088/3589752. ------ 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. ------ 50089/3589779. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 50090/3589797. ------ 1. ==[ start ]==> (((a a)(a b))(c (^c.a))) 2. ==[ alpha ]==> (((a a)(a b))(c (^x.a))) REDUCED to normal form. ------ 50091/3589824. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(b (^y.b))) REDUCED to normal form. ------ 50092/3589851. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a (^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 50093/3589878. ------ 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. ------ 50094/3589932. ------ 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) 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. ------ 50095/3589950. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (a a))(^y.(y y)))) 3. ==[ beta ]==> (b ((a (a a))(^y.(y y)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 50096/3589959. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 50097/3589986. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 50098/3590211. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b ((a a) a))) 5. ==[ beta ]==> ((a a)(b ((a a) a))) REDUCED to normal form. ------ 50099/3590238. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(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. ------ 50100/3590247. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 50101/3590292. ------ 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)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 11. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 13. ==[ beta ]==> ((^y.y)(a (^z.z))) 14. ==[ alpha ]==> ((^x.x)(a (^y.y))) 15. ==[ beta ]==> (a (^y.y)) 16. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 50102/3590301. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 50103/3590373. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 50104/3590472. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(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. ------ 50105/3590499. ------ 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))((^z.z) a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> ((a ((a a) a))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((a ((a a) a))(a ((^y.y) a))) 8. ==[ alpha ]==> ((a ((a a) a))(a ((^x.x) a))) 9. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 50106/3590526. ------ 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)))) 5. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 50107/3590553. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 50108/3590580. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y)((a a) a))) 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. ------ 50109/3590598. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a) a)) 2. ==[ alpha ]==> (((^x.b) c)(((a a) a) a)) 3. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 50110/3590607. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 50111/3590634. ------ 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))(^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. ------ 50112/3590661. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 50113/3590697. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(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. ------ 50114/3590832. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 50115/3590841. ------ 1. ==[ start ]==> (((a b) c)((^b.a) d)) 2. ==[ alpha ]==> (((a b) c)((^x.a) d)) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 50116/3590949. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 50117/3590976. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a (^x.b))(a (^z.a))) 6. ==[ alpha ]==> ((a (^x.b))(a (^y.a))) REDUCED to normal form. ------ 50118/3591030. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50119/3591057. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(^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. ------ 50120/3591084. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a)) b)) REDUCED to normal form. ------ 50121/3591174. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 50122/3591282. ------ 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. ------ 50123/3591309. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 50124/3591336. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))(a a))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))(a a))) 5. ==[ beta ]==> (((a b) a)((a a)(a a))) REDUCED to normal form. ------ 50125/3591363. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 50126/3591390. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 50127/3591417. ------ 1. ==[ start ]==> ((a (b a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(a (a a)))) 3. ==[ beta ]==> ((a (b a))(a (a a))) REDUCED to normal form. ------ 50128/3591507. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b ((^z.z) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b ((^z.z) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b ((^z.z) a))) 5. ==[ beta ]==> (b (b ((^z.z) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 50129/3591588. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 50130/3591651. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (^y.y))) REDUCED to normal form. ------ 50131/3591696. ------ 1. ==[ start ]==> (((^a.a)(b a))(b c)) 2. ==[ alpha ]==> (((^x.x)(b a))(b c)) 3. ==[ beta ]==> ((b a)(b c)) REDUCED to normal form. ------ 50132/3591759. ------ 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)) REDUCED to normal form. ------ 50133/3591777. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b (a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b))(b (a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a b))(b (a (^x.x)))) REDUCED to normal form. ------ 50134/3591786. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a) c)) REDUCED to normal form. ------ 50135/3591840. ------ 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)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 50136/3591858. ------ 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 (^y.y)))) 4. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 50137/3591867. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) c)) 3. ==[ beta ]==> (((a b)(^x.(x x))) c) REDUCED to normal form. ------ 50138/3591894. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 50139/3591921. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 50140/3591966. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 50141/3591984. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 50142/3592011. ------ 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. ------ 50143/3592038. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(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)))) 5. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 50144/3592065. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(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. ------ 50145/3592092. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 50146/3592119. ------ 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)(^y.y))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 50147/3593850. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50148/3596055. ------ 1. ==[ start ]==> ((^a.(b a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(z z)))) 3. ==[ eta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 50149/3596940. ------ 1. ==[ start ]==> (((a a) b)(^c.(b a))) 2. ==[ alpha ]==> (((a a) b)(^x.(b a))) REDUCED to normal form. ------ 50150/3596958. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50151/3597036. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(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. ------ 50152/3597228. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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)) REDUCED to normal form. ------ 50153/3597507. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(b y))) 3. ==[ eta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 50154/3598254. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50155/3598494. ------ 1. ==[ start ]==> ((^a.(^a.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50156/3598497. ------ 1. ==[ start ]==> ((a (^a.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50157/3598674. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.y))(^z.b))) 3. ==[ beta ]==> (((a (^y.y))(^z.b)) b) 4. ==[ alpha ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 50158/3598938. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 50159/3599268. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)(^x1.(^y1.y1)))(((^z.z) a)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((^y.y) a)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 50160/3599523. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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. ------ 50161/3599532. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(z b))) REDUCED to normal form. ------ 50162/3600699. ------ 1. ==[ start ]==> ((^a.(b a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((a a)(^y.(y y)))) 3. ==[ eta ]==> (b ((a a)(^y.(y y)))) 4. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 50163/3600702. ------ 1. ==[ start ]==> ((a (b a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 50164/3601008. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(^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. ------ 50165/3601152. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 50166/3601248. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50167/3601269. ------ 1. ==[ start ]==> (((a a)(b a))(^c.b)) 2. ==[ alpha ]==> (((a a)(b a))(^x.b)) REDUCED to normal form. ------ 50168/3601323. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.b)) 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. ------ 50169/3601350. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 50170/3601404. ------ 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)(^y.y))(^z.a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.a)) REDUCED to normal form. ------ 50171/3601452. ------ 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)))) 5. ==[ beta ]==> (a (((a a) a)(^y.y))) 6. ==[ alpha ]==> (a (((a a) a)(^x.x))) REDUCED to normal form. ------ 50172/3601479. ------ 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)((^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. ------ 50173/3601506. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 50174/3601533. ------ 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 (a ((^y.y)(a a)))) 6. ==[ alpha ]==> (b (a ((^x.x)(a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 50175/3601560. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 50176/3601587. ------ 1. ==[ start ]==> (((a a) b)((a a)(b a))) REDUCED to normal form. ------ 50177/3601605. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50178/3601686. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(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. ------ 50179/3601704. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a b)(^y.(y y)))) REDUCED to normal form. ------ 50180/3601731. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 50181/3601767. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^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. ------ 50182/3601794. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 50183/3601848. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 50184/3601875. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 50185/3602037. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 9. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50186/3602064. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 50187/3602100. ------ 1. ==[ start ]==> ((((^a.a) a) b)(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a b)(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((a b)(c (a a))) REDUCED to normal form. ------ 50188/3602127. ------ 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. ------ 50189/3602154. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(a (b a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (b a))) REDUCED to normal form. ------ 50190/3602181. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 50191/3602208. ------ 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. ------ 50192/3602235. ------ 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))(^x.x))((a b) a)) REDUCED to normal form. ------ 50193/3602343. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 50194/3602388. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50195/3602469. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50196/3602550. ------ 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.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. ------ 50197/3602604. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.a)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)(a b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 50198/3602676. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 50199/3602703. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a) b)) REDUCED to normal form. ------ 50200/3602730. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b) c)) 3. ==[ beta ]==> ((a ((^y.y) a))((a b) c)) 4. ==[ alpha ]==> ((a ((^x.x) a))((a b) c)) 5. ==[ beta ]==> ((a a)((a b) c)) REDUCED to normal form. ------ 50201/3602847. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.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. ------ 50202/3602901. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 50203/3602937. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(a a))) 5. ==[ beta ]==> (b (((^y.y)(a a))(a a))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(a a))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 50204/3602964. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)(a (^x.x)))) REDUCED to normal form. ------ 50205/3603018. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (a a))) REDUCED to normal form. ------ 50206/3603045. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 50207/3603072. ------ 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. ------ 50208/3603099. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50209/3603126. ------ 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)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 50210/3603144. ------ 1. ==[ start ]==> ((a (^a.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 50211/3603162. ------ 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. ------ 50212/3603189. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 50213/3603216. ------ 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. ------ 50214/3603243. ------ 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)(^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. ------ 50215/3603270. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 50216/3603324. ------ 1. ==[ start ]==> ((a (a b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))((a (^x.x))(^y.b))) REDUCED to normal form. ------ 50217/3603333. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 50218/3603414. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 50219/3603495. ------ 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 ((^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. ------ 50220/3603522. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 50221/3603531. ------ 1. ==[ start ]==> (((a a)(^a.b))(c ((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(c ((a a) a))) REDUCED to normal form. ------ 50222/3603549. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((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. ------ 50223/3603585. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 50224/3603612. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a b)(a a))) REDUCED to normal form. ------ 50225/3603639. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(((a a) a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.a)(((a a) a)(a (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50226/3603666. ------ 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))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^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. ------ 50227/3603693. ------ 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. ------ 50228/3603810. ------ 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. ------ 50229/3603837. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> (a (((a a) a)(^y.(^z.z)))) 8. ==[ alpha ]==> (a (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 50230/3603864. ------ 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))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.a)) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.a)) REDUCED to normal form. ------ 50231/3603891. ------ 1. ==[ start ]==> (((a b)(a a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 50232/3603918. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^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. ------ 50233/3603927. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50234/3603954. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^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. ------ 50235/3604008. ------ 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)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 50236/3604089. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (b ((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 50237/3604152. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b ((a a) a))) REDUCED to normal form. ------ 50238/3604170. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 50239/3604179. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a (a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (a b))) REDUCED to normal form. ------ 50240/3604233. ------ 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)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 50241/3604260. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(y y))((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.(x x))((a (a a))((^y.y) a))) 7. ==[ beta ]==> (((a (a a))((^y.y) a))((a (a a))((^y.y) a))) 8. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (a a))((^y.y) a))) 9. ==[ beta ]==> (((a (a a)) a)((a (a a))((^y.y) a))) 10. ==[ alpha ]==> (((a (a a)) a)((a (a a))((^x.x) a))) 11. ==[ beta ]==> (((a (a a)) a)((a (a a)) a)) REDUCED to normal form. ------ 50242/3604287. ------ 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. ------ 50243/3604305. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 50244/3604314. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 50245/3604341. ------ 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. ------ 50246/3604377. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(^y.y))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 50247/3604404. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(^a.a))(^a.(^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. ------ 50248/3604431. ------ 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. ------ 50249/3604458. ------ 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.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.(z z)))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 50250/3604485. ------ 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. ------ 50251/3604539. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 50252/3604566. ------ 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))((^y.y) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 50253/3604629. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 50254/3604773. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)((^y.y) a))) 3. ==[ beta ]==> (((a b) c)(a ((^y.y) a))) 4. ==[ alpha ]==> (((a b) c)(a ((^x.x) a))) 5. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 50255/3604800. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 50256/3604827. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 50257/3604872. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a 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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50258/3604926. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 50259/3605007. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))(^a.a))) 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. ------ 50260/3605133. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(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. ------ 50261/3605160. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(y y)) b)) 3. ==[ beta ]==> ((a (a b))((^y.(y y)) b)) 4. ==[ alpha ]==> ((a (a b))((^x.(x x)) b)) 5. ==[ beta ]==> ((a (a b))(b b)) REDUCED to normal form. ------ 50262/3605187. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.a) c)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.a) c)) 3. ==[ beta ]==> (((a (a a))((a a) a)) a) REDUCED to normal form. ------ 50263/3605268. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a b) a)((a (a a))(^y.y))) 4. ==[ alpha ]==> (((a b) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 50264/3605295. ------ 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. ------ 50265/3605322. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 50266/3605349. ------ 1. ==[ start ]==> ((a (b a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 50267/3605439. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50268/3605520. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 50269/3605628. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^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. ------ 50270/3605655. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^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. ------ 50271/3605691. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (a a))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (a a))) REDUCED to normal form. ------ 50272/3605709. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 50273/3605718. ------ 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. ------ 50274/3605772. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 50275/3605790. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b (^a.(^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. ------ 50276/3605799. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 50277/3605826. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c a)) 3. ==[ beta ]==> (((a a)(^y.a))(c a)) 4. ==[ alpha ]==> (((a a)(^x.a))(c a)) REDUCED to normal form. ------ 50278/3605853. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b b)) REDUCED to normal form. ------ 50279/3605898. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 50280/3605916. ------ 1. ==[ start ]==> (((a a)(b a))((a a) b)) REDUCED to normal form. ------ 50281/3605943. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 50282/3605970. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y) b)) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 50283/3605997. ------ 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. ------ 50284/3606024. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a a) a)) 3. ==[ beta ]==> (((^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. ------ 50285/3606051. ------ 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)(^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. ------ 50286/3606077. ------ 1. ==[ start ]==> (^a.((a b)(a (a a)))) 2. ==[ alpha ]==> (^x.((x b)(x (x x)))) REDUCED to normal form. ------ 50287/3606078. ------ 1. ==[ start ]==> (a ((a b)(a (a a)))) REDUCED to normal form. ------ 50288/3610728. ------ 1. ==[ start ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 50289/3610734. ------ 1. ==[ start ]==> ((^a.a)((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.x)((a b)(a (a a)))) 3. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 50290/3610761. ------ 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)((^y.y)(^z.z)))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(^x.x))(((a a) a)(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 50291/3610788. ------ 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 REDUCED to normal form. ------ 50292/3610869. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^z.z))((a a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 50293/3610917. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 50294/3610986. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (^x.(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (^x.((a a)(^z.a))) 6. ==[ alpha ]==> (^x.((a a)(^y.a))) REDUCED to normal form. ------ 50295/3611187. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 a))) REDUCED to normal form. ------ 50296/3611229. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 50297/3611679. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50298/3612888. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 50299/3613482. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.z))) REDUCED to normal form. ------ 50300/3613833. ------ 1. ==[ start ]==> (((^a.b) c)(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)(^y.((a a) a))) 3. ==[ beta ]==> (b (^y.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 50301/3614292. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 50302/3614436. ------ 1. ==[ start ]==> (((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)))) 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))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 50303/3614886. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.(z z)))) REDUCED to normal form. ------ 50304/3615129. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 50305/3615198. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50306/3615246. ------ 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)))) REDUCED to normal form. ------ 50307/3615327. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((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. ------ 50308/3615354. ------ 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)(^y.y))(^z.(z z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 50309/3615381. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.a)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 50310/3615393. ------ 1. ==[ start ]==> ((a a)((a b)(a (a a)))) REDUCED to normal form. ------ 50311/3615420. ------ 1. ==[ start ]==> ((a (a a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 50312/3615447. ------ 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)((^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. ------ 50313/3615501. ------ 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. ------ 50314/3615528. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 50315/3615573. ------ 1. ==[ start ]==> (((a (^a.a)) a)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 50316/3615591. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((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. ------ 50317/3615618. ------ 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)(^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. ------ 50318/3615645. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^x.a))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 50319/3615681. ------ 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)((^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. ------ 50320/3615726. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 50321/3615753. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 50322/3615762. ------ 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 (^x.x)) b)((a b)(a b))) REDUCED to normal form. ------ 50323/3615789. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.a)((^a.a)(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) a) REDUCED to normal form. ------ 50324/3615816. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 50325/3615843. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b a)) REDUCED to normal form. ------ 50326/3615888. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 50327/3616059. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 50328/3616185. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 50329/3616230. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 50330/3616257. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 9. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 10. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 50331/3616284. ------ 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. ------ 50332/3616311. ------ 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. ------ 50333/3616338. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 50334/3616428. ------ 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))(^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. ------ 50335/3616437. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(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. ------ 50336/3616464. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)((^z.z) a))) 5. ==[ beta ]==> (a ((^y.b)((^z.z) a))) 6. ==[ alpha ]==> (a ((^x.b)((^y.y) a))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 50337/3616482. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(y y)))) 7. ==[ beta ]==> (((a a) a)(^y.(y y))) 8. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 50338/3616491. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 50339/3616509. ------ 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)(^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. ------ 50340/3616518. ------ 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.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. ------ 50341/3616545. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((a (^x.a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 50342/3616563. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.b))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.b))) REDUCED to normal form. ------ 50343/3616572. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.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. ------ 50344/3616599. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50345/3616941. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.b) c)) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b) c)) 3. ==[ beta ]==> (((a a) a)((^y.b) c)) 4. ==[ alpha ]==> (((a a) a)((^x.b) c)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 50346/3617085. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 50347/3617274. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)((a a) a))) 3. ==[ beta ]==> (b ((^y.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50348/3617292. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.b)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 50349/3617373. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b) b)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a b) b)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b) b)) IRREDUCIBLE: cycle. ------ 50350/3617436. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 50351/3617463. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(^y.(^z.z)))) 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. ------ 50352/3617490. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 50353/3617544. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 50354/3617562. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(a a)) a)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a)) a)) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 50355/3617688. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) 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. ------ 50356/3617715. ------ 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))) REDUCED to normal form. ------ 50357/3617742. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a a)(a b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a a)(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)(a b))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a b))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a b))) REDUCED to normal form. ------ 50358/3617841. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50359/3617886. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50360/3617913. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 50361/3617967. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((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. ------ 50362/3618057. ------ 1. ==[ start ]==> (((a b) b)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(x x))(^y.(y y)))) 3. ==[ beta ]==> (((a b) b)((^y.(y y))(^y.(y y)))) 4. ==[ alpha ]==> (((a b) b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 50363/3618084. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 50364/3618111. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^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. ------ 50365/3618138. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.b)) REDUCED to normal form. ------ 50366/3618273. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 50367/3618300. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 50368/3618489. ------ 1. ==[ start ]==> (((^a.b) c)((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 50369/3618723. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^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. ------ 50370/3618732. ------ 1. ==[ start ]==> (((a b) c)(d (^b.a))) 2. ==[ alpha ]==> (((a b) c)(d (^x.a))) REDUCED to normal form. ------ 50371/3618759. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c (^y.(y y)))) 3. ==[ beta ]==> (((a a) b)(c (^y.(y y)))) 4. ==[ alpha ]==> (((a a) b)(c (^x.(x x)))) REDUCED to normal form. ------ 50372/3618786. ------ 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. ------ 50373/3618831. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^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. ------ 50374/3618840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 50375/3618867. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.b))((a (^z.z))(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 50376/3618885. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) 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. ------ 50377/3618921. ------ 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.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50378/3618948. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 50379/3618966. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50380/3618975. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))(^a.a))) 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. ------ 50381/3619002. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^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. ------ 50382/3619029. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 50383/3619065. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 50384/3619092. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 50385/3619119. ------ 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. ------ 50386/3619146. ------ 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. ------ 50387/3619173. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) 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 (^x.x)) a) REDUCED to normal form. ------ 50388/3619200. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 50389/3619398. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z)) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z)) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z)) c)) 5. ==[ beta ]==> (b ((a (^z.z)) c)) 6. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 50390/3619479. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 50391/3619542. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (^y.(y y)))) REDUCED to normal form. ------ 50392/3619587. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 50393/3619614. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a 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. ------ 50394/3619650. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 50395/3619668. ------ 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)) REDUCED to normal form. ------ 50396/3619677. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^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. ------ 50397/3619731. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 50398/3619749. ------ 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50399/3619758. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 50400/3619785. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(a (^z.a))) 3. ==[ beta ]==> (((a a)(^y.a))(a (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.a))) REDUCED to normal form. ------ 50401/3619812. ------ 1. ==[ start ]==> ((((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 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. ------ 50402/3619857. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) a)) REDUCED to normal form. ------ 50403/3619875. ------ 1. ==[ start ]==> (((a a)(b a))(b (a a))) REDUCED to normal form. ------ 50404/3619902. ------ 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)))) REDUCED to normal form. ------ 50405/3619929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(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))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 50406/3619956. ------ 1. ==[ start ]==> (((a (a a))(a b))(b a)) REDUCED to normal form. ------ 50407/3619983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((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. ------ 50408/3620010. ------ 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)(^y.y))(a (a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (a a))) REDUCED to normal form. ------ 50409/3620037. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 50410/3621759. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50411/3624696. ------ 1. ==[ start ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 50412/3624720. ------ 1. ==[ start ]==> ((^a.(^a.a))((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. ------ 50413/3624801. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50414/3625452. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(b x1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.z) a)) b) 4. ==[ beta ]==> ((^y.y) b) 5. ==[ alpha ]==> ((^x.x) b) 6. ==[ beta ]==> b REDUCED to normal form. ------ 50415/3625530. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50416/3625956. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 50417/3626088. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2))))((^z2.(^x3.x3))(^y3.(^z3.z3)))) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))((^z2.(^x3.x3))(^y3.(^z3.z3)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50418/3626421. ------ 1. ==[ start ]==> ((^a.(^a.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50419/3626424. ------ 1. ==[ start ]==> ((a (^a.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.b))(^y.(a a))) REDUCED to normal form. ------ 50420/3626601. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((a a) a))) 3. ==[ beta ]==> (((^y.a)((a a) a)) b) 4. ==[ alpha ]==> (((^x.a)((a a) a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 50421/3626883. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 50422/3626988. ------ 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. ------ 50423/3627090. ------ 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. ------ 50424/3627195. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.(z z))(a (a a)))((^z.(z z))(a (a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y))(a (a a)))((^z.(z z))(a (a a))))) 5. ==[ beta ]==> (((^y.(y y))(a (a a)))((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y))(a (a a)))) 7. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y))(a (a a)))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(a (a a)))) 9. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 50425/3627657. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.b))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.b))) REDUCED to normal form. ------ 50426/3627810. ------ 1. ==[ start ]==> (((^a.b) c)(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 50427/3627819. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 50428/3627870. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1))(^y1.(^z1.z1)))((^z.(^x1.x1))(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2))))(^z2.z2)) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))(^z2.z2)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))(^z1.z1)) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50429/3628413. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50430/3628548. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50431/3628626. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ eta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50432/3629106. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.c)) 3. ==[ beta ]==> (((a a)(^y.a))(^z.c)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.c)) REDUCED to normal form. ------ 50433/3629223. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 50434/3629277. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50435/3629304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((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. ------ 50436/3629331. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 50437/3629358. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 50438/3629388. ------ 1. ==[ start ]==> ((a (^a.a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 50439/3629415. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 50440/3629442. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((a a)((^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. ------ 50441/3629469. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(a b))) REDUCED to normal form. ------ 50442/3629523. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50443/3629550. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(b a))) 3. ==[ beta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 50444/3629586. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 50445/3629613. ------ 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))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 50446/3629649. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 50447/3629667. ------ 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)((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. ------ 50448/3629676. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 50449/3629748. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(^y.b))) REDUCED to normal form. ------ 50450/3629775. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(a (^y.(a a)))) 6. ==[ alpha ]==> ((a a)(a (^x.(a a)))) REDUCED to normal form. ------ 50451/3629802. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 50452/3629856. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b a) a)) 3. ==[ beta ]==> ((a (^y.y))((b a) a)) 4. ==[ alpha ]==> ((a (^x.x))((b a) a)) REDUCED to normal form. ------ 50453/3629919. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 50454/3629946. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 50455/3630090. ------ 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. ------ 50456/3630117. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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. ------ 50457/3630171. ------ 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 (^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. ------ 50458/3630180. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a)) c)) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 50459/3630198. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 50460/3630333. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50461/3630360. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a a)((a a)(^x1.x1)))) 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. ------ 50462/3630423. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 50463/3630450. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 50464/3630477. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 50465/3630504. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 50466/3630531. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.a))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.a))((a (a a))(^y.a))) REDUCED to normal form. ------ 50467/3630558. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 50468/3630585. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(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. ------ 50469/3630621. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 50470/3630675. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 50471/3630702. ------ 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. ------ 50472/3630756. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 50473/3630846. ------ 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)))) 7. ==[ beta ]==> (a (b (a a))) REDUCED to normal form. ------ 50474/3630882. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^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. ------ 50475/3630909. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a)) b)) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 50476/3630927. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((a a) a)((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((a a) a)((a b)(a (^x.x)))) REDUCED to normal form. ------ 50477/3630954. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a) a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^y1.y1) 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. ------ 50478/3630963. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a) d)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a) d)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 50479/3631008. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((a (a a))((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a a)((a (a a))((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a a)((a (a a))(^y.y))) 10. ==[ alpha ]==> ((a a)((a (a a))(^x.x))) REDUCED to normal form. ------ 50480/3631089. ------ 1. ==[ start ]==> ((a (^a.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.b))((a a)(a a))) REDUCED to normal form. ------ 50481/3631134. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 50482/3631161. ------ 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. ------ 50483/3631215. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 50484/3631242. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 10. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 50485/3631260. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 50486/3631269. ------ 1. ==[ start ]==> ((a (a b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((a a) a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 50487/3631548. ------ 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 ((^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. ------ 50488/3631557. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 50489/3631584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.b) b)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b) b)) 5. ==[ beta ]==> ((^y.a)((^z.b) b)) 6. ==[ alpha ]==> ((^x.a)((^y.b) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50490/3631629. ------ 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 (((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50491/3631656. ------ 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. ------ 50492/3631728. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b (^x1.b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b (^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (^z.b))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.b))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.b))) REDUCED to normal form. ------ 50493/3631755. ------ 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. ------ 50494/3631782. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.b)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.b)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(a a))) 5. ==[ beta ]==> (((^y.y) a)((^z.b)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.b)(a a))) 7. ==[ beta ]==> (a ((^y.b)(a a))) 8. ==[ alpha ]==> (a ((^x.b)(a a))) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 50495/3631827. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 50496/3631836. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 50497/3631863. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> ((a (a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 50498/3632115. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b ((a a) a))) 3. ==[ beta ]==> ((^y.y)(b ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 50499/3632169. ------ 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)(^z.z))((^y.y)(^z.z)))(((a a) a)(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(a a))) 9. ==[ beta ]==> ((^y.y)(((a a) a)(a a))) 10. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 11. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 50500/3632178. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 50501/3632205. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z)) c)) 7. ==[ beta ]==> (((^y.(^z.z)) c)((^y.(^z.z)) c)) 8. ==[ alpha ]==> (((^x.(^y.y)) c)((^z.(^x1.x1)) c)) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 11. ==[ beta ]==> ((^y.(^z.z)) c) 12. ==[ alpha ]==> ((^x.(^y.y)) c) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50502/3632250. ------ 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. ------ 50503/3632322. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(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. ------ 50504/3632349. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 50505/3632376. ------ 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 (^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)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 50506/3632403. ------ 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 z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((a (a a))(^x.x))(a ((^z.z) a))) 8. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y) a))) 9. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 50507/3632430. ------ 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)))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 50508/3632457. ------ 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) 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. ------ 50509/3632475. ------ 1. ==[ start ]==> (((^a.b) c)((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)((a a)(^y.a))) 3. ==[ beta ]==> (b ((a a)(^y.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 50510/3632484. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a) a)) REDUCED to normal form. ------ 50511/3632538. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 50512/3632709. ------ 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. ------ 50513/3632718. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a)) c)) 2. ==[ alpha ]==> (((a b) c)((^x.(x x)) c)) 3. ==[ beta ]==> (((a b) c)(c c)) REDUCED to normal form. ------ 50514/3632790. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 50515/3632826. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 50516/3632853. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 50517/3632907. ------ 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 (^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50518/3632934. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 50519/3632961. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y) a)) 5. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 50520/3632988. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a)) b)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 50521/3633051. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(^x1.(x1 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. ------ 50522/3633078. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(^x1.(^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. ------ 50523/3633186. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 50524/3633213. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(a (^b.(^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. ------ 50525/3633240. ------ 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))(a a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))(a a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 50526/3633267. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 50527/3633294. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 50528/3633384. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c (a (^z.z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(c (a (^z.z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c (a (^z.z)))) 5. ==[ beta ]==> (b (c (a (^z.z)))) 6. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 50529/3633465. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 50530/3633573. ------ 1. ==[ start ]==> (((^a.a)(b a))(c b)) 2. ==[ alpha ]==> (((^x.x)(b a))(c b)) 3. ==[ beta ]==> ((b a)(c b)) REDUCED to normal form. ------ 50531/3633600. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(b c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(b c)) 3. ==[ beta ]==> ((^y.y)(b c)) 4. ==[ alpha ]==> ((^x.x)(b c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 50532/3633636. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) 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. ------ 50533/3633654. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (a a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (a a))) 3. ==[ beta ]==> (((a b)(a b))(c (a a))) REDUCED to normal form. ------ 50534/3633663. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y)) b)) REDUCED to normal form. ------ 50535/3633717. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 50536/3633735. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.y))(a a))) 3. ==[ beta ]==> (b ((a (^y.y))(a a))) 4. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 50537/3633744. ------ 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)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 50538/3633771. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z) c)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) c)) 5. ==[ beta ]==> (((a a)(^x.a)) c) REDUCED to normal form. ------ 50539/3633798. ------ 1. ==[ start ]==> ((((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.y1))) REDUCED to normal form. ------ 50540/3633861. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 50541/3633888. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 50542/3633915. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (^a.a))) 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. ------ 50543/3633942. ------ 1. ==[ start ]==> (((a (a a))(a b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 50544/3633969. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(a a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 50545/3633996. ------ 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)(^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. ------ 50546/3634023. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 50547/3638508. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50548/3638691. ------ 1. ==[ start ]==> (((a b)(a (a a))) c) REDUCED to normal form. ------ 50549/3638916. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 50550/3638967. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(^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)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50551/3639039. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a) a)(^z.(^x1.x1)))) 3. ==[ eta ]==> ((^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. ------ 50552/3639465. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(b z))) 3. ==[ eta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 50553/3640221. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((y y)(^z.z)))) 5. ==[ beta ]==> (b (^y.((y y)(^z.z)))) 6. ==[ alpha ]==> (b (^x.((x x)(^y.y)))) REDUCED to normal form. ------ 50554/3640425. ------ 1. ==[ start ]==> ((^a.(^a.b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(b (^z.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50555/3640605. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)(^z.a))) 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) REDUCED to normal form. ------ 50556/3640887. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^b.(^b.(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. ------ 50557/3640896. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 50558/3641199. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a (a a))(^z.(z z)))((a (a a))(^z.(z z))))) 4. ==[ alpha ]==> ((^x.x)(((a (a a))(^y.(y y)))((a (a a))(^z.(z z))))) 5. ==[ beta ]==> (((a (a a))(^y.(y y)))((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 50559/3641292. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.(x x))(^y.(^z.z))) a) 4. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z))) a) 5. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) a) 6. ==[ beta ]==> ((^y.y) a) 7. ==[ alpha ]==> ((^x.x) a) 8. ==[ beta ]==> a REDUCED to normal form. ------ 50560/3641823. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 50561/3641874. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((((^z.z)(^x1.x1)) b)(((^z.z)(^x1.x1)) b))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1)) b))(^y1.y1)) 5. ==[ beta ]==> ((((^y.y) b)(((^z.z)(^x1.x1)) b))(^y1.y1)) 6. ==[ alpha ]==> ((((^x.x) b)(((^y.y)(^z.z)) b))(^x1.x1)) 7. ==[ beta ]==> ((b (((^y.y)(^z.z)) b))(^x1.x1)) 8. ==[ alpha ]==> ((b (((^x.x)(^y.y)) b))(^z.z)) 9. ==[ beta ]==> ((b ((^y.y) b))(^z.z)) 10. ==[ alpha ]==> ((b ((^x.x) b))(^y.y)) 11. ==[ beta ]==> ((b b)(^y.y)) 12. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 50562/3642291. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^b.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 50563/3642630. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))(^z.a))) 3. ==[ eta ]==> (b ((a (^y.y))(^z.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 50564/3642867. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^y.a)) REDUCED to normal form. ------ 50565/3643056. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.((^a.a) a))) 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. ------ 50566/3643110. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 50567/3643179. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50568/3643182. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a (^y1.y1)))) REDUCED to normal form. ------ 50569/3643281. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.b)) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 50570/3643362. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.a)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.a)) REDUCED to normal form. ------ 50571/3643410. ------ 1. ==[ start ]==> (((^a.a) a)((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x) a)((a b)(a (a a)))) 3. ==[ beta ]==> (a ((a b)(a (a a)))) REDUCED to normal form. ------ 50572/3643437. ------ 1. ==[ start ]==> (((a a) a)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 50573/3643464. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 50574/3643491. ------ 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. ------ 50575/3643518. ------ 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))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 50576/3643545. ------ 1. ==[ start ]==> (((a a) b)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 50577/3643572. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(b a))) REDUCED to normal form. ------ 50578/3643590. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 50579/3643644. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 50580/3643662. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 50581/3643689. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a b)(^y.(y y)))) REDUCED to normal form. ------ 50582/3643716. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 50583/3643725. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 50584/3643752. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50585/3643806. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> (a ((^y.a)((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((^x.a)((^y.y)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50586/3643833. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50587/3643905. ------ 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) a)(((a a)(^y.y)) b)) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 50588/3644022. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50589/3644076. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(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. ------ 50590/3644112. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 50591/3644139. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (b a))) REDUCED to normal form. ------ 50592/3644166. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 50593/3644193. ------ 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 (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a a)(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 50594/3644301. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (a a))((a a) a))) 3. ==[ beta ]==> ((b b)((a (a a))((a a) a))) REDUCED to normal form. ------ 50595/3644346. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50596/3644373. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 50597/3644481. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z) a))) 7. ==[ beta ]==> ((^y.b)((^z.z) a)) 8. ==[ alpha ]==> ((^x.b)((^y.y) a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 50598/3644562. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 50599/3644661. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 50600/3644688. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((a a)(((^y.y)(a a)) b)) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a)) b)) 7. ==[ beta ]==> ((a a)((a a) b)) REDUCED to normal form. ------ 50601/3644715. ------ 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. ------ 50602/3644805. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.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. ------ 50603/3644859. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 50604/3644895. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(a ((a a)(^y.y)))) 5. ==[ beta ]==> (b (a ((a a)(^y.y)))) 6. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 50605/3644922. ------ 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. ------ 50606/3644976. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a) a)) REDUCED to normal form. ------ 50607/3645003. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.(x x)))(a (a a))) REDUCED to normal form. ------ 50608/3645030. ------ 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)))) 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. ------ 50609/3645057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) 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. ------ 50610/3645084. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 50611/3645102. ------ 1. ==[ start ]==> ((a (^a.b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(b (^y.(a a)))) REDUCED to normal form. ------ 50612/3645147. ------ 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 a))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 50613/3645174. ------ 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. ------ 50614/3645201. ------ 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))) 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. ------ 50615/3645228. ------ 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)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 9. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 10. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 50616/3645255. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 50617/3645282. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> ((a (a b))(a (^y.a))) 4. ==[ alpha ]==> ((a (a b))(a (^x.a))) REDUCED to normal form. ------ 50618/3645291. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((a a) a))) 3. ==[ beta ]==> ((^y.b)((^z.a)((a a) a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((a a) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 50619/3645372. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.x1))) IRREDUCIBLE: cycle. ------ 50620/3645453. ------ 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 ((^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. ------ 50621/3645480. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 50622/3645507. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((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. ------ 50623/3645543. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^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. ------ 50624/3645561. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (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. ------ 50625/3645570. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 50626/3645597. ------ 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 REDUCED to normal form. ------ 50627/3645624. ------ 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 (^z.z)))) REDUCED to normal form. ------ 50628/3645651. ------ 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. ------ 50629/3645795. ------ 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. ------ 50630/3645822. ------ 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)))) REDUCED to normal form. ------ 50631/3645849. ------ 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))((^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. ------ 50632/3645876. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))(^y.(y y)))) 3. ==[ beta ]==> ((a (a a))((a (a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a (a a))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 50633/3645885. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50634/3645912. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50635/3645966. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a b))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(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. ------ 50636/3646047. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50637/3646101. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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. ------ 50638/3646110. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 50639/3646128. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^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. ------ 50640/3646137. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b ((a a) a))) REDUCED to normal form. ------ 50641/3646191. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 50642/3646218. ------ 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)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((((^y.y)(^z.z))(a (^x1.x1)))(((^y.y)(^z.z))(a (^x1.x1)))) 8. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 9. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 10. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 11. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 12. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a (^x1.x1)))) 13. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.x1)))) 14. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 15. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 16. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 50643/3646245. ------ 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))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a (a a)) a)) REDUCED to normal form. ------ 50644/3646272. ------ 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. ------ 50645/3646299. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 50646/3646362. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a) a)(^y.y))) REDUCED to normal form. ------ 50647/3646389. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a) a))((^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. ------ 50648/3646416. ------ 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))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 50649/3646443. ------ 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)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) 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. ------ 50650/3646470. ------ 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)))) 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. ------ 50651/3646497. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 50652/3646524. ------ 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. ------ 50653/3646551. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y) b)) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 50654/3646587. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 50655/3646731. ------ 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. ------ 50656/3646758. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> (((a a) b)(a ((^y.y) a))) 6. ==[ alpha ]==> (((a a) b)(a ((^x.x) a))) 7. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 50657/3646785. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 50658/3646803. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 50659/3646884. ------ 1. ==[ start ]==> (((^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.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 50660/3646920. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c d)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c d)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c d)) 5. ==[ beta ]==> ((^y.(^z.z))(c d)) 6. ==[ alpha ]==> ((^x.(^y.y))(c d)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50661/3646965. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 50662/3647118. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^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. ------ 50663/3647145. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(x x)) b)) 3. ==[ beta ]==> (((a (a a))((a a) a))(b b)) REDUCED to normal form. ------ 50664/3647172. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a) c)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a) c)) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a) c)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) c)) 7. ==[ beta ]==> ((^y.y)((^z.a) c)) 8. ==[ alpha ]==> ((^x.x)((^y.a) c)) 9. ==[ beta ]==> ((^y.a) c) 10. ==[ alpha ]==> ((^x.a) c) 11. ==[ beta ]==> a REDUCED to normal form. ------ 50665/3647253. ------ 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))(^z.z))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 50666/3647280. ------ 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)(^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. ------ 50667/3647307. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 50668/3647397. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50669/3647541. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a) a)) REDUCED to normal form. ------ 50670/3647586. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.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) REDUCED to normal form. ------ 50671/3647613. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50672/3647667. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.y))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 50673/3647676. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (a a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (a a))) REDUCED to normal form. ------ 50674/3647730. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 50675/3647748. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c (^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 50676/3647757. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 50677/3647784. ------ 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)))) REDUCED to normal form. ------ 50678/3647856. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 50679/3647874. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x)) a)) REDUCED to normal form. ------ 50680/3647901. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a) b)) REDUCED to normal form. ------ 50681/3647928. ------ 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. ------ 50682/3647955. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a) b)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x) b)) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 50683/3647982. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a a)(^z.z))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a a)(^y.y))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 50684/3648009. ------ 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)(^y.y))((a a) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a) a)) REDUCED to normal form. ------ 50685/3648036. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x) a)) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 50686/3648062. ------ 1. ==[ start ]==> (^a.(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (^x.(((^y.y)(x x))((^z.z) x))) 3. ==[ beta ]==> (^x.((x x)((^z.z) x))) 4. ==[ alpha ]==> (^x.((x x)((^y.y) x))) 5. ==[ beta ]==> (^x.((x x) x)) REDUCED to normal form. ------ 50687/3648063. ------ 1. ==[ start ]==> (a (((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (a (((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> (a ((a a)((^y.y) a))) 4. ==[ alpha ]==> (a ((a a)((^x.x) a))) 5. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 50688/3652740. ------ 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) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 50689/3652746. ------ 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)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 50690/3652773. ------ 1. ==[ start ]==> ((^a.(a a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x x))((a b)(a (a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))((a b)(a (a a)))) REDUCED to normal form. ------ 50691/3652800. ------ 1. ==[ start ]==> ((^a.b)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 50692/3652881. ------ 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) a)((^x1.x1)(a a)))(^y.y)) 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. ------ 50693/3652956. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 50694/3652998. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 50695/3653226. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(b 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))) REDUCED to normal form. ------ 50696/3653241. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b a) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b a) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 50697/3653565. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50698/3653691. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50699/3654252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50700/3654927. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 50701/3655323. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.b))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.b))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 7. ==[ beta ]==> (^y.(^z.b)) 8. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 50702/3656196. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.z))) REDUCED to normal form. ------ 50703/3656322. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50704/3656331. ------ 1. ==[ start ]==> (((a b)(^b.a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 50705/3656475. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^a.((^a.a)(^a.a)))) 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))(^x.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 50706/3656583. ------ 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)))) REDUCED to normal form. ------ 50707/3656661. ------ 1. ==[ start ]==> ((^a.(b a))(c c)) 2. ==[ alpha ]==> ((^x.(b x))(c c)) 3. ==[ eta ]==> (b (c c)) REDUCED to normal form. ------ 50708/3657006. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^b.((^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)))(^y.a)) REDUCED to normal form. ------ 50709/3657087. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 50710/3657168. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.x1))) REDUCED to normal form. ------ 50711/3657210. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50712/3657231. ------ 1. ==[ start ]==> (((a a)(b a))(^a.c)) 2. ==[ alpha ]==> (((a a)(b a))(^x.c)) REDUCED to normal form. ------ 50713/3657285. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(y (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a (a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 50714/3657312. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(a a))) REDUCED to normal form. ------ 50715/3657366. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.b)) REDUCED to normal form. ------ 50716/3657393. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 50717/3657420. ------ 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)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 50718/3657432. ------ 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)((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. ------ 50719/3657459. ------ 1. ==[ start ]==> ((a (a a))((a b)(a (a a)))) REDUCED to normal form. ------ 50720/3657486. ------ 1. ==[ start ]==> ((a b)(((a a) a)((^a.a)(^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. ------ 50721/3657540. ------ 1. ==[ start ]==> (((a a)(a a))((a (a a))(a b))) REDUCED to normal form. ------ 50722/3657567. ------ 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)))) 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. ------ 50723/3657585. ------ 1. ==[ start ]==> (((a a) b)(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 50724/3657639. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 50725/3657657. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 50726/3657684. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 50727/3657720. ------ 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)((^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. ------ 50728/3657765. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 50729/3657801. ------ 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 (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 50730/3657828. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y y))(a b))) 3. ==[ beta ]==> ((a a)((^y.(y y))(a b))) 4. ==[ alpha ]==> ((a a)((^x.(x x))(a b))) 5. ==[ beta ]==> ((a a)((a b)(a b))) REDUCED to normal form. ------ 50731/3657846. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (a (((^y.y) a)(^z.(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. ------ 50732/3657855. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 50733/3657882. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 50734/3657909. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(b a))) 5. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 50735/3657927. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b a) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((b a) a)) REDUCED to normal form. ------ 50736/3658017. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a a)((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((a a)((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 50737/3658098. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((a b)((^y.b)(^y.b))) 6. ==[ alpha ]==> ((a b)((^x.b)(^y.b))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 50738/3658125. ------ 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) a) REDUCED to normal form. ------ 50739/3658251. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 50740/3658269. ------ 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. ------ 50741/3658296. ------ 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. ------ 50742/3658323. ------ 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)(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (a (^x.x)))((^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. ------ 50743/3658350. ------ 1. ==[ start ]==> (((a (a a))(a a))((a (a a))((a a) a))) REDUCED to normal form. ------ 50744/3658377. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a b))) 5. ==[ beta ]==> ((a (^x.x))(a (a b))) REDUCED to normal form. ------ 50745/3658467. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 50746/3658476. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 50747/3658503. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) 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 a)) REDUCED to normal form. ------ 50748/3658521. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 7. ==[ beta ]==> ((a b)(^y.a)) 8. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 50749/3658530. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 50750/3658548. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^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. ------ 50751/3658584. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 50752/3658611. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 50753/3658638. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> ((^y.y)((^z.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 REDUCED to normal form. ------ 50754/3658935. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 50755/3658980. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a) a)((^y.(a a)) b)) 4. ==[ alpha ]==> (((a a) a)((^x.(a a)) b)) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 50756/3659007. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.b) c)) 3. ==[ beta ]==> ((^y.y)((^y1.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. ------ 50757/3659160. ------ 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. ------ 50758/3659313. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 50759/3659331. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 50760/3659412. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a)) a)) IRREDUCIBLE: cycle. ------ 50761/3659475. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 50762/3659502. ------ 1. ==[ start ]==> (((a b) a)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 50763/3659529. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.(^x1.x1))(^z.(^x1.x1)))) 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. ------ 50764/3659583. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^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. ------ 50765/3659610. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 50766/3659682. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.a) c)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a) c)) 3. ==[ beta ]==> (b ((^y.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50767/3659727. ------ 1. ==[ start ]==> (((a a)(a b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 50768/3659754. ------ 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)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(a (^y.y))) REDUCED to normal form. ------ 50769/3659781. ------ 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 (^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))((a a) a))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 50770/3659808. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a a)(a b))) REDUCED to normal form. ------ 50771/3659880. ------ 1. ==[ start ]==> (((^a.b) b)((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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) REDUCED to normal form. ------ 50772/3659925. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.(a a))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.(a a))((a (a a))(^y.(y y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 50773/3659952. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^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. ------ 50774/3660006. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)(^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.b))) 5. ==[ beta ]==> ((^y.y)((a a)(^y1.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. ------ 50775/3660087. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) c)) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1)) c)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) c)) 5. ==[ beta ]==> (b ((^y.y) c)) 6. ==[ alpha ]==> (b ((^x.x) c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 50776/3660096. ------ 1. ==[ start ]==> (((a b) b)((^b.(^a.a))(^b.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. ------ 50777/3660123. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 50778/3660150. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a)(^b.(^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. ------ 50779/3660177. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^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. ------ 50780/3660222. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.b) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.b) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b) a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b) a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b) a)) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) a)) 9. ==[ beta ]==> ((^y.y)((^z.b) a)) 10. ==[ alpha ]==> ((^x.x)((^y.b) a)) 11. ==[ beta ]==> ((^y.b) a) 12. ==[ alpha ]==> ((^x.b) a) 13. ==[ beta ]==> b REDUCED to normal form. ------ 50781/3660375. ------ 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. ------ 50782/3660528. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^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. ------ 50783/3660627. ------ 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)) c)) 4. ==[ alpha ]==> ((^x.x)((a (a a)) c)) 5. ==[ beta ]==> ((a (a a)) c) REDUCED to normal form. ------ 50784/3660762. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 50785/3660879. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(a (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (^z.a))) REDUCED to normal form. ------ 50786/3660906. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 50787/3660924. ------ 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))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 50788/3660960. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50789/3660987. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(a (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. ------ 50790/3661005. ------ 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 ((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 50791/3661014. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 50792/3661041. ------ 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))(^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. ------ 50793/3661068. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 50794/3661131. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(b (a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(b (a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (a (a a)))) REDUCED to normal form. ------ 50795/3661158. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(a ((^a.a)(^a.a)))) 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)))) 5. ==[ beta ]==> ((a (a b))(a (^y.y))) 6. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 50796/3661185. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (a a))(a a))) REDUCED to normal form. ------ 50797/3661212. ------ 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 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 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. ------ 50798/3661239. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a (^x.x))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 50799/3661266. ------ 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. ------ 50800/3661347. ------ 1. ==[ start ]==> ((a (b a))(c c)) REDUCED to normal form. ------ 50801/3661437. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) a) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) a) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a) b)) 5. ==[ beta ]==> (b (((^z.z) a) b)) 6. ==[ alpha ]==> (b (((^x.x) a) b)) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 50802/3661518. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 50803/3661581. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (^y.a))) REDUCED to normal form. ------ 50804/3661626. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((b a)(a (^y.y))) 6. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 50805/3661653. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^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. ------ 50806/3661689. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 50807/3661707. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) 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. ------ 50808/3661716. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 50809/3661770. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.a)(^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. ------ 50810/3661788. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a) a)) 3. ==[ beta ]==> (b ((^y.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 50811/3661797. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (^y.y))) REDUCED to normal form. ------ 50812/3661824. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 50813/3661851. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.a))) REDUCED to normal form. ------ 50814/3661896. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 50815/3661914. ------ 1. ==[ start ]==> (((a a)(b a))(a c)) REDUCED to normal form. ------ 50816/3661941. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (a a))) REDUCED to normal form. ------ 50817/3661968. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(a (a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(a (a (^y.y)))) 5. ==[ beta ]==> ((a (a a))(a (a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(a (a (^x.x)))) REDUCED to normal form. ------ 50818/3661995. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)(a a))) REDUCED to normal form. ------ 50819/3662022. ------ 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. ------ 50820/3662049. ------ 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)(^y.y))(a b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a b)) REDUCED to normal form. ------ 50821/3662076. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (a a))) REDUCED to normal form. ------ 50822/3662103. ------ 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. ------ 50823/3666789. ------ 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) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 50824/3666813. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50825/3666894. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50826/3667128. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.b)(a (a a)))) 3. ==[ eta ]==> ((^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. ------ 50827/3667398. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.b)(^x1.(x1 x1)))((^y1.b)(^z1.(z1 z1))))) 5. ==[ beta ]==> (b (((^z.b)(^x1.(x1 x1)))((^y1.b)(^z1.(z1 z1))))) 6. ==[ alpha ]==> (b (((^x.b)(^y.(y y)))((^z.b)(^x1.(x1 x1))))) 7. ==[ beta ]==> (b (b ((^z.b)(^x1.(x1 x1))))) 8. ==[ alpha ]==> (b (b ((^x.b)(^y.(y y))))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 50828/3667623. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 50829/3668076. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 50830/3668514. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))(a b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50831/3668694. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))((^z.z)(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z))) b) 5. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z))) b) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1))) b) 7. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1))) b) 8. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z))) b) 9. ==[ beta ]==> (((^y.y)(^z.z)) b) 10. ==[ alpha ]==> (((^x.x)(^y.y)) b) 11. ==[ beta ]==> ((^y.y) b) 12. ==[ alpha ]==> ((^x.x) b) 13. ==[ beta ]==> b REDUCED to normal form. ------ 50832/3669081. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.((((^z.z)(^x1.x1))((^y1.y1) a))(((^z.z)(^x1.x1))((^y1.y1) a)))) 4. ==[ alpha ]==> (^x.((((^y.y)(^z.z))((^x1.x1) a))(((^y1.y1)(^z1.z1))((^x2.x2) a)))) 5. ==[ beta ]==> (^x.(((^z.z)((^x1.x1) a))(((^y1.y1)(^z1.z1))((^x2.x2) a)))) 6. ==[ alpha ]==> (^x.(((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a)))) 7. ==[ beta ]==> (^x.(((^z.z) a)(((^x1.x1)(^y1.y1))((^z1.z1) a)))) 8. ==[ alpha ]==> (^x.(((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) a)))) 9. ==[ beta ]==> (^x.(a (((^z.z)(^x1.x1))((^y1.y1) a)))) 10. ==[ alpha ]==> (^x.(a (((^y.y)(^z.z))((^x1.x1) a)))) 11. ==[ beta ]==> (^x.(a ((^z.z)((^x1.x1) a)))) 12. ==[ alpha ]==> (^x.(a ((^y.y)((^z.z) a)))) 13. ==[ beta ]==> (^x.(a ((^z.z) a))) 14. ==[ alpha ]==> (^x.(a ((^y.y) a))) 15. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 50833/3669210. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(y y)))) 7. ==[ beta ]==> (a (^y.(^z.(y y)))) 8. ==[ alpha ]==> (a (^x.(^y.(x x)))) REDUCED to normal form. ------ 50834/3669288. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((^y1.y1) a))((^z.(^x1.x1))((^y1.y1) a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1) a))((^y1.(^z1.z1))((^x2.x2) a)))) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) a))((^y1.(^z1.z1))((^x2.x2) a))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))((^z1.z1) a))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50835/3669597. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(x1 b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(y1 b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(y1 b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 b))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z b))) 9. ==[ beta ]==> ((^y.y)(^z.(z b))) 10. ==[ alpha ]==> ((^x.x)(^y.(y b))) 11. ==[ beta ]==> (^y.(y b)) 12. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 50836/3669777. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.b))) REDUCED to normal form. ------ 50837/3669939. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(^y.((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(^y.((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))(^x.((a a) a))) REDUCED to normal form. ------ 50838/3670389. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50839/3670533. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50840/3670668. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50841/3670719. ------ 1. ==[ start ]==> ((^a.(b a))((^b.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) REDUCED to normal form. ------ 50842/3670893. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(z (z z)))) 3. ==[ beta ]==> (b (^z.(z (z z)))) 4. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 50843/3671064. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 50844/3671145. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 50845/3671163. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^a.((^a.a) a))) 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. ------ 50846/3671226. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.c)) REDUCED to normal form. ------ 50847/3671268. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50848/3671289. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 50849/3671343. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 50850/3671397. ------ 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. ------ 50851/3671424. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^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. ------ 50852/3671451. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 50853/3671478. ------ 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))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 50854/3671508. ------ 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))((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. ------ 50855/3671535. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((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. ------ 50856/3671562. ------ 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. ------ 50857/3671589. ------ 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))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 50858/3671643. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((^y1.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. ------ 50859/3671670. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 50860/3671697. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(b a))) 3. ==[ beta ]==> ((a (^y.y))((a a)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(b a))) REDUCED to normal form. ------ 50861/3671733. ------ 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. ------ 50862/3671787. ------ 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)(((^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. ------ 50863/3671796. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 50864/3671823. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.b)(a (a a)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 50865/3671868. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.a)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.a)) REDUCED to normal form. ------ 50866/3671895. ------ 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. ------ 50867/3671922. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 50868/3672066. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 50869/3672093. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 50870/3672237. ------ 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)(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. ------ 50871/3672291. ------ 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)(^y.y))(a a))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 50872/3672318. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 50873/3672453. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50874/3672480. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 50875/3672543. ------ 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. ------ 50876/3672570. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (a ((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> (a ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 50877/3672597. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 50878/3672624. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 50879/3672651. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 50880/3672705. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.b))) 7. ==[ beta ]==> (((^y.y) a)(^z.b)) 8. ==[ alpha ]==> (((^x.x) a)(^y.b)) 9. ==[ beta ]==> (a (^y.b)) 10. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 50881/3672741. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 50882/3672768. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)(^y.y))) REDUCED to normal form. ------ 50883/3672822. ------ 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. ------ 50884/3672849. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a a)((^y.b)(^z.a))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.a))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 50885/3672966. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c (a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c (a b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c (a b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c (a b))) 5. ==[ beta ]==> (a (c (a b))) REDUCED to normal form. ------ 50886/3673047. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(a a))) 5. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 50887/3673074. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (^y1.y1)))) 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. ------ 50888/3673083. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 50889/3673128. ------ 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)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(a (a a)))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a (a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (a a)))) 9. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 10. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 11. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 50890/3673209. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a b))) REDUCED to normal form. ------ 50891/3673227. ------ 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. ------ 50892/3673281. ------ 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. ------ 50893/3673308. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 50894/3673362. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 50895/3673380. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))(^b.(^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. ------ 50896/3673389. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z))((^y.y)(^z.z)))) 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. ------ 50897/3673542. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a) a) c)) REDUCED to normal form. ------ 50898/3673668. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(b (a b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b (a b))) REDUCED to normal form. ------ 50899/3673704. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a)) a)) 5. ==[ beta ]==> ((^y.a)((^z.(a a)) a)) 6. ==[ alpha ]==> ((^x.a)((^y.(a a)) a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50900/3673731. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 50901/3673749. ------ 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 (^y.y)))) 4. ==[ alpha ]==> (b (((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 50902/3673758. ------ 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. ------ 50903/3673776. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 50904/3673875. ------ 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. ------ 50905/3673902. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^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. ------ 50906/3673929. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.b)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) b) REDUCED to normal form. ------ 50907/3673947. ------ 1. ==[ start ]==> (((^a.b) b)(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (b (((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 50908/3673956. ------ 1. ==[ start ]==> (((a b)(a a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 50909/3673983. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 50910/3674163. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(^y.y)) c)) 3. ==[ beta ]==> (((a b) b)((^y.y) c)) 4. ==[ alpha ]==> (((a b) b)((^x.x) c)) 5. ==[ beta ]==> (((a b) b) c) REDUCED to normal form. ------ 50911/3674235. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> (c ((^y.y)(^z.z))) 6. ==[ alpha ]==> (c ((^x.x)(^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 50912/3674289. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(a (a b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(a (a b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a (a b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a (a b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (a b))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (a b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (a b))) 9. ==[ beta ]==> ((^y.y)(a (a b))) 10. ==[ alpha ]==> ((^x.x)(a (a b))) 11. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 50913/3674298. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 50914/3674352. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 50915/3674370. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (b ((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x) a))) 5. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 50916/3674442. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(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. ------ 50917/3674469. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.b))) REDUCED to normal form. ------ 50918/3674523. ------ 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.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(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. ------ 50919/3674550. ------ 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 z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a (a a))((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((a (a a))((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((a (a a))(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a (a a))(a ((^y.y) a))) 10. ==[ alpha ]==> ((a (a a))(a ((^x.x) a))) 11. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 50920/3674577. ------ 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)))) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 50921/3674595. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((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. ------ 50922/3674604. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^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. ------ 50923/3674631. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((a a) a))) 5. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 50924/3674829. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.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. ------ 50925/3674838. ------ 1. ==[ start ]==> (((a b) c)((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 50926/3674865. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(y y)) c)) 3. ==[ beta ]==> (((a a) b)((^y.(y y)) c)) 4. ==[ alpha ]==> (((a a) b)((^x.(x x)) c)) 5. ==[ beta ]==> (((a a) b)(c c)) REDUCED to normal form. ------ 50927/3674910. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 50928/3674937. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a a)((^x1.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. ------ 50929/3674973. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.b))(^z.z)) 8. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 50930/3675027. ------ 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)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 50931/3675054. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 50932/3675081. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 50933/3675108. ------ 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)(^y1.y1)) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 50934/3675135. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a)) b)) REDUCED to normal form. ------ 50935/3675171. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.a)(^b.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. ------ 50936/3675198. ------ 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.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 50937/3675225. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)(^b.(^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. ------ 50938/3675333. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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. ------ 50939/3675360. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^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)))) REDUCED to normal form. ------ 50940/3675387. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(a a))) REDUCED to normal form. ------ 50941/3675414. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 50942/3675585. ------ 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 (a (a (a a)))) REDUCED to normal form. ------ 50943/3675648. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 50944/3675756. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a a)(^z.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 50945/3675783. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) 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. ------ 50946/3675837. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a a) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a) c)) REDUCED to normal form. ------ 50947/3675855. ------ 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 (a ((^y.y) a))) 4. ==[ alpha ]==> (b (a ((^x.x) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 50948/3675864. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a) a)) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 50949/3675891. ------ 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))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 50950/3675963. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 50951/3675981. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(b a))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(b a))(a (^x.x))) REDUCED to normal form. ------ 50952/3676008. ------ 1. ==[ start ]==> (((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.y1))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 50953/3676035. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 50954/3676062. ------ 1. ==[ start ]==> (((a (a a))(a b))(b (^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(b (^x.x))) REDUCED to normal form. ------ 50955/3676089. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(a (^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 50956/3676116. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a) a)(^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. ------ 50957/3676143. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)(^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. ------ 50958/3676170. ------ 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. ------ 50959/3676686. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(z a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 50960/3681117. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 50961/3681213. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a b)(^z.(z z)))) 3. ==[ eta ]==> ((^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. ------ 50962/3681384. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(b a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 50963/3681387. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y a))) REDUCED to normal form. ------ 50964/3681666. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(^z.z))) b) 4. ==[ beta ]==> ((a (^y.(^z.z))) b) 5. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 50965/3682422. ------ 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. ------ 50966/3682599. ------ 1. ==[ start ]==> ((^a.(^a.b))(c (^a.b))) 2. ==[ alpha ]==> ((^x.(^y.b))(c (^z.b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 50967/3682779. ------ 1. ==[ start ]==> ((^a.(a b))((a (a a))(^b.(^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. ------ 50968/3682872. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(a a)))) IRREDUCIBLE: cycle. ------ 50969/3683097. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((^y.a)(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> ((^x.a)(^y.((^z.z)(y y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 50970/3683373. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))(^y1.a))(((^z.z)(^x1.x1))(^y1.a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(^x1.a))(((^y1.y1)(^z1.z1))(^x2.a)))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.a))(((^y1.y1)(^z1.z1))(^x2.a))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(^y1.y1))(^z1.a))) 7. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(^y1.y1))(^z1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 9. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(^y1.a))) 10. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(^x1.a))) 11. ==[ beta ]==> a REDUCED to normal form. ------ 50971/3683682. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 11. ==[ beta ]==> (^y.(^z.y)) 12. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 50972/3683691. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 50973/3684048. ------ 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. ------ 50974/3684339. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 50975/3684804. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ eta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 50976/3684978. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 50977/3685086. ------ 1. ==[ start ]==> (((^a.a)(b a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b a)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 50978/3685167. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)(a b))(^y.((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y) a))) 5. ==[ beta ]==> (((a b)(a b))(^x.a)) REDUCED to normal form. ------ 50979/3685248. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.(^b.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. ------ 50980/3685257. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^a.((^a.a) a))) 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. ------ 50981/3685353. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 50982/3685374. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 50983/3685482. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.b)) 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. ------ 50984/3685536. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.a)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.a)) REDUCED to normal form. ------ 50985/3685563. ------ 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)) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 50986/3685611. ------ 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))) 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. ------ 50987/3685638. ------ 1. ==[ start ]==> (((a a) a)((a b)(a (a a)))) REDUCED to normal form. ------ 50988/3685665. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 50989/3685692. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (b ((^y.y)((a a) a))) 6. ==[ alpha ]==> (b ((^x.x)((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 50990/3685719. ------ 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. ------ 50991/3685746. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a) b)(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a) b)(a (a a))) REDUCED to normal form. ------ 50992/3685773. ------ 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)))) REDUCED to normal form. ------ 50993/3685800. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(b a))) REDUCED to normal form. ------ 50994/3685818. ------ 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 (^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. ------ 50995/3685863. ------ 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)))) REDUCED to normal form. ------ 50996/3685890. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.a))) REDUCED to normal form. ------ 50997/3685917. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a 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. ------ 50998/3685926. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)(a (a a)))) 3. ==[ beta ]==> ((^y.a)((^z.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.b)(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 50999/3686007. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(a b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(a b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(a b))) 5. ==[ beta ]==> (a ((^y.(y y))(a b))) 6. ==[ alpha ]==> (a ((^x.(x x))(a b))) 7. ==[ beta ]==> (a ((a b)(a b))) REDUCED to normal form. ------ 51000/3686034. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.a)((^y1.y1)(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. ------ 51001/3686088. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(b a))) 3. ==[ beta ]==> ((a (^x.(x x)))(b a)) REDUCED to normal form. ------ 51002/3686106. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b a) a)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b a) a)) 3. ==[ beta ]==> (((a a) a)((b a) a)) REDUCED to normal form. ------ 51003/3686133. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 51004/3686196. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.b)(^z.(z z)))((^y.b)(^z.(z z)))) 6. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.b)(^x1.(x1 x1)))) 7. ==[ beta ]==> (b ((^z.b)(^x1.(x1 x1)))) 8. ==[ alpha ]==> (b ((^x.b)(^y.(y y)))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51005/3686223. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51006/3686277. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.b))) 7. ==[ beta ]==> ((^y.(y y))(^z.b)) 8. ==[ alpha ]==> ((^x.(x x))(^y.b)) 9. ==[ beta ]==> ((^y.b)(^y.b)) 10. ==[ alpha ]==> ((^x.b)(^y.b)) 11. ==[ beta ]==> b REDUCED to normal form. ------ 51007/3686304. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.a)(^b.(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. ------ 51008/3686340. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 51009/3686367. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 51010/3686394. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 51011/3686430. ------ 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. ------ 51012/3686502. ------ 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.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. ------ 51013/3686682. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51014/3686709. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((^y.b)((^z.z) a)) 6. ==[ alpha ]==> ((^x.b)((^y.y) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 51015/3686763. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.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. ------ 51016/3686835. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 51017/3686889. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y)) a)) 5. ==[ beta ]==> ((a a)(((a a)(^y.y)) a)) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 51018/3686916. ------ 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. ------ 51019/3686943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a b) c)) 3. ==[ beta ]==> (((^y.y)(a a))((a b) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((a b) c)) 5. ==[ beta ]==> ((a a)((a b) c)) REDUCED to normal form. ------ 51020/3687006. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51021/3687060. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.b))) 5. ==[ beta ]==> (a ((^z.a)(^x1.b))) 6. ==[ alpha ]==> (a ((^x.a)(^y.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51022/3687096. ------ 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)))) 7. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 51023/3687123. ------ 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. ------ 51024/3687177. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(a (^x1.x1)))) REDUCED to normal form. ------ 51025/3687204. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(((a a) a) a)) REDUCED to normal form. ------ 51026/3687231. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a (a a))) REDUCED to normal form. ------ 51027/3687258. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51028/3687285. ------ 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. ------ 51029/3687303. ------ 1. ==[ start ]==> ((a (^a.b))(c (^a.b))) 2. ==[ alpha ]==> ((a (^x.b))(c (^y.b))) REDUCED to normal form. ------ 51030/3687375. ------ 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. ------ 51031/3687402. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 51032/3687429. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a) a)(^z.a))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 51033/3687456. ------ 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. ------ 51034/3687483. ------ 1. ==[ start ]==> ((a (a b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 51035/3687492. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 51036/3687573. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.x1)(a a)))) IRREDUCIBLE: cycle. ------ 51037/3687654. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51038/3687681. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 51039/3687708. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((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. ------ 51040/3687744. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c ((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c ((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c ((a a) a))) REDUCED to normal form. ------ 51041/3687762. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^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. ------ 51042/3687771. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(b (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b (a b))) REDUCED to normal form. ------ 51043/3687798. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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 REDUCED to normal form. ------ 51044/3687825. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 51045/3687852. ------ 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. ------ 51046/3688023. ------ 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. ------ 51047/3688050. ------ 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. ------ 51048/3688077. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 51049/3688086. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51050/3688113. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 51051/3688167. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51052/3688248. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51053/3688302. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a a)((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> ((a a)((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 51054/3688329. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a)(^b.(^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. ------ 51055/3688338. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(c (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(c (^z.z))) REDUCED to normal form. ------ 51056/3688383. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(^z1.b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.b))) 9. ==[ beta ]==> ((^y.y)((^z.z)(^x1.b))) 10. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 11. ==[ beta ]==> ((^y.y)(^z.b)) 12. ==[ alpha ]==> ((^x.x)(^y.b)) 13. ==[ beta ]==> (^y.b) 14. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 51057/3688392. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 51058/3688419. ------ 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. ------ 51059/3688446. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 51060/3688473. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 51061/3688500. ------ 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. ------ 51062/3688590. ------ 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. ------ 51063/3688617. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 51064/3688644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))(^y.a))) 5. ==[ beta ]==> ((a (a a))((a (a a))(^y.a))) 6. ==[ alpha ]==> ((a (a a))((a (a a))(^x.a))) REDUCED to normal form. ------ 51065/3688671. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> ((((a a) a) a)(a (^y.(y y)))) 6. ==[ alpha ]==> ((((a a) a) a)(a (^x.(x x)))) REDUCED to normal form. ------ 51066/3688698. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 51067/3688752. ------ 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. ------ 51068/3688788. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(^a.a))(^a.(^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. ------ 51069/3688932. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(^y.y))(a a))) 3. ==[ beta ]==> (((a b) c)((^y.y)(a a))) 4. ==[ alpha ]==> (((a b) c)((^x.x)(a a))) 5. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 51070/3688959. ------ 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. ------ 51071/3688986. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 51072/3689031. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(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. ------ 51073/3689040. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.z))) REDUCED to normal form. ------ 51074/3689085. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 51075/3689166. ------ 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 ((^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. ------ 51076/3689346. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(^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. ------ 51077/3689373. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1)) b)) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1)) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) b)) 7. ==[ beta ]==> ((^y.y)((^z.(z z)) b)) 8. ==[ alpha ]==> ((^x.x)((^y.(y y)) b)) 9. ==[ beta ]==> ((^y.(y y)) b) 10. ==[ alpha ]==> ((^x.(x x)) b) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51078/3689400. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.a) c)) 3. ==[ beta ]==> ((((a a) a)(a (a a))) a) REDUCED to normal form. ------ 51079/3689481. ------ 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. ------ 51080/3689508. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) 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. ------ 51081/3689598. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (b ((^z.(z z))(^x1.x1))) 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. ------ 51082/3689679. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 51083/3689742. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 51084/3689787. ------ 1. ==[ start ]==> (((^a.a)(b a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(a (^y.(y y)))) 3. ==[ beta ]==> ((b a)(a (^y.(y y)))) 4. ==[ alpha ]==> ((b a)(a (^x.(x x)))) REDUCED to normal form. ------ 51085/3689814. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 5. ==[ beta ]==> ((^y.a)(a a)) 6. ==[ alpha ]==> ((^x.a)(a a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51086/3689850. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b c)) 3. ==[ beta ]==> ((a (^y.(a a)))(b c)) 4. ==[ alpha ]==> ((a (^x.(a a)))(b c)) REDUCED to normal form. ------ 51087/3689868. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^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. ------ 51088/3689931. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 51089/3689949. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 51090/3689958. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(a ((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 51091/3689985. ------ 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))) REDUCED to normal form. ------ 51092/3690012. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 51093/3690057. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 51094/3690075. ------ 1. ==[ start ]==> (((a a)(b a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 51095/3690102. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 51096/3690129. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a a) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a a) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a) b)) 5. ==[ beta ]==> ((a (a a))((a a) b)) REDUCED to normal form. ------ 51097/3690156. ------ 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. ------ 51098/3690183. ------ 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. ------ 51099/3690210. ------ 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)(^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 51100/3690237. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a) a)) REDUCED to normal form. ------ 51101/3690264. ------ 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) a)((^y.y) a)) 6. ==[ alpha ]==> (((a a) a)((^x.x) a)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 51102/3690290. ------ 1. ==[ start ]==> (^a.(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (^x.(((x x)(^y.y))(x (^z.z)))) REDUCED to normal form. ------ 51103/3690291. ------ 1. ==[ start ]==> (a (((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (a (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 51104/3694995. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a))) a) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 51105/3695001. ------ 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. ------ 51106/3695028. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^z.z) a))(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(a a))((^z.z) a))) 7. ==[ beta ]==> (((a a) a)(((^y.y)(a a))((^z.z) a))) 8. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((^y.y) a))) 9. ==[ beta ]==> (((a a) a)((a a)((^y.y) a))) 10. ==[ alpha ]==> (((a a) a)((a a)((^x.x) a))) 11. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 51107/3695055. ------ 1. ==[ start ]==> ((^a.b)((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.b)((a b)(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 51108/3695136. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(a b))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 51109/3695238. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 51110/3695253. ------ 1. ==[ start ]==> ((^a.(^b.a))((b a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((b a)(^z.z))) 3. ==[ beta ]==> (^y.((b a)(^z.z))) 4. ==[ alpha ]==> (^x.((b a)(^y.y))) REDUCED to normal form. ------ 51111/3695820. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51112/3695946. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (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. ------ 51113/3696534. ------ 1. ==[ start ]==> ((((a a) a) a)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 51114/3697209. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51115/3697278. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.a) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a) c)) 3. ==[ beta ]==> (^y.(((^z.a) c)((^z.a) c))) 4. ==[ alpha ]==> (^x.(((^y.a) c)((^z.a) c))) 5. ==[ beta ]==> (^x.(a ((^z.a) c))) 6. ==[ alpha ]==> (^x.(a ((^y.a) c))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 51116/3697803. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 51117/3697974. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.((a a) a))) REDUCED to normal form. ------ 51118/3698478. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(^x1.z))) 3. ==[ beta ]==> ((a (^y.b))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.y))) REDUCED to normal form. ------ 51119/3698613. ------ 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)(^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)))(^z.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 51120/3698757. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^x.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 51121/3699090. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.d)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.d)) 3. ==[ beta ]==> (b (^z.d)) 4. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 51122/3699279. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.a))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.a))) REDUCED to normal form. ------ 51123/3699288. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^y.a)) REDUCED to normal form. ------ 51124/3699360. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.y)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 51125/3699369. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 51126/3699465. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51127/3699567. ------ 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. ------ 51128/3699648. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.b)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.b)) REDUCED to normal form. ------ 51129/3699675. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(z z))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(z z))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(y y))) 5. ==[ beta ]==> (((a a) a)(^y.(y y))) 6. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 51130/3699702. ------ 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. ------ 51131/3699714. ------ 1. ==[ start ]==> ((a a)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 51132/3699741. ------ 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))((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. ------ 51133/3699768. ------ 1. ==[ start ]==> ((a b)((a b)(a (a a)))) REDUCED to normal form. ------ 51134/3699822. ------ 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))((^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. ------ 51135/3699849. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(a b))) REDUCED to normal form. ------ 51136/3699948. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 51137/3699966. ------ 1. ==[ start ]==> ((a (^b.a))((b a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))((b a)(^y.y))) REDUCED to normal form. ------ 51138/3700002. ------ 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)((^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. ------ 51139/3700047. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a b)(^z.(z z)))) 3. ==[ beta ]==> ((^y.a)((a b)(^z.(z z)))) 4. ==[ alpha ]==> ((^x.a)((a b)(^y.(y y)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 51140/3700074. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a) 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. ------ 51141/3700083. ------ 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 (^x.x)) b) a) REDUCED to normal form. ------ 51142/3700110. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(^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)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 51143/3700128. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))(^z.b))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))(^z.b))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))(^y.b))) 5. ==[ beta ]==> (a ((a (a a))(^y.b))) 6. ==[ alpha ]==> (a ((a (a a))(^x.b))) REDUCED to normal form. ------ 51144/3700137. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 51145/3700155. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1) a)(^y1.(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. ------ 51146/3700164. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 51147/3700191. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 51148/3700299. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 51149/3700380. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(^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. ------ 51150/3700407. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(x x))(^y.b))) 3. ==[ beta ]==> (((a (a a)) a)((^y.b)(^y.b))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.b)(^y.b))) 5. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 51151/3700434. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 51152/3700461. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^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. ------ 51153/3700533. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 51154/3700551. ------ 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. ------ 51155/3700578. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a b)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((a b)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a b)((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x)) a)((a b) a)) REDUCED to normal form. ------ 51156/3700605. ------ 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. ------ 51157/3700632. ------ 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. ------ 51158/3700659. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 51159/3700803. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 51160/3700812. ------ 1. ==[ start ]==> (((a a)(^b.(^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 a)) REDUCED to normal form. ------ 51161/3700830. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 51162/3700839. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 51163/3700866. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 51164/3700884. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 51165/3700893. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^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. ------ 51166/3700920. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a) a))) 7. ==[ beta ]==> ((^y.(y y))((a a) a)) 8. ==[ alpha ]==> ((^x.(x x))((a a) a)) 9. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 51167/3701217. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 51168/3701289. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(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. ------ 51169/3701442. ------ 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. ------ 51170/3701469. ------ 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))(^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))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 51171/3701595. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^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. ------ 51172/3701613. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))(^b.(^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. ------ 51173/3701694. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(^z.(a a)))) IRREDUCIBLE: cycle. ------ 51174/3701757. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 51175/3701775. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 51176/3701784. ------ 1. ==[ start ]==> (((a b) a)((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 51177/3701811. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 51178/3701865. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 51179/3701892. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(^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. ------ 51180/3701919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51181/3701964. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.b) b)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.b) b)) 3. ==[ beta ]==> (b ((^y.b) b)) 4. ==[ alpha ]==> (b ((^x.b) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51182/3701991. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.a) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a) c)) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 51183/3702009. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^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. ------ 51184/3702036. ------ 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. ------ 51185/3702063. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^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)))) 9. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 51186/3702090. ------ 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. ------ 51187/3702117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 51188/3702162. ------ 1. ==[ start ]==> (((^a.b) b)((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.b)(a a))) 3. ==[ beta ]==> (b ((^y.b)(a a))) 4. ==[ alpha ]==> (b ((^x.b)(a a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51189/3702207. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51190/3702234. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 51191/3702288. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.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. ------ 51192/3702369. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 51193/3702378. ------ 1. ==[ start ]==> (((a b) b)((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 51194/3702405. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 51195/3702432. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 51196/3702459. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a)(^b.(^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. ------ 51197/3702513. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 51198/3702585. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(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. ------ 51199/3702657. ------ 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)(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. ------ 51200/3702684. ------ 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. ------ 51201/3702810. ------ 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)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51202/3702909. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^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. ------ 51203/3703044. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a) a)) 3. ==[ beta ]==> (b ((^z.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51204/3703161. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 51205/3703188. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(a (^z.a))) 3. ==[ beta ]==> ((a (^y.b))(a (^z.a))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.a))) REDUCED to normal form. ------ 51206/3703206. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 8. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 51207/3703242. ------ 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 y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51208/3703269. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 51209/3703287. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((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. ------ 51210/3703296. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^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. ------ 51211/3703323. ------ 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)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^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. ------ 51212/3703350. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 51213/3703440. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(b (a (a a)))) 3. ==[ beta ]==> ((a (a b))(b (a (a a)))) REDUCED to normal form. ------ 51214/3703467. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(a ((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(a (^x.x))) REDUCED to normal form. ------ 51215/3703494. ------ 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. ------ 51216/3703521. ------ 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. ------ 51217/3703548. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b) a)((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a b) a)((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a b) a)((a (^x.x)) a)) REDUCED to normal form. ------ 51218/3703575. ------ 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. ------ 51219/3703719. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (a a)) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (a a)) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a)) a)) 5. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 51220/3703863. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (^y.(^z.z)))) REDUCED to normal form. ------ 51221/3703935. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^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. ------ 51222/3703971. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 51223/3703989. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.a))) REDUCED to normal form. ------ 51224/3703998. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z) a)) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y) a)) 5. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 51225/3704052. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 51226/3704070. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a a) c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a a) c)) 3. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 51227/3704079. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.a)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 51228/3704106. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (^z.z))) 3. ==[ beta ]==> (((a a)(^y.a))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 51229/3704133. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 51230/3704178. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 51231/3704196. ------ 1. ==[ start ]==> (((a a)(b a))(b b)) REDUCED to normal form. ------ 51232/3704250. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b (a a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b (a a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (a a))) 5. ==[ beta ]==> ((a (a a))(b (a a))) REDUCED to normal form. ------ 51233/3704277. ------ 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. ------ 51234/3704304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a a)(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a a)(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a a)(a a))) 5. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 51235/3704331. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b a)) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b a)) REDUCED to normal form. ------ 51236/3704358. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a b)) REDUCED to normal form. ------ 51237/3704385. ------ 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. ------ 51238/3704412. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 51239/3707583. ------ 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)(^z.z)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 51240/3709125. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a))) b) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 51241/3709149. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51242/3709230. ------ 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)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51243/3709464. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(a a))((^x1.x1) a))) 3. ==[ eta ]==> ((^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. ------ 51244/3709656. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^b.(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(y a))) 3. ==[ beta ]==> (((a a) a)(^y.(y a))) 4. ==[ alpha ]==> (((a a) a)(^x.(x a))) REDUCED to normal form. ------ 51245/3709734. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.a))(((^z.(a a))(^x1.a))((^y1.(a a))(^z1.a)))) 5. ==[ beta ]==> ((a a)(((^z.(a a))(^x1.a))((^y1.(a a))(^z1.a)))) 6. ==[ alpha ]==> ((a a)(((^x.(a a))(^y.a))((^z.(a a))(^x1.a)))) 7. ==[ beta ]==> ((a a)((a a)((^z.(a a))(^x1.a)))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a))(^y.a)))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 51246/3709935. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(b y))) 3. ==[ eta ]==> (((^x.(x x))(a a)) b) 4. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 51247/3709959. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51248/3710439. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 51249/3710517. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.b)(^z.a))) 3. ==[ beta ]==> ((((^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))) 5. ==[ beta ]==> ((b ((^z.b)(^x1.a)))((^y1.b)(^z1.a))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.a)))((^z.b)(^x1.a))) 7. ==[ beta ]==> ((b b)((^z.b)(^x1.a))) 8. ==[ alpha ]==> ((b b)((^x.b)(^y.a))) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 51250/3710691. ------ 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. ------ 51251/3710850. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 51252/3711030. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^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. ------ 51253/3711417. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (^y.((((a a) a)(a (^z.z)))(((a a) a)(a (^z.z))))) 4. ==[ alpha ]==> (^x.((((a a) a)(a (^y.y)))(((a a) a)(a (^z.z))))) REDUCED to normal form. ------ 51254/3711573. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 51255/3712140. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(^z.b))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.b))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.b))) REDUCED to normal form. ------ 51256/3712299. ------ 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. ------ 51257/3712302. ------ 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. ------ 51258/3712473. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.((z z) z))) 3. ==[ beta ]==> (b (^z.((z z) z))) 4. ==[ alpha ]==> (b (^x.((x x) x))) REDUCED to normal form. ------ 51259/3712896. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 51260/3713031. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 51261/3713055. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))(a a))) 3. ==[ eta ]==> (b ((^y.(y y))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 51262/3713337. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.((^z.z) a))) 3. ==[ beta ]==> ((b a)(^y.((^z.z) a))) 4. ==[ alpha ]==> ((b a)(^x.((^y.y) a))) 5. ==[ beta ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 51263/3713427. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 51264/3713508. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 51265/3713652. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 51266/3713706. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 51267/3713760. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 51268/3713787. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 51269/3713814. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.z))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 51270/3713841. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 51271/3713871. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 51272/3713898. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y) a)) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 51273/3713925. ------ 1. ==[ start ]==> (((^a.a)(a a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a b)(a (a a)))) 3. ==[ beta ]==> ((a a)((a b)(a (a a)))) REDUCED to normal form. ------ 51274/3713952. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 51275/3714006. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51276/3714033. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 51277/3714060. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 51278/3714087. ------ 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)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 51279/3714150. ------ 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)(((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. ------ 51280/3714186. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a a)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 51281/3714231. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 51282/3714285. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(^y.b))) REDUCED to normal form. ------ 51283/3714312. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 51284/3714375. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(b a))) 3. ==[ beta ]==> (((a a) a)((^y.y)(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 51285/3714456. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 51286/3714654. ------ 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 a))(a (b a))) REDUCED to normal form. ------ 51287/3714681. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 51288/3714816. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51289/3714843. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 51290/3714897. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)((a a)(^x1.x1)))) 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. ------ 51291/3714933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.z))) 5. ==[ beta ]==> (a (((a a)(^y.y))(^z.z))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 51292/3714960. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 51293/3714987. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a b)(^z.a))) REDUCED to normal form. ------ 51294/3715014. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 51295/3715041. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^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. ------ 51296/3715104. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a b))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 51297/3715131. ------ 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)(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. ------ 51298/3715158. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 51299/3715212. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 51300/3715239. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.b)(^y.a))) 3. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 51301/3715410. ------ 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. ------ 51302/3715437. ------ 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 a))(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(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. ------ 51303/3715446. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 51304/3715473. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.b) c)) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.b) c)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.b) c)) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 51305/3715491. ------ 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) a)((^y.y) a))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)((^z.z) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)((^y.y) a))) 7. ==[ beta ]==> ((a 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. ------ 51306/3715500. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.a) d)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a) d)) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 51307/3715572. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((a (^x.b))(a ((a a) a))) REDUCED to normal form. ------ 51308/3715617. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(a a)))) REDUCED to normal form. ------ 51309/3715671. ------ 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))) 5. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 51310/3715698. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 51311/3715743. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 51312/3715752. ------ 1. ==[ start ]==> ((a (a b))((^b.(^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. ------ 51313/3715905. ------ 1. ==[ start ]==> ((((a a) a) b)((a b) b)) REDUCED to normal form. ------ 51314/3715932. ------ 1. ==[ start ]==> (((a b) a)(((a a) a) c)) REDUCED to normal form. ------ 51315/3716094. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 51316/3716112. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)(a a))) 2. ==[ alpha ]==> (((^x.b)(a a))((a b)(a a))) 3. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 51317/3716121. ------ 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. ------ 51318/3716139. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 51319/3716265. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(b (^x1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b (^x1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (^z.b))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.b))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.b))) 7. ==[ beta ]==> (a (b (^y.b))) 8. ==[ alpha ]==> (a (b (^x.b))) REDUCED to normal form. ------ 51320/3716292. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 51321/3716310. ------ 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. ------ 51322/3716319. ------ 1. ==[ start ]==> (((a b)(a a))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.b)(a a))) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 51323/3716526. ------ 1. ==[ start ]==> (((a b) b)(((a a) a) b)) REDUCED to normal form. ------ 51324/3716652. ------ 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)(^z.z))((^y.y)(^z.z)))(b ((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b ((a a) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b ((a a) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((a a) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b ((a a) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b ((a a) a))) 9. ==[ beta ]==> ((^y.y)(b ((a a) a))) 10. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 11. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 51325/3716688. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b) a)) 5. ==[ beta ]==> ((^y.(y y))((^z.b) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.b) a)) 7. ==[ beta ]==> (((^y.b) a)((^y.b) a)) 8. ==[ alpha ]==> (((^x.b) a)((^y.b) a)) 9. ==[ beta ]==> (b ((^y.b) a)) 10. ==[ alpha ]==> (b ((^x.b) a)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51326/3716715. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a) b)) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 51327/3716733. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 51328/3716742. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 51329/3716832. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.a))) REDUCED to normal form. ------ 51330/3716859. ------ 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. ------ 51331/3716913. ------ 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.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 51332/3716940. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> ((((a a) a) a)(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((((a a) a) a)(a ((^y.y) a))) 8. ==[ alpha ]==> ((((a a) a) a)(a ((^x.x) a))) 9. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 51333/3716958. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(z z)))) 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. ------ 51334/3716967. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 51335/3716994. ------ 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))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 51336/3717021. ------ 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. ------ 51337/3717192. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a ((a a) a))) 3. ==[ beta ]==> (b (a ((a a) a))) REDUCED to normal form. ------ 51338/3717201. ------ 1. ==[ start ]==> (((a b) c)((^c.a) a)) 2. ==[ alpha ]==> (((a b) c)((^x.a) a)) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 51339/3717228. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(^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)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 51340/3717273. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 51341/3717300. ------ 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 (^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. ------ 51342/3717390. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51343/3717417. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (^y.a))) REDUCED to normal form. ------ 51344/3717435. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c d)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c d)) 3. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 51345/3717444. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 51346/3717471. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 51347/3717498. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 51348/3717534. ------ 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))(^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. ------ 51349/3717561. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 51350/3717588. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 51351/3717615. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.a)(^b.(^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. ------ 51352/3717696. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(c (^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(c (^y.a))) 3. ==[ beta ]==> (((a b) a)(c (^y.a))) 4. ==[ alpha ]==> (((a b) a)(c (^x.a))) REDUCED to normal form. ------ 51353/3717723. ------ 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)))) REDUCED to normal form. ------ 51354/3717750. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 51355/3717777. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))(a a))) 3. ==[ beta ]==> ((a (b a))((a a)(a a))) REDUCED to normal form. ------ 51356/3717948. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 51357/3718011. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 51358/3718056. ------ 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. ------ 51359/3718119. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 51360/3718137. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b c)) 3. ==[ beta ]==> (((a b)(a b))(b c)) REDUCED to normal form. ------ 51361/3718146. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 51362/3718200. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 51363/3718218. ------ 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. ------ 51364/3718227. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a) c)) REDUCED to normal form. ------ 51365/3718254. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a) a)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a) a)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a) a)) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 51366/3718281. ------ 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)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 51367/3718344. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 51368/3718371. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 51369/3718398. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 51370/3718425. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 51371/3718452. ------ 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. ------ 51372/3718479. ------ 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)))) REDUCED to normal form. ------ 51373/3718506. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(a a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 51374/3718533. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a) 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. ------ 51375/3718560. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 51376/3718833. ------ 1. ==[ start ]==> ((^a.(^b.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 51377/3723045. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51378/3723558. ------ 1. ==[ start ]==> ((^a.(^b.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 51379/3723561. ------ 1. ==[ start ]==> ((a (^b.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 51380/3723630. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(a a))(^x1.a))) 3. ==[ eta ]==> ((^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. ------ 51381/3723801. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 51382/3724110. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^a.(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(b y))) 3. ==[ eta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 51383/3724353. ------ 1. ==[ start ]==> (((a (a a)) b)(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 51384/3724683. ------ 1. ==[ start ]==> ((^a.((a a) a))((a b) c)) 2. ==[ alpha ]==> ((^x.((x x) x))((a b) c)) 3. ==[ beta ]==> ((((a b) c)((a b) c))((a b) c)) REDUCED to normal form. ------ 51385/3724857. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^b.(^c.(^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. ------ 51386/3725196. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^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. ------ 51387/3725541. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 51388/3725790. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((((a a) a)(^z.(^x1.x1)))(((a a) a)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((((a a) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 51389/3726135. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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 ]==> ((^y.(y b)) b) 10. ==[ alpha ]==> ((^x.(x b)) b) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51390/3726639. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^b.(^c.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. ------ 51391/3726648. ------ 1. ==[ start ]==> (((a b) c)(^a.((a a) a))) 2. ==[ alpha ]==> (((a b) c)(^x.((x x) x))) REDUCED to normal form. ------ 51392/3726783. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^c.((^a.a)(^a.a)))) 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))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 51393/3727221. ------ 1. ==[ start ]==> ((^a.(b a))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b x))((a (a a))(^y.y))) 3. ==[ eta ]==> (b ((a (a a))(^y.y))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 51394/3727314. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.(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)))) REDUCED to normal form. ------ 51395/3727530. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^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. ------ 51396/3727701. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.((^a.a) a))) 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. ------ 51397/3727770. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51398/3727773. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.x1))) REDUCED to normal form. ------ 51399/3727872. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.b)) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.b)) REDUCED to normal form. ------ 51400/3727926. ------ 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)) REDUCED to normal form. ------ 51401/3727953. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 51402/3728007. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.a)) REDUCED to normal form. ------ 51403/3728055. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(^a.a))(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)))) REDUCED to normal form. ------ 51404/3728082. ------ 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)((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. ------ 51405/3728109. ------ 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. ------ 51406/3728136. ------ 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. ------ 51407/3728163. ------ 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. ------ 51408/3728190. ------ 1. ==[ start ]==> (((a a) b)((a (a a))(a b))) REDUCED to normal form. ------ 51409/3728217. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) 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. ------ 51410/3728244. ------ 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)))) REDUCED to normal form. ------ 51411/3728271. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(b a))) REDUCED to normal form. ------ 51412/3728289. ------ 1. ==[ start ]==> ((a (^b.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 51413/3728307. ------ 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. ------ 51414/3728334. ------ 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))(^z.(^x1.x1)))) REDUCED to normal form. ------ 51415/3728361. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 51416/3728370. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(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. ------ 51417/3728397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 51418/3728451. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(^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)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 51419/3728478. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a b))) 5. ==[ beta ]==> ((^y.(y y))(a b)) 6. ==[ alpha ]==> ((^x.(x x))(a b)) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 51420/3728532. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 51421/3728577. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a) a)) REDUCED to normal form. ------ 51422/3728604. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a)(^y.y)) b)) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 51423/3728640. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((^y.(a a))(^z.a))((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (((^x.(a a))(^y.a))((^z.(a a))(^x1.a))) 7. ==[ beta ]==> ((a a)((^z.(a a))(^x1.a))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 51424/3728667. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 51425/3728721. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^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. ------ 51426/3728748. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((a (a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(^y.b))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 51427/3728775. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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. ------ 51428/3728784. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(c (a a))) REDUCED to normal form. ------ 51429/3728811. ------ 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. ------ 51430/3728838. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(a (b a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (b a))) REDUCED to normal form. ------ 51431/3728901. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(a a)) c)) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a)) c)) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 51432/3728946. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b b)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 51433/3729072. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(b (^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 51434/3729081. ------ 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. ------ 51435/3729153. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51436/3729279. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.b))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.b))) REDUCED to normal form. ------ 51437/3729306. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 51438/3729360. ------ 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. ------ 51439/3729387. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((a a)(((^y.y)(a a)) b)) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a)) b)) 7. ==[ beta ]==> ((a a)((a a) b)) REDUCED to normal form. ------ 51440/3729414. ------ 1. ==[ start ]==> ((a ((a a) a))((a b) c)) REDUCED to normal form. ------ 51441/3729450. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(z1 z1)))) 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. ------ 51442/3729504. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (a ((^z.(z z))(^x1.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. ------ 51443/3729540. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c (a b))) 3. ==[ beta ]==> (((^y.y) b)(c (a b))) 4. ==[ alpha ]==> (((^x.x) b)(c (a b))) 5. ==[ beta ]==> (b (c (a b))) REDUCED to normal form. ------ 51444/3729567. ------ 1. ==[ start ]==> ((((a a) a) a)(b ((^a.a)(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. ------ 51445/3729621. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a a))) REDUCED to normal form. ------ 51446/3729648. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 51447/3729675. ------ 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))) 3. ==[ beta ]==> (((a (a a))(^x.a))(((a a) a) a)) REDUCED to normal form. ------ 51448/3729702. ------ 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)(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(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. ------ 51449/3729729. ------ 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)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 51450/3729846. ------ 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))(^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. ------ 51451/3729873. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 51452/3729900. ------ 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. ------ 51453/3729927. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a (a b))(^y.(y y))) 6. ==[ alpha ]==> ((a (a b))(^x.(x x))) REDUCED to normal form. ------ 51454/3729936. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^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. ------ 51455/3730017. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a b))) IRREDUCIBLE: cycle. ------ 51456/3730098. ------ 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 ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51457/3730125. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 51458/3730152. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))(^y1.(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. ------ 51459/3730206. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 51460/3730242. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(b (a b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(b (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(b (a b))) 5. ==[ beta ]==> ((^y.a)(b (a b))) 6. ==[ alpha ]==> ((^x.a)(b (a b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51461/3730269. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 51462/3730296. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 51463/3730332. ------ 1. ==[ start ]==> (((a a)(a b))((^c.a) c)) 2. ==[ alpha ]==> (((a a)(a b))((^x.a) c)) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 51464/3730494. ------ 1. ==[ start ]==> (((a b)(a a))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)(a a))((a b)(^x.x))) REDUCED to normal form. ------ 51465/3730521. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 51466/3730530. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51467/3730557. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 51468/3730611. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 51469/3730692. ------ 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))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51470/3730746. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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. ------ 51471/3730773. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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. ------ 51472/3730836. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 51473/3730863. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (a b))) 5. ==[ beta ]==> ((^y.(y y))(a (a b))) 6. ==[ alpha ]==> ((^x.(x x))(a (a b))) 7. ==[ beta ]==> ((a (a b))(a (a b))) REDUCED to normal form. ------ 51474/3730890. ------ 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. ------ 51475/3730917. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 51476/3730944. ------ 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)(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 51477/3731061. ------ 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)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 51478/3731088. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 10. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 51479/3731115. ------ 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))) 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. ------ 51480/3731133. ------ 1. ==[ start ]==> (((^a.b) c)(d d)) 2. ==[ alpha ]==> (((^x.b) c)(d d)) 3. ==[ beta ]==> (b (d d)) REDUCED to normal form. ------ 51481/3731142. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 51482/3731169. ------ 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. ------ 51483/3731232. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51484/3731367. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (b ((^z.z)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 51485/3731376. ------ 1. ==[ start ]==> (((a b) c)(a ((a a) a))) REDUCED to normal form. ------ 51486/3731403. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(a a))) 5. ==[ beta ]==> (((a a) b)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) b)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 51487/3731430. ------ 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. ------ 51488/3731484. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 51489/3731511. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 51490/3731610. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) 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. ------ 51491/3731619. ------ 1. ==[ start ]==> (((a b)(^b.a))(c d)) 2. ==[ alpha ]==> (((a b)(^x.a))(c d)) REDUCED to normal form. ------ 51492/3731709. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 51493/3731817. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(^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. ------ 51494/3731844. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(x x)) b)) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b b)) REDUCED to normal form. ------ 51495/3731871. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.a) c)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a) c)) 3. ==[ beta ]==> (((a b) a)((^y.a) c)) 4. ==[ alpha ]==> (((a b) a)((^x.a) c)) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 51496/3731952. ------ 1. ==[ start ]==> ((a (b a))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((a (b a))((a (a a))(^x.x))) REDUCED to normal form. ------ 51497/3732042. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(a (a a)))) 5. ==[ beta ]==> (b ((^z.z)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 51498/3732123. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 51499/3732186. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (a a))) REDUCED to normal form. ------ 51500/3732231. ------ 1. ==[ start ]==> (((^a.a)(b a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.x)(b a))(b (^y.a))) 3. ==[ beta ]==> ((b a)(b (^y.a))) 4. ==[ alpha ]==> ((b a)(b (^x.a))) REDUCED to normal form. ------ 51501/3732258. ------ 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 (^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. ------ 51502/3732294. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c b)) 3. ==[ beta ]==> ((a (^y.(a a)))(c b)) 4. ==[ alpha ]==> ((a (^x.(a a)))(c b)) REDUCED to normal form. ------ 51503/3732312. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 51504/3732321. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b c)) REDUCED to normal form. ------ 51505/3732375. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 51506/3732393. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^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. ------ 51507/3732402. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b (a (^y.y)))) REDUCED to normal form. ------ 51508/3732429. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(a ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.a))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.a))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 51509/3732456. ------ 1. ==[ start ]==> ((((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 a))) REDUCED to normal form. ------ 51510/3732501. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.a))) REDUCED to normal form. ------ 51511/3732519. ------ 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. ------ 51512/3732546. ------ 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)))) REDUCED to normal form. ------ 51513/3732573. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.z)) a)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.z)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y)) a)) 5. ==[ beta ]==> ((a (a a))((a (^y.y)) a)) 6. ==[ alpha ]==> ((a (a a))((a (^x.x)) a)) REDUCED to normal form. ------ 51514/3732600. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a) b)) REDUCED to normal form. ------ 51515/3732627. ------ 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. ------ 51516/3732654. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.z) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y) b)) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 51517/3732681. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 51518/3732708. ------ 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. ------ 51519/3732735. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 51520/3732761. ------ 1. ==[ start ]==> (^a.((b a)(a a))) 2. ==[ alpha ]==> (^x.((b x)(x x))) REDUCED to normal form. ------ 51521/3732762. ------ 1. ==[ start ]==> (a ((b a)(a a))) REDUCED to normal form. ------ 51522/3737229. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51523/3737499. ------ 1. ==[ start ]==> ((^a.a)((b a)(a a))) 2. ==[ alpha ]==> ((^x.x)((b a)(a a))) 3. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 51524/3737526. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^y.y))(a (^z.z)))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 51525/3737553. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 51526/3737634. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))((a a) a))(^y.y)) 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. ------ 51527/3738444. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51528/3739734. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 51529/3739776. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.b) b)) 3. ==[ beta ]==> (^y.(((^z.b) b)((^z.b) b))) 4. ==[ alpha ]==> (^x.(((^y.b) b)((^z.b) b))) 5. ==[ beta ]==> (^x.(b ((^z.b) b))) 6. ==[ alpha ]==> (^x.(b ((^y.b) b))) 7. ==[ beta ]==> (^x.(b b)) REDUCED to normal form. ------ 51530/3739950. ------ 1. ==[ start ]==> (((^a.b) b)(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.(y y)))) 3. ==[ beta ]==> (b (^y.(^z.(y y)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 51531/3740328. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.y))) 7. ==[ beta ]==> ((^y.(^z.y))(^y.(^z.y))) 8. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.z))) 9. ==[ beta ]==> (^y.(^z.(^x1.z))) 10. ==[ alpha ]==> (^x.(^y.(^z.y))) REDUCED to normal form. ------ 51532/3740841. ------ 1. ==[ start ]==> (((a b) c)(^b.(^c.a))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.a))) REDUCED to normal form. ------ 51533/3741138. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 51534/3741282. ------ 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.((^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 ]==> (^x.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51535/3741507. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 51536/3741894. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 51537/3741966. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.c)) REDUCED to normal form. ------ 51538/3742092. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(y (^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 51539/3742173. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.b)) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.b)) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.b)) 5. ==[ beta ]==> (((a a) a)(^y.b)) 6. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 51540/3742200. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(z z))) REDUCED to normal form. ------ 51541/3742239. ------ 1. ==[ start ]==> ((a a)((b a)(a a))) REDUCED to normal form. ------ 51542/3742266. ------ 1. ==[ start ]==> ((a (a a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 51543/3742293. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))((^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. ------ 51544/3742347. ------ 1. ==[ start ]==> (((a a)(a a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 51545/3742374. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (a (^x.x)))((^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. ------ 51546/3742572. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 51547/3742599. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((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. ------ 51548/3742608. ------ 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 (^x.x)) b) b) REDUCED to normal form. ------ 51549/3742662. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^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)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 51550/3742680. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 51551/3742689. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a b)(a b))) REDUCED to normal form. ------ 51552/3742716. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 51553/3742905. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a)(^b.(^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. ------ 51554/3742932. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 51555/3742959. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 51556/3742986. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 51557/3743076. ------ 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. ------ 51558/3743103. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(a a))(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a)((a a)(a (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a a)(a (^y.y)))) REDUCED to normal form. ------ 51559/3743130. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((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. ------ 51560/3743157. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 51561/3743184. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 51562/3743283. ------ 1. ==[ start ]==> (((a (a a)) b)(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 51563/3743328. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 51564/3743337. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(^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)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 51565/3743355. ------ 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))(^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. ------ 51566/3743364. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 51567/3743391. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.a))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 51568/3743409. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 51569/3743445. ------ 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.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51570/3743742. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.b))) 5. ==[ beta ]==> (b ((^y.a)(^z.b))) 6. ==[ alpha ]==> (b ((^x.a)(^y.b))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51571/3743769. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 51572/3743868. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.b) c)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.b) c)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b) c)) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.b) c)) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.b) c)) 7. ==[ beta ]==> ((a a)((^y.b) c)) 8. ==[ alpha ]==> ((a a)((^x.b) c)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 51573/3743967. ------ 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. ------ 51574/3743994. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a b))) REDUCED to normal form. ------ 51575/3744021. ------ 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. ------ 51576/3744120. ------ 1. ==[ start ]==> (((^a.b) a)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51577/3744138. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 51578/3744219. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))(^x1.b))) IRREDUCIBLE: cycle. ------ 51579/3744282. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(^y.y))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 51580/3744300. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 51581/3744309. ------ 1. ==[ start ]==> (((a b) a)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 51582/3744327. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a) a) c)) 3. ==[ beta ]==> ((a b)(((a a) a) c)) REDUCED to normal form. ------ 51583/3744336. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 51584/3744390. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 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. ------ 51585/3744417. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 51586/3744444. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51587/3744471. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 51588/3744489. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a)) a)) 3. ==[ beta ]==> (b ((^y.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 51589/3744516. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.b) b)) 3. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 51590/3744534. ------ 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. ------ 51591/3744561. ------ 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)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z) a)) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y) a)) 7. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 51592/3744588. ------ 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. ------ 51593/3744615. ------ 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. ------ 51594/3744642. ------ 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. ------ 51595/3744669. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 51596/3744687. ------ 1. ==[ start ]==> (((^a.b) b)(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(a (^y.(a a)))) 3. ==[ beta ]==> (b (a (^y.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 51597/3744732. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51598/3744759. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 51599/3744813. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(^x2.x2)))) 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. ------ 51600/3744894. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b) a)) 3. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 51601/3744903. ------ 1. ==[ start ]==> (((a b) b)((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a b) b)((^x.b)(^y.y))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 51602/3744957. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(^a.a))(^b.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. ------ 51603/3744984. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 51604/3745038. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^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. ------ 51605/3745065. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.b))) 7. ==[ beta ]==> (((^y.y)(^z.b))((^y.y)(^z.b))) 8. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.b))) 9. ==[ beta ]==> ((^y.b)((^z.z)(^x1.b))) 10. ==[ alpha ]==> ((^x.b)((^y.y)(^z.b))) 11. ==[ beta ]==> b REDUCED to normal form. ------ 51606/3745110. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)(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. ------ 51607/3745182. ------ 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. ------ 51608/3745209. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 51609/3745236. ------ 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. ------ 51610/3745335. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z) 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. ------ 51611/3745434. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 51612/3745578. ------ 1. ==[ start ]==> (((a b) c)((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a b) c)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b) c)(^y.a)) 4. ==[ alpha ]==> (((a b) c)(^x.a)) REDUCED to normal form. ------ 51613/3745686. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(c (^z.(z z)))) REDUCED to normal form. ------ 51614/3745713. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 51615/3745767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51616/3745794. ------ 1. ==[ start ]==> ((((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.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 51617/3745812. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 51618/3745821. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 51619/3745848. ------ 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.(^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. ------ 51620/3745875. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 51621/3745965. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(c ((^y.y) a))) 3. ==[ beta ]==> ((a (a b))(c ((^y.y) a))) 4. ==[ alpha ]==> ((a (a b))(c ((^x.x) a))) 5. ==[ beta ]==> ((a (a b))(c a)) REDUCED to normal form. ------ 51622/3745992. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(b (a (a a)))) REDUCED to normal form. ------ 51623/3746019. ------ 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 ((^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))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 51624/3746046. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (a a))(a a))) REDUCED to normal form. ------ 51625/3746073. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) 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)))) 5. ==[ beta ]==> (((a b) a)(a (a (^y.y)))) 6. ==[ alpha ]==> (((a b) a)(a (a (^x.x)))) REDUCED to normal form. ------ 51626/3746100. ------ 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.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 51627/3746127. ------ 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. ------ 51628/3746244. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(^z.(z z)))) 5. ==[ beta ]==> (b ((a a)(^z.(z z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 51629/3746325. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.z)) c)) 3. ==[ beta ]==> (b ((a (^z.z)) c)) 4. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 51630/3746433. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^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. ------ 51631/3746496. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.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) REDUCED to normal form. ------ 51632/3746514. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 51633/3746523. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^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. ------ 51634/3746577. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.a)(^a.a))) 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. ------ 51635/3746595. ------ 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)) REDUCED to normal form. ------ 51636/3746604. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 51637/3746631. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.a)) REDUCED to normal form. ------ 51638/3746721. ------ 1. ==[ start ]==> (((a a)(b a))(c a)) REDUCED to normal form. ------ 51639/3746748. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b b)) REDUCED to normal form. ------ 51640/3746802. ------ 1. ==[ start ]==> (((a (a a))(a b))(b (a a))) REDUCED to normal form. ------ 51641/3746829. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(a (a (^z.z)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(a (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(a (a (^y.y)))) 5. ==[ beta ]==> (((a a) a)(a (a (^y.y)))) 6. ==[ alpha ]==> (((a a) a)(a (a (^x.x)))) REDUCED to normal form. ------ 51642/3746856. ------ 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)(^y.y))((a a)(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 51643/3746883. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b a)) REDUCED to normal form. ------ 51644/3746910. ------ 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. ------ 51645/3746937. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a (a a))) REDUCED to normal form. ------ 51646/3747228. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(b a))) 3. ==[ beta ]==> (^y.(^z.(b a))) 4. ==[ alpha ]==> (^x.(^y.(b a))) REDUCED to normal form. ------ 51647/3747795. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((^x.(^y.(^z.z))) b) 4. ==[ beta ]==> (^y.(^z.z)) 5. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51648/3750891. ------ 1. ==[ start ]==> ((^a.(b a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(^x1.x1)))) 3. ==[ eta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 51649/3751728. ------ 1. ==[ start ]==> ((^a.(^a.a))((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. ------ 51650/3751809. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51651/3751971. ------ 1. ==[ start ]==> ((^a.(^b.a))((a a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a a)(b a))) 3. ==[ beta ]==> (^y.((a a)(b a))) 4. ==[ alpha ]==> (^x.((a a)(b a))) REDUCED to normal form. ------ 51652/3751974. ------ 1. ==[ start ]==> ((a (^b.a))(^c.(b a))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(b a))) REDUCED to normal form. ------ 51653/3751992. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 51654/3752262. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z a))) REDUCED to normal form. ------ 51655/3752538. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51656/3752541. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(b z))) 3. ==[ eta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 51657/3753045. ------ 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. ------ 51658/3753096. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1))))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1))))((^x2.(a a))(^y2.(^z2.z2)))) 5. ==[ beta ]==> (((a a)((^x1.(a a))(^y1.(^z1.z1))))((^x2.(a a))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(a a))((^x1.(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 51659/3753297. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.((y1 y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y)(^z.z)))) 5. ==[ beta ]==> (^y.((y y)(^z.z))) 6. ==[ alpha ]==> (^x.((x x)(^y.y))) REDUCED to normal form. ------ 51660/3753429. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 51661/3753609. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((^y.a)((^z.z) a)) b) 4. ==[ alpha ]==> (((^x.a)((^y.y) a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 51662/3753972. ------ 1. ==[ start ]==> (((^a.b)(a a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (b (^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(x x)))) 5. ==[ beta ]==> (b (^x.(x x))) REDUCED to normal form. ------ 51663/3753996. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)(a a))) 3. ==[ beta ]==> (^y.(((a b)(a a))((a b)(a a)))) 4. ==[ alpha ]==> (^x.(((a b)(a a))((a b)(a a)))) REDUCED to normal form. ------ 51664/3754179. ------ 1. ==[ start ]==> (((a b)(a a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 51665/3754203. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.b)(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.b)(a a))((^z.b)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.b)(a a))((^z.b)(a a)))) 5. ==[ beta ]==> (((^y.b)(a a))((^z.b)(a a))) 6. ==[ alpha ]==> (((^x.b)(a a))((^y.b)(a a))) 7. ==[ beta ]==> (b ((^y.b)(a a))) 8. ==[ alpha ]==> (b ((^x.b)(a a))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 51666/3754746. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 51667/3754878. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1))((^y1.y1)(^z1.z1)))((^z.(^x1.x1))((^y1.y1)(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2))))(^z2.z2)) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2))))(^z2.z2)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1))))(^z1.z1)) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51668/3755502. ------ 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.(^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. ------ 51669/3755634. ------ 1. ==[ start ]==> ((^a.(b a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(a (^y.(^z.z)))) 3. ==[ eta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 51670/3755637. ------ 1. ==[ start ]==> ((a (b a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 51671/3756114. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 51672/3756183. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51673/3756204. ------ 1. ==[ start ]==> (((a a)(b a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.x))) REDUCED to normal form. ------ 51674/3756258. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(a (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(a (^z.z)))) 6. ==[ alpha ]==> ((a (a a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 51675/3756312. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(^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. ------ 51676/3756366. ------ 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. ------ 51677/3756393. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(a a))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(a a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(a a))) 5. ==[ beta ]==> (((a a) a)(^y.(a a))) 6. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 51678/3756420. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 51679/3756477. ------ 1. ==[ start ]==> ((a (^a.a))((b a)(a a))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(a a))) REDUCED to normal form. ------ 51680/3756504. ------ 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 ]==> ((^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. ------ 51681/3756531. ------ 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. ------ 51682/3756558. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(a (a a)))) REDUCED to normal form. ------ 51683/3756612. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^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. ------ 51684/3756639. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a b))) 5. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 51685/3756666. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 51686/3756693. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (^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. ------ 51687/3756720. ------ 1. ==[ start ]==> ((a (^b.a))((a a)(b a))) 2. ==[ alpha ]==> ((a (^x.a))((a a)(b a))) REDUCED to normal form. ------ 51688/3756738. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 51689/3756756. ------ 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 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. ------ 51690/3756837. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.(y y)))) REDUCED to normal form. ------ 51691/3756864. ------ 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. ------ 51692/3756891. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.a)) REDUCED to normal form. ------ 51693/3756918. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(^x1.b))) REDUCED to normal form. ------ 51694/3756945. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 51695/3756981. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 51696/3757008. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b a)) REDUCED to normal form. ------ 51697/3757053. ------ 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 a)(^y.y)) b)) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 51698/3757260. ------ 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 a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 51699/3757287. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 51700/3757422. ------ 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.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 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. ------ 51701/3757449. ------ 1. ==[ start ]==> (((^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) 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. ------ 51702/3757503. ------ 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.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 9. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 51703/3757566. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 51704/3757593. ------ 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 51705/3757620. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)(^z.a))) 3. ==[ beta ]==> ((a (^y.a))((a b)(^z.a))) 4. ==[ alpha ]==> ((a (^x.a))((a b)(^y.a))) REDUCED to normal form. ------ 51706/3757647. ------ 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.(z z)))) REDUCED to normal form. ------ 51707/3757674. ------ 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))(^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. ------ 51708/3757710. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 51709/3757737. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (a a))) a) REDUCED to normal form. ------ 51710/3757764. ------ 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)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 51711/3757791. ------ 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. ------ 51712/3757845. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(a a))(^a.(^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. ------ 51713/3758016. ------ 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)))) 5. ==[ beta ]==> (((a a) a)(b (a a))) REDUCED to normal form. ------ 51714/3758043. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(a ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(a ((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a a)(^y.y))) 6. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 51715/3758052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) 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. ------ 51716/3758079. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(a a)) b)) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a)) b)) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 51717/3758097. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)(a (^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a b)(a (^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a 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. ------ 51718/3758106. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.b) c)) 3. ==[ beta ]==> (((a (a a))(^x.a)) b) REDUCED to normal form. ------ 51719/3758178. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.b))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.y))) REDUCED to normal form. ------ 51720/3758250. ------ 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. ------ 51721/3758304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))(a a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 51722/3758331. ------ 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. ------ 51723/3758349. ------ 1. ==[ start ]==> (((^a.b) a)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b) a)(((a a) a)(^y.a))) 3. ==[ beta ]==> (b (((a a) a)(^y.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 51724/3758358. ------ 1. ==[ start ]==> ((a (a b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 51725/3758511. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(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. ------ 51726/3758538. ------ 1. ==[ start ]==> (((a b) a)((a b) b)) REDUCED to normal form. ------ 51727/3758565. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a) a) c)) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a) a) c)) REDUCED to normal form. ------ 51728/3758718. ------ 1. ==[ start ]==> (((^a.b)(a a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(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. ------ 51729/3758727. ------ 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. ------ 51730/3758745. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)(a a))) REDUCED to normal form. ------ 51731/3758898. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (^y.b))) REDUCED to normal form. ------ 51732/3758925. ------ 1. ==[ start ]==> (((a b)(a a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 51733/3758952. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(a a))) 3. ==[ beta ]==> ((a (a a))((^y.b)(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(a a))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 51734/3759132. ------ 1. ==[ start ]==> (((a b) b)((a b) a)) REDUCED to normal form. ------ 51735/3759159. ------ 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. ------ 51736/3759186. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) c)) 5. ==[ beta ]==> (((a a)(^x.(a a))) c) REDUCED to normal form. ------ 51737/3759321. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b) a)) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 51738/3759339. ------ 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. ------ 51739/3759348. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 51740/3759375. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 51741/3759438. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 51742/3759465. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(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. ------ 51743/3759492. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a (^z.b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(a (^z.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.b))) REDUCED to normal form. ------ 51744/3759546. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 51745/3759564. ------ 1. ==[ start ]==> (((^a.b) c)((a (a a))(^b.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. ------ 51746/3759573. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a b)(a (^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 51747/3759600. ------ 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) REDUCED to normal form. ------ 51748/3759627. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 51749/3759798. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 51750/3759834. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a) a)) 3. ==[ beta ]==> (((a a) b)((^y.a) a)) 4. ==[ alpha ]==> (((a a) b)((^x.a) a)) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 51751/3759861. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 51752/3759879. ------ 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. ------ 51753/3759906. ------ 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)((^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. ------ 51754/3759960. ------ 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)((^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. ------ 51755/3759996. ------ 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)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51756/3760023. ------ 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))(^y.(^z.z)))) REDUCED to normal form. ------ 51757/3760050. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.a))) REDUCED to normal form. ------ 51758/3760077. ------ 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 (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 51759/3760104. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 51760/3760140. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 51761/3760167. ------ 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 z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 8. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 51762/3760194. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (a b))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a (a b))((^x.a)(^y.a))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 51763/3760221. ------ 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)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.x)) REDUCED to normal form. ------ 51764/3760248. ------ 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)(^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. ------ 51765/3760356. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.(y y)))) REDUCED to normal form. ------ 51766/3760383. ------ 1. ==[ start ]==> ((a (b a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 51767/3760554. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c (a (^z.z)))) 3. ==[ beta ]==> (b (c (a (^z.z)))) 4. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 51768/3760617. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 51769/3760662. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b a)((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b a)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 51770/3760689. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((a 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. ------ 51771/3760725. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 51772/3760743. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c b)) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c b)) 3. ==[ beta ]==> (((a b)(a b))(c b)) REDUCED to normal form. ------ 51773/3760752. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 51774/3760806. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) 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. ------ 51775/3760824. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c (a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(c (a a))) 3. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 51776/3760833. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 51777/3760860. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a a) c)) 3. ==[ beta ]==> (((a a)(^y.a))((a a) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((a a) c)) REDUCED to normal form. ------ 51778/3760887. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 51779/3760932. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 51780/3760950. ------ 1. ==[ start ]==> (((a a)(b a))(a (^b.a))) 2. ==[ alpha ]==> (((a a)(b a))(a (^x.a))) REDUCED to normal form. ------ 51781/3760977. ------ 1. ==[ start ]==> (((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 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. ------ 51782/3761004. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 51783/3761031. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^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. ------ 51784/3761058. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^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. ------ 51785/3761085. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 51786/3761112. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 51787/3761139. ------ 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))) 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. ------ 51788/3761166. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 51789/3761210. ------ 1. ==[ start ]==> (^a.((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1))) x)) 3. ==[ eta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51790/3761211. ------ 1. ==[ start ]==> (a ((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (a ((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 51791/3765960. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a) a) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 51792/3765966. ------ 1. ==[ start ]==> ((^a.a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51793/3766020. ------ 1. ==[ start ]==> ((^a.b)((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) c)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 51794/3766290. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^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. ------ 51795/3766461. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 51796/3766560. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((^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))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((((a a)(^y.y)) b)(((a a)(^z.z)) b))) REDUCED to normal form. ------ 51797/3767343. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((^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)) 4. ==[ alpha ]==> (((((^x.x)(a a)) b)(((^y.y)(a a)) b))(((^z.z)(a a)) b)) 5. ==[ beta ]==> ((((a a) b)(((^y.y)(a a)) b))(((^z.z)(a a)) b)) 6. ==[ alpha ]==> ((((a a) b)(((^x.x)(a a)) b))(((^y.y)(a a)) b)) 7. ==[ beta ]==> ((((a a) b)((a a) b))(((^y.y)(a a)) b)) 8. ==[ alpha ]==> ((((a a) b)((a a) b))(((^x.x)(a a)) b)) 9. ==[ beta ]==> ((((a a) b)((a a) b))((a a) b)) REDUCED to normal form. ------ 51798/3767544. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51799/3767553. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 51800/3767856. ------ 1. ==[ start ]==> ((^a.(a b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a) a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(^y.a)) b) 4. ==[ alpha ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 51801/3768219. ------ 1. ==[ start ]==> (((^a.b)(a a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 51802/3768228. ------ 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. ------ 51803/3768417. ------ 1. ==[ start ]==> (((^a.b) b)(^c.(a b))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(a b))) 3. ==[ beta ]==> (b (^y.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 51804/3768450. ------ 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. ------ 51805/3768624. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.z))) a) 4. ==[ beta ]==> (b a) REDUCED to normal form. ------ 51806/3768822. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(y b))) REDUCED to normal form. ------ 51807/3769125. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a (^z.z))(^x1.(^y1.y1)))((a (^z.z))(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1))))(^x2.x2)) REDUCED to normal form. ------ 51808/3769164. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^b.((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)) REDUCED to normal form. ------ 51809/3769308. ------ 1. ==[ start ]==> (((a b) c)(^d.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) c)(^x.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 51810/3769335. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.((y y) y))) 3. ==[ beta ]==> (((a a) b)(^y.((y y) y))) 4. ==[ alpha ]==> (((a a) b)(^x.((x x) x))) REDUCED to normal form. ------ 51811/3770118. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(y (y y)))) REDUCED to normal form. ------ 51812/3770388. ------ 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) 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. ------ 51813/3770430. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 51814/3770451. ------ 1. ==[ start ]==> (((a a)(b a))(^b.c)) 2. ==[ alpha ]==> (((a a)(b a))(^x.c)) REDUCED to normal form. ------ 51815/3770613. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.b)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 51816/3770712. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 51817/3770717. ------ 1. ==[ start ]==> (^a.(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 51818/3770718. ------ 1. ==[ start ]==> (a (^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 51819/3770724. ------ 1. ==[ start ]==> ((a a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 51820/3770742. ------ 1. ==[ start ]==> (((^a.a) a)((b a)(a a))) 2. ==[ alpha ]==> (((^x.x) a)((b a)(a a))) 3. ==[ beta ]==> (a ((b a)(a a))) REDUCED to normal form. ------ 51821/3770769. ------ 1. ==[ start ]==> (((a a) a)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 51822/3770778. ------ 1. ==[ start ]==> ((a b)((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((a b)((^x.(^y.y)) c)) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 51823/3770796. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 51824/3770823. ------ 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. ------ 51825/3770850. ------ 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. ------ 51826/3770877. ------ 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)((^y.y)((a a) a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)((a a) a))) 5. ==[ beta ]==> (((a a) b)((a a) a)) REDUCED to normal form. ------ 51827/3770904. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))(a b))) REDUCED to normal form. ------ 51828/3770931. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(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. ------ 51829/3770958. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 51830/3771021. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.y))) REDUCED to normal form. ------ 51831/3771048. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 51832/3771057. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(^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. ------ 51833/3771084. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51834/3771165. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))((a 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. ------ 51835/3771219. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 51836/3771291. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b a) a)) 3. ==[ beta ]==> ((a (a a))((b a) a)) REDUCED to normal form. ------ 51837/3771318. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((a (a (a a)))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 51838/3771354. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(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. ------ 51839/3771435. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 51840/3771462. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 51841/3771525. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 51842/3771615. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(a a)) c)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a)) c)) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 51843/3771633. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 51844/3771768. ------ 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 (^x.x))(a a))) REDUCED to normal form. ------ 51845/3771795. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a a)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) a)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) a)((a a)((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> (a ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 51846/3771894. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 51847/3771993. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) a)(^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. ------ 51848/3772020. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 51849/3772074. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y)) a)) 5. ==[ beta ]==> ((a a)(((a a)(^y.y)) a)) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 51850/3772101. ------ 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. ------ 51851/3772137. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.a))) 5. ==[ beta ]==> ((^y.b)(^z.a)) 6. ==[ alpha ]==> ((^x.b)(^y.a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 51852/3772191. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 51853/3772272. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 51854/3772308. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 51855/3772335. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 51856/3772362. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a b)(a (^y.y)))) REDUCED to normal form. ------ 51857/3772389. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51858/3772416. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (a a))) REDUCED to normal form. ------ 51859/3772560. ------ 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 a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.z))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 51860/3772587. ------ 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. ------ 51861/3772614. ------ 1. ==[ start ]==> ((a (a b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a (a b))(((a a) a)(^x.a))) REDUCED to normal form. ------ 51862/3772623. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.b)((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((^z.z) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 51863/3772704. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((a a) a))) IRREDUCIBLE: cycle. ------ 51864/3772785. ------ 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 ((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 51865/3772812. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 51866/3772893. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 51867/3772929. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(c ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c ((a a) a))) 5. ==[ beta ]==> ((^y.a)(c ((a a) a))) 6. ==[ alpha ]==> ((^x.a)(c ((a a) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51868/3772956. ------ 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. ------ 51869/3772974. ------ 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 ((^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. ------ 51870/3772983. ------ 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. ------ 51871/3773019. ------ 1. ==[ start ]==> (((a a)(a b))((^a.b) b)) 2. ==[ alpha ]==> (((a a)(a b))((^x.b) b)) 3. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 51872/3773172. ------ 1. ==[ start ]==> (((^a.b) b)((a a)(a b))) 2. ==[ alpha ]==> (((^x.b) b)((a a)(a b))) 3. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 51873/3773208. ------ 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. ------ 51874/3773217. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(a a))) 3. ==[ beta ]==> ((^y.(a a))((^z.b)(a a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.b)(a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 51875/3773244. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 51876/3773298. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 7. ==[ beta ]==> ((^y.(y y))(a (a a))) 8. ==[ alpha ]==> ((^x.(x x))(a (a a))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 51877/3773379. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (b ((^x1.x1)(a b))) 4. ==[ alpha ]==> (b ((^x.x)(a b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 51878/3773460. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(^a.a))(^b.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. ------ 51879/3773514. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 11. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 12. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 13. ==[ beta ]==> a REDUCED to normal form. ------ 51880/3773523. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(c (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 51881/3773550. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b ((a a) a))) 5. ==[ beta ]==> ((^y.(y y))(b ((a a) a))) 6. ==[ alpha ]==> ((^x.(x x))(b ((a a) a))) 7. ==[ beta ]==> ((b ((a a) a))(b ((a a) a))) REDUCED to normal form. ------ 51882/3773577. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (a b))) REDUCED to normal form. ------ 51883/3773604. ------ 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. ------ 51884/3773631. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 51885/3773775. ------ 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. ------ 51886/3773802. ------ 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)(^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. ------ 51887/3773829. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 51888/3773856. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.(y y)))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.(x x)))) REDUCED to normal form. ------ 51889/3773883. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 51890/3773919. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 51891/3774054. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^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. ------ 51892/3774063. ------ 1. ==[ start ]==> (((a b) c)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(b ((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b) c)(b (^y.y))) 4. ==[ alpha ]==> (((a b) c)(b (^x.x))) REDUCED to normal form. ------ 51893/3774090. ------ 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. ------ 51894/3774117. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 51895/3774171. ------ 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)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 51896/3774198. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 51897/3774216. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(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. ------ 51898/3774297. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^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. ------ 51899/3774396. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 51900/3774423. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (a a)) b)) REDUCED to normal form. ------ 51901/3774450. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) a) c)) 3. ==[ beta ]==> ((a (a b))(((^y.y) a) c)) 4. ==[ alpha ]==> ((a (a b))(((^x.x) a) c)) 5. ==[ beta ]==> ((a (a b))(a c)) REDUCED to normal form. ------ 51902/3774531. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(^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. ------ 51903/3774558. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y)) b)) 3. ==[ beta ]==> (((a b) a)((^y.(y y)) b)) 4. ==[ alpha ]==> (((a b) a)((^x.(x x)) b)) 5. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 51904/3774585. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.a) c)) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a) c)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a) c)) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 51905/3774729. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 51906/3774810. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 51907/3774873. ------ 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. ------ 51908/3774918. ------ 1. ==[ start ]==> (((^a.a)(b a))(c (^a.(^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. ------ 51909/3774945. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> ((^y.y)(b (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 51910/3774999. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.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) REDUCED to normal form. ------ 51911/3775008. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c b)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c b)) REDUCED to normal form. ------ 51912/3775080. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 51913/3775089. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (a a))) REDUCED to normal form. ------ 51914/3775116. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.a))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (a (^y.y)))) REDUCED to normal form. ------ 51915/3775143. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 51916/3775188. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 51917/3775206. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a) c)) 2. ==[ alpha ]==> (((a a)(b a))((^x.x) c)) 3. ==[ beta ]==> (((a a)(b a)) c) REDUCED to normal form. ------ 51918/3775233. ------ 1. ==[ start ]==> (((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.x1))) REDUCED to normal form. ------ 51919/3775260. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 51920/3775287. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.x)) a)) REDUCED to normal form. ------ 51921/3775314. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a a) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))((a a) b)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a a) b)) 5. ==[ beta ]==> (((a a) a)((a a) b)) REDUCED to normal form. ------ 51922/3775341. ------ 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)(^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 51923/3775368. ------ 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. ------ 51924/3775395. ------ 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. ------ 51925/3775422. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a) a)) REDUCED to normal form. ------ 51926/3775467. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 51927/3775473. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a)))) a) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z)))) a) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 51928/3775475. ------ 1. ==[ start ]==> (^a.(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(x (x (^y.(^z.z))))) REDUCED to normal form. ------ 51929/3775476. ------ 1. ==[ start ]==> (a (a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (a (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 51930/3775479. ------ 1. ==[ start ]==> ((^a.a)(^a.(a (^a.(^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)))) REDUCED to normal form. ------ 51931/3779394. ------ 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)))) REDUCED to normal form. ------ 51932/3780225. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a) b) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 51933/3780231. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.x1)) 3. ==[ beta ]==> ((^x1.x1)(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 51934/3780234. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a)))) a) 2. ==[ alpha ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 51935/3780240. ------ 1. ==[ start ]==> ((^a.a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (a (a (^y.(^z.z)))) 4. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 51936/3780243. ------ 1. ==[ start ]==> ((a a)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 51937/3780249. ------ 1. ==[ start ]==> ((^a.(^a.a))((^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. ------ 51938/3780267. ------ 1. ==[ start ]==> ((^a.(a a))((b a)(a a))) 2. ==[ alpha ]==> ((^x.(x x))((b a)(a a))) 3. ==[ beta ]==> (((b a)(a a))((b a)(a a))) REDUCED to normal form. ------ 51939/3780294. ------ 1. ==[ start ]==> ((^a.b)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 51940/3780375. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((^z.z)(^x1.x1)))(^y.y)) 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. ------ 51941/3780531. ------ 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)(^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. ------ 51942/3780735. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 51943/3781080. ------ 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. ------ 51944/3781185. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a 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. ------ 51945/3781827. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 51946/3782286. ------ 1. ==[ start ]==> ((((a a) a) b)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(^x.(a a))) REDUCED to normal form. ------ 51947/3782502. ------ 1. ==[ start ]==> (((a b)(^a.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 51948/3782517. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a)) a)) 3. ==[ beta ]==> (^y.(((^z.(a a)) a)((^z.(a a)) a))) 4. ==[ alpha ]==> (^x.(((^y.(a a)) a)((^z.(a a)) a))) 5. ==[ beta ]==> (^x.((a a)((^z.(a a)) a))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a)) a))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 51949/3782700. ------ 1. ==[ start ]==> (((a b)(a a))(^c.(a b))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(a b))) REDUCED to normal form. ------ 51950/3782898. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> (b (^x1.(^y1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 51951/3782907. ------ 1. ==[ start ]==> (((a b) b)(^b.(a b))) 2. ==[ alpha ]==> (((a b) b)(^x.(a x))) 3. ==[ eta ]==> (((a b) b) a) REDUCED to normal form. ------ 51952/3783096. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 51953/3783438. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^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. ------ 51954/3783609. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(^z.a))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.a))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.a))) REDUCED to normal form. ------ 51955/3783771. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 51956/3784050. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 51957/3784155. ------ 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. ------ 51958/3784158. ------ 1. ==[ start ]==> ((a (b a))(^c.(a (a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(a (a a)))) REDUCED to normal form. ------ 51959/3784392. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.(z z)))) REDUCED to normal form. ------ 51960/3784500. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 51961/3784581. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 51962/3784662. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.a))) REDUCED to normal form. ------ 51963/3784704. ------ 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. ------ 51964/3784725. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 51965/3784806. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.c)) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.c)) REDUCED to normal form. ------ 51966/3784860. ------ 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)(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 51967/3784887. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 51968/3784941. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.b)) REDUCED to normal form. ------ 51969/3784986. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.(^a.a))) 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. ------ 51970/3784992. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a a)) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 51971/3784995. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 51972/3785000. ------ 1. ==[ start ]==> (^a.(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 51973/3785001. ------ 1. ==[ start ]==> (a (^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 51974/3785007. ------ 1. ==[ start ]==> ((a a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 51975/3785016. ------ 1. ==[ start ]==> ((a (^a.a))((^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. ------ 51976/3785034. ------ 1. ==[ start ]==> ((a (a a))((b a)(a a))) REDUCED to normal form. ------ 51977/3785061. ------ 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. ------ 51978/3785115. ------ 1. ==[ start ]==> (((a a)(a a))((a b)(a (a a)))) REDUCED to normal form. ------ 51979/3785142. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (^x.x)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 51980/3785277. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(b a))) REDUCED to normal form. ------ 51981/3785295. ------ 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)(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. ------ 51982/3785340. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 51983/3785367. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 51984/3785376. ------ 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 (^x.x)) b)(a a)) REDUCED to normal form. ------ 51985/3785403. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.b)(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.b)(a (a a)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 51986/3785421. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (a (((a a) a)(^y.(^z.z)))) 6. ==[ alpha ]==> (a (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 51987/3785430. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 51988/3785457. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(^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. ------ 51989/3785484. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a b))) 5. ==[ beta ]==> ((a (^x.x))((a b)(a b))) REDUCED to normal form. ------ 51990/3785502. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(a a)))) REDUCED to normal form. ------ 51991/3785610. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y)) b)) 5. ==[ beta ]==> ((((a a)(^y.y)) b)(((a a)(^y.y)) b)) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(^y.y)) b)) REDUCED to normal form. ------ 51992/3785637. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^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. ------ 51993/3785673. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a b)((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((a b)((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 51994/3785727. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 51995/3785754. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.b)(^x1.b))) 5. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 51996/3785781. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 51997/3785844. ------ 1. ==[ start ]==> (((a a)(a (a a)))(a (b a))) REDUCED to normal form. ------ 51998/3785871. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a)(^z.z))(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))) REDUCED to normal form. ------ 51999/3785898. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(a 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. ------ 52000/3785925. ------ 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. ------ 52001/3785952. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^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. ------ 52002/3786051. ------ 1. ==[ start ]==> (((a (a a)) b)(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(c (^x.(a a)))) REDUCED to normal form. ------ 52003/3786078. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(b (^c.(^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. ------ 52004/3786123. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 52005/3786159. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 52006/3786177. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a b)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 52007/3786186. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 52008/3786420. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((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. ------ 52009/3786510. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.a))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.a))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 7. ==[ beta ]==> (b ((^y.a)(^y.a))) 8. ==[ alpha ]==> (b ((^x.a)(^y.a))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52010/3786537. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 52011/3786591. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.a)(^c.(^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. ------ 52012/3786636. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(a a)) b)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(a a)) b)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a)) b)) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a)) b)) 6. ==[ alpha ]==> ((a ((^x.x) 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 a)) REDUCED to normal form. ------ 52013/3786735. ------ 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. ------ 52014/3786762. ------ 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)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((a a) a))) REDUCED to normal form. ------ 52015/3786789. ------ 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. ------ 52016/3786816. ------ 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. ------ 52017/3786888. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 52018/3786906. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((^y.b)(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52019/3787050. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)((^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. ------ 52020/3787068. ------ 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 (((^z.z)(a a)) a)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) a)) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 52021/3787077. ------ 1. ==[ start ]==> (((a b) a)((^b.(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. ------ 52022/3787095. ------ 1. ==[ start ]==> (((^a.a)(a b))((a b) b)) 2. ==[ alpha ]==> (((^x.x)(a b))((a b) b)) 3. ==[ beta ]==> ((a b)((a b) b)) REDUCED to normal form. ------ 52023/3787104. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 52024/3787158. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 52025/3787185. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52026/3787212. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 52027/3787239. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^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. ------ 52028/3787266. ------ 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. ------ 52029/3787284. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 52030/3787302. ------ 1. ==[ start ]==> (((a a)(a b))((a b)(a a))) REDUCED to normal form. ------ 52031/3787329. ------ 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. ------ 52032/3787356. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a))) 9. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 10. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 11. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 52033/3787383. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 52034/3787410. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a (((^y.y) a)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (a (((^x.x) a)((^y.y)(^z.z)))) 9. ==[ beta ]==> (a (a ((^y.y)(^z.z)))) 10. ==[ alpha ]==> (a (a ((^x.x)(^y.y)))) 11. ==[ beta ]==> (a (a (^y.y))) 12. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 52035/3787437. ------ 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))) REDUCED to normal form. ------ 52036/3787455. ------ 1. ==[ start ]==> (((^a.b) b)(b (^a.b))) 2. ==[ alpha ]==> (((^x.b) b)(b (^y.b))) 3. ==[ beta ]==> (b (b (^y.b))) 4. ==[ alpha ]==> (b (b (^x.b))) REDUCED to normal form. ------ 52037/3787464. ------ 1. ==[ start ]==> (((a b)(a a))((a a)(a b))) REDUCED to normal form. ------ 52038/3787500. ------ 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. ------ 52039/3787527. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a) a)(^a.(^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. ------ 52040/3787581. ------ 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))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((a (a a))(^y.(y y))) 8. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 52041/3787662. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> (b ((a a)(^x1.b))) 4. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 52042/3787671. ------ 1. ==[ start ]==> (((a b) b)((^a.a)(a b))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(a b))) 3. ==[ beta ]==> (((a b) b)(a b)) REDUCED to normal form. ------ 52043/3787698. ------ 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))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 52044/3787716. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a) a) b)) 5. ==[ beta ]==> ((a a)(((a a) a) b)) REDUCED to normal form. ------ 52045/3787725. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)(^a.(^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. ------ 52046/3787743. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> (((^y.y)(^z.z)) c) 6. ==[ alpha ]==> (((^x.x)(^y.y)) c) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 52047/3787752. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(^a.a))(^b.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. ------ 52048/3787806. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.a)(^b.(^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. ------ 52049/3787860. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.b)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.b)) REDUCED to normal form. ------ 52050/3787878. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.b) a)) 3. ==[ beta ]==> (b ((^z.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 52051/3787950. ------ 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. ------ 52052/3787977. ------ 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. ------ 52053/3788004. ------ 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. ------ 52054/3788031. ------ 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. ------ 52055/3788103. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 52056/3788202. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((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. ------ 52057/3788346. ------ 1. ==[ start ]==> (((a b) c)((^a.(^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. ------ 52058/3788373. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a) b)(^y.a)) 6. ==[ alpha ]==> (((a a) b)(^x.a)) REDUCED to normal form. ------ 52059/3788418. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 52060/3788481. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(c (^z.(z z)))) 3. ==[ beta ]==> ((a (^y.b))(c (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.b))(c (^y.(y y)))) REDUCED to normal form. ------ 52061/3788535. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a (^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52062/3788562. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52063/3788580. ------ 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))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 52064/3788589. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 52065/3788616. ------ 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)((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 52066/3788643. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 52067/3788787. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (a (a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b (a (a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (a a)))) 7. ==[ beta ]==> ((^y.y)(b (a (a a)))) 8. ==[ alpha ]==> ((^x.x)(b (a (a a)))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 52068/3788814. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(a ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 52069/3788841. ------ 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. ------ 52070/3788868. ------ 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 (^x.x)))(a (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 52071/3788895. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^y.y)) a)) REDUCED to normal form. ------ 52072/3788922. ------ 1. ==[ start ]==> ((a (b a))((a a)(a (a a)))) REDUCED to normal form. ------ 52073/3789012. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (b ((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 52074/3789093. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 52075/3789156. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(z z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(y y))) REDUCED to normal form. ------ 52076/3789201. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a) b)) 3. ==[ beta ]==> ((b a)((^y.a) b)) 4. ==[ alpha ]==> ((b a)((^x.a) b)) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 52077/3789264. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> ((a (^y.(a a)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 52078/3789282. ------ 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 b)(a b))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a b)(a b))(a (^y.y))) 6. ==[ alpha ]==> (((a b)(a b))(a (^x.x))) REDUCED to normal form. ------ 52079/3789291. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 52080/3789345. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^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. ------ 52081/3789363. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) 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. ------ 52082/3789372. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 52083/3789399. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 52084/3789426. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.a)) REDUCED to normal form. ------ 52085/3789471. ------ 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))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 52086/3789489. ------ 1. ==[ start ]==> (((a a)(b a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 52087/3789543. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(b b)) 5. ==[ beta ]==> ((a (a a))(b b)) REDUCED to normal form. ------ 52088/3789570. ------ 1. ==[ start ]==> (((a (a a))(a b))(a c)) REDUCED to normal form. ------ 52089/3789597. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(b (a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(b (a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(b (a a))) 5. ==[ beta ]==> (((a a) a)(b (a a))) REDUCED to normal form. ------ 52090/3789624. ------ 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)(^y.y))(a (a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 52091/3789651. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 52092/3789678. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(b a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(b a)) 3. ==[ beta ]==> (((a a)((^y.y) a))(b a)) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b a)) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 52093/3789705. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a b)) REDUCED to normal form. ------ 52094/3789750. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a (^a.a))) 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. ------ 52095/3789756. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a)))) b) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z)))) b) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 52096/3789759. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 52097/3789767. ------ 1. ==[ start ]==> (^a.((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52098/3789768. ------ 1. ==[ start ]==> (a ((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52099/3789771. ------ 1. ==[ start ]==> ((^a.a)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52100/3789780. ------ 1. ==[ start ]==> ((^a.(^a.a))(^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. ------ 52101/3792048. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (^y.((^z.((^x1.x1)(z z)))(^z.((^x1.x1)(z z))))) 4. ==[ alpha ]==> (^x.((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.((^y1.y1)(x1 x1)))(^x1.((^y1.y1)(x1 x1)))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.((^x1.x1)(z z)))(^y1.((^z1.z1)(y1 y1)))))) 7. ==[ beta ]==> (^x.((^z.((^x1.x1)(z z)))(^y1.((^z1.z1)(y1 y1))))) 8. ==[ alpha ]==> (^x.((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))) IRREDUCIBLE: cycle. ------ 52102/3792255. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(z z)))(^z.(^x1.(z z))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(y y)))(^x1.(^y1.(x1 x1))))) 5. ==[ beta ]==> ((^y.(^z.(y y)))(^x1.(^y1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(z z)))) 7. ==[ beta ]==> (^y.((^z.(^x1.(z z)))(^z.(^x1.(z z))))) 8. ==[ alpha ]==> (^x.((^y.(^z.(y y)))(^x1.(^y1.(x1 x1))))) 9. ==[ beta ]==> (^x.(^z.((^x1.(^y1.(x1 x1)))(^x1.(^y1.(x1 x1)))))) 10. ==[ alpha ]==> (^x.(^y.((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1)))))) 11. ==[ beta ]==> (^x.(^y.(^x1.((^y1.(^z1.(y1 y1)))(^y1.(^z1.(y1 y1))))))) 12. ==[ alpha ]==> (^x.(^y.(^z.((^x1.(^y1.(x1 x1)))(^z1.(^x2.(z1 z1))))))) 13. ==[ beta ]==> (^x.(^y.(^z.(^y1.((^z1.(^x2.(z1 z1)))(^z1.(^x2.(z1 z1)))))))) 14. ==[ alpha ]==> (^x.(^y.(^z.(^x1.((^y1.(^z1.(y1 y1)))(^x2.(^y2.(x2 x2)))))))) 15. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^z1.((^x2.(^y2.(x2 x2)))(^x2.(^y2.(x2 x2))))))))) 16. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.((^z1.(^x2.(z1 z1)))(^y2.(^z2.(y2 y2))))))))) 17. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^x2.((^y2.(^z2.(y2 y2)))(^y2.(^z2.(y2 y2)))))))))) 18. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.((^x2.(^y2.(x2 x2)))(^z2.(^x3.(z2 z2)))))))))) 19. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^y2.((^z2.(^x3.(z2 z2)))(^z2.(^x3.(z2 z2))))))))))) 20. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.((^y2.(^z2.(y2 y2)))(^x3.(^y3.(x3 x3))))))))))) 21. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^z2.((^x3.(^y3.(x3 x3)))(^x3.(^y3.(x3 x3)))))))))))) 22. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.((^z2.(^x3.(z2 z2)))(^y3.(^z3.(y3 y3)))))))))))) 23. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^x3.((^y3.(^z3.(y3 y3)))(^y3.(^z3.(y3 y3))))))))))))) 24. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.((^x3.(^y3.(x3 x3)))(^z3.(^x4.(z3 z3))))))))))))) 25. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^y3.((^z3.(^x4.(z3 z3)))(^z3.(^x4.(z3 z3)))))))))))))) 26. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.((^y3.(^z3.(y3 y3)))(^x4.(^y4.(x4 x4)))))))))))))) 27. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^z3.((^x4.(^y4.(x4 x4)))(^x4.(^y4.(x4 x4))))))))))))))) 28. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.((^z3.(^x4.(z3 z3)))(^y4.(^z4.(y4 y4))))))))))))))) 29. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^x4.((^y4.(^z4.(y4 y4)))(^y4.(^z4.(y4 y4)))))))))))))))) 30. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.((^x4.(^y4.(x4 x4)))(^z4.(^x5.(z4 z4)))))))))))))))) 31. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^y4.((^z4.(^x5.(z4 z4)))(^z4.(^x5.(z4 z4))))))))))))))))) 32. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.((^y4.(^z4.(y4 y4)))(^x5.(^y5.(x5 x5))))))))))))))))) 33. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^z4.((^x5.(^y5.(x5 x5)))(^x5.(^y5.(x5 x5)))))))))))))))))) 34. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^y4.((^z4.(^x5.(z4 z4)))(^y5.(^z5.(y5 y5)))))))))))))))))) 35. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^y4.(^x5.((^y5.(^z5.(y5 y5)))(^y5.(^z5.(y5 y5))))))))))))))))))) UNREDUCED: maximal number of reductions reached. ------ 52103/3794523. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.(^a.a))) 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. ------ 52104/3794526. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a)))) b) 2. ==[ alpha ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 52105/3794535. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a)))) a) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) a) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52106/3794541. ------ 1. ==[ start ]==> ((^a.a)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52107/3794544. ------ 1. ==[ start ]==> ((a a)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52108/3794550. ------ 1. ==[ start ]==> ((^a.(^a.a))(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. ------ 52109/3794553. ------ 1. ==[ start ]==> ((a (^a.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 52110/3794631. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52111/3794793. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((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)))) REDUCED to normal form. ------ 52112/3794841. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 52113/3795111. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(b 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. ------ 52114/3795360. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52115/3795894. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 52116/3796251. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 52117/3796431. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((^y.b)(a (^z.z))) b) 4. ==[ alpha ]==> (((^x.b)(a (^y.y))) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 52118/3796587. ------ 1. ==[ start ]==> ((((a a) a) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 52119/3796818. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (^y.((a ((^z.z)(a a)))(a ((^z.z)(a a))))) 4. ==[ alpha ]==> (^x.((a ((^y.y)(a a)))(a ((^z.z)(a a))))) 5. ==[ beta ]==> (^x.((a (a a))(a ((^z.z)(a a))))) 6. ==[ alpha ]==> (^x.((a (a a))(a ((^y.y)(a a))))) 7. ==[ beta ]==> (^x.((a (a a))(a (a a)))) REDUCED to normal form. ------ 52120/3796821. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 52121/3797025. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(a (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(a a)))(a (^z.(a a))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(a a)))(a (^z.(a a))))) 5. ==[ beta ]==> ((a (^y.(a a)))(a (^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 52122/3797028. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 52123/3797208. ------ 1. ==[ start ]==> (((a b) b)(^c.(^a.b))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.b))) REDUCED to normal form. ------ 52124/3797415. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(z b))) 3. ==[ beta ]==> (b (^z.(z b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 52125/3797595. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.b))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.b))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.b))) REDUCED to normal form. ------ 52126/3797700. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((((^z.a)(a (a a)))((^z.a)(a (a a))))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)(a (a a)))((^y.a)(a (a a))))(^z.z)) 5. ==[ beta ]==> ((a ((^y.a)(a (a a))))(^z.z)) 6. ==[ alpha ]==> ((a ((^x.a)(a (a a))))(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 52127/3798216. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.((^z.z)(^x1.x1)))) 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. ------ 52128/3798351. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52129/3798456. ------ 1. ==[ start ]==> ((^a.(b a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(b (^y.(y y)))) 3. ==[ eta ]==> (b (b (^y.(y y)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 52130/3798693. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.d)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.d)) REDUCED to normal form. ------ 52131/3798882. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 52132/3799005. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52133/3799053. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 52134/3799107. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(a (^y.y)))) REDUCED to normal form. ------ 52135/3799161. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52136/3799215. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52137/3799242. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(a a))) REDUCED to normal form. ------ 52138/3799287. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 52139/3799293. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a (^a.a))) 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. ------ 52140/3799296. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 52141/3799305. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52142/3799317. ------ 1. ==[ start ]==> ((a a)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52143/3799326. ------ 1. ==[ start ]==> ((a (^a.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 52144/3799335. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (a ((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (a ((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 52145/3799353. ------ 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. ------ 52146/3799380. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 52147/3799407. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 52148/3799461. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52149/3799488. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))((a 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. ------ 52150/3799515. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))(a b))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 52151/3799542. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^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. ------ 52152/3799569. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 52153/3799614. ------ 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. ------ 52154/3799686. ------ 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 (^x.x)) b)((a a)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.a))) REDUCED to normal form. ------ 52155/3799713. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a 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. ------ 52156/3799740. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 52157/3799794. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.b))) REDUCED to normal form. ------ 52158/3799830. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 52159/3799857. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 52160/3799884. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(b a))) 3. ==[ beta ]==> ((a (a a))((^y.y)(b a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(b a))) 5. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 52161/3799902. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b a) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)((b a) a)) 3. ==[ beta ]==> ((a a)((b a) a)) REDUCED to normal form. ------ 52162/3800136. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 52163/3800226. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 52164/3800271. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52165/3800298. ------ 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.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. ------ 52166/3800352. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(a b))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(a b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a b))) 7. ==[ beta ]==> (((^y.y) a)(a b)) 8. ==[ alpha ]==> (((^x.x) a)(a b)) 9. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 52167/3800406. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a a)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 52168/3800442. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 52169/3800469. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 52170/3800496. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 52171/3800523. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(y y)))) 7. ==[ beta ]==> (((a a) a)(^y.(y y))) 8. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 52172/3800559. ------ 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.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 52173/3800586. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 52174/3800613. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(a b))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(a b))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(a b))) 5. ==[ beta ]==> ((a a)((^y.a)(a b))) 6. ==[ alpha ]==> ((a a)((^x.a)(a b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 52175/3800640. ------ 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. ------ 52176/3800667. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 52177/3800892. ------ 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))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 52178/3800946. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(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))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(a a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(a a))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 52179/3800955. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(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. ------ 52180/3800982. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52181/3801027. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (^x.b))(a (a a))) REDUCED to normal form. ------ 52182/3801126. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(b (^b.(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. ------ 52183/3801180. ------ 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. ------ 52184/3801198. ------ 1. ==[ start ]==> (((^a.b) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 52185/3801207. ------ 1. ==[ start ]==> ((a (a b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 52186/3801360. ------ 1. ==[ start ]==> ((((a a) a) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 52187/3801387. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(a a)) a)) 3. ==[ beta ]==> (((a b) a)((a a) a)) REDUCED to normal form. ------ 52188/3801414. ------ 1. ==[ start ]==> (((a a)(^a.b))((a b) b)) 2. ==[ alpha ]==> (((a a)(^x.b))((a b) b)) REDUCED to normal form. ------ 52189/3801567. ------ 1. ==[ start ]==> (((^a.b)(a a))(b (a b))) 2. ==[ alpha ]==> (((^x.b)(a a))(b (a b))) 3. ==[ beta ]==> (b (b (a b))) REDUCED to normal form. ------ 52190/3801594. ------ 1. ==[ start ]==> ((a (^b.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (a a))) REDUCED to normal form. ------ 52191/3801774. ------ 1. ==[ start ]==> (((a b)(a a))(b (^a.b))) 2. ==[ alpha ]==> (((a b)(a a))(b (^x.b))) REDUCED to normal form. ------ 52192/3801801. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(a (^y.(a a)))) 3. ==[ beta ]==> ((a (a a))(a (^y.(a a)))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(a a)))) REDUCED to normal form. ------ 52193/3801981. ------ 1. ==[ start ]==> (((a b) b)((a a)(^a.b))) 2. ==[ alpha ]==> (((a b) b)((a a)(^x.b))) REDUCED to normal form. ------ 52194/3802008. ------ 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. ------ 52195/3802035. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a) b)) REDUCED to normal form. ------ 52196/3802062. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1) c)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z) c)) 5. ==[ beta ]==> (((a (^x.x))(^y.b)) c) REDUCED to normal form. ------ 52197/3802188. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 52198/3802197. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 52199/3802341. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^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))) REDUCED to normal form. ------ 52200/3802368. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(a (^z.b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(a (^z.b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(a (^y.b))) 5. ==[ beta ]==> ((a (a a))(a (^y.b))) 6. ==[ alpha ]==> ((a (a a))(a (^x.b))) REDUCED to normal form. ------ 52201/3802413. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(^a.a))(^a.(^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. ------ 52202/3802422. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(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. ------ 52203/3802449. ------ 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))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))(a ((^y.y) a))) 8. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) a))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 52204/3802476. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 52205/3802647. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (a (a a)))) 3. ==[ beta ]==> (b (c (a (a a)))) REDUCED to normal form. ------ 52206/3802728. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 52207/3802755. ------ 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. ------ 52208/3802764. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(z z)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(c c)) REDUCED to normal form. ------ 52209/3802809. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 52210/3802872. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52211/3802899. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 52212/3802926. ------ 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)(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 52213/3802953. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 52214/3802989. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 52215/3803016. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(^a.a))(^a.a))) 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. ------ 52216/3803043. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (a b))(^y.y)) 8. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 52217/3803070. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.a)(^b.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. ------ 52218/3803097. ------ 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.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 9. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52219/3803124. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.a)(^b.(^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. ------ 52220/3803232. ------ 1. ==[ start ]==> ((a (b a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))(b (^x.(x x)))) REDUCED to normal form. ------ 52221/3803322. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c c)) 3. ==[ beta ]==> (((^y.b)(^y.b))(c c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c c)) 5. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 52222/3803511. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(a a))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(a a))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(a a))) 5. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 52223/3803538. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^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. ------ 52224/3803601. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.y))) REDUCED to normal form. ------ 52225/3803655. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 52226/3803682. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) 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. ------ 52227/3803709. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.z)) b)) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y)) b)) REDUCED to normal form. ------ 52228/3803781. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 52229/3803799. ------ 1. ==[ start ]==> (((a a)(b a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 52230/3803826. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 52231/3803853. ------ 1. ==[ start ]==> ((((^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))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(a a))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a a))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 52232/3803880. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a b))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a b))(a (^x.x))) REDUCED to normal form. ------ 52233/3803907. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 52234/3803934. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^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. ------ 52235/3803961. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b (^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 52236/3803988. ------ 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. ------ 52237/3804015. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 52238/3804060. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a) 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. ------ 52239/3804069. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 52240/3804078. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52241/3804099. ------ 1. ==[ start ]==> ((^a.(^a.a))(^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. ------ 52242/3806367. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(a a)))(^z.(^x1.(a a))))) 4. ==[ alpha ]==> (^x.((^y.(^z.(a a)))(^x1.(^y1.(a a))))) 5. ==[ beta ]==> (^x.(^z.(a a))) 6. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 52243/3808842. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.a)) 3. ==[ beta ]==> ((^x1.a)(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 52244/3808854. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a)))) b) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) b) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52245/3808878. ------ 1. ==[ start ]==> ((^a.(^a.a))((^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. ------ 52246/3808881. ------ 1. ==[ start ]==> ((a (^a.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 52247/3808890. ------ 1. ==[ start ]==> (((^a.a) a)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (a (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 52248/3808896. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1))) a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1))) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52249/3809121. ------ 1. ==[ start ]==> ((^a.(^b.a))(c (^c.(^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. ------ 52250/3809160. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^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. ------ 52251/3809193. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)(^z.z))) 3. ==[ eta ]==> ((^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. ------ 52252/3809364. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z z))(a b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 52253/3809463. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b a) a)) 2. ==[ alpha ]==> ((^x.(x (x x)))((b a) a)) 3. ==[ beta ]==> (((b a) a)(((b a) a)((b a) a))) REDUCED to normal form. ------ 52254/3809688. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52255/3809970. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 52256/3810246. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(^y.y)) a)) 3. ==[ beta ]==> (((((a a)(^y.y)) a)(((a a)(^y.y)) a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> (((((a a)(^x.x)) a)(((a a)(^y.y)) a))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 52257/3810483. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 52258/3810759. ------ 1. ==[ start ]==> ((^a.(a b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.(^z.z))) b) 4. ==[ alpha ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 52259/3810933. ------ 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 (^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 52260/3811146. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.(a a)))((^z.z)(^x1.(a a))))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.(a a)))((^x1.x1)(^y1.(a a))))) 5. ==[ beta ]==> (^x.((^z.(a a))((^x1.x1)(^y1.(a a))))) 6. ==[ alpha ]==> (^x.((^y.(a a))((^z.z)(^x1.(a a))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 52261/3811149. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 52262/3811365. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.(y y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52263/3811743. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> (b (^z.(^x1.z))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 52264/3811752. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 52265/3812028. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((((^z.z) a)(^x1.(x1 x1)))(((^z.z) a)(^x1.(x1 x1))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) a)(^y.(y y)))(((^z.z) a)(^x1.(x1 x1))))(^y1.y1)) 5. ==[ beta ]==> (((a (^y.(y y)))(((^z.z) a)(^x1.(x1 x1))))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(x x)))(((^y.y) a)(^z.(z z))))(^x1.x1)) 7. ==[ beta ]==> (((a (^x.(x x)))(a (^z.(z z))))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.(x x)))(a (^y.(y y))))(^z.z)) REDUCED to normal form. ------ 52266/3812265. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.((y y) y))) REDUCED to normal form. ------ 52267/3812400. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52268/3813129. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.((^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)))(^y.a)) REDUCED to normal form. ------ 52269/3813147. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(z z)))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(y y)))) REDUCED to normal form. ------ 52270/3813228. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((^z.z) a))) 3. ==[ beta ]==> (b (^y.((^z.z) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 52271/3813381. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.c)) REDUCED to normal form. ------ 52272/3813435. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52273/3813543. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.b)) 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)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 52274/3813615. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 52275/3813621. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.a) 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. ------ 52276/3813624. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.a)) REDUCED to normal form. ------ 52277/3813633. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52278/3813663. ------ 1. ==[ start ]==> ((a (^a.a))((^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. ------ 52279/3813672. ------ 1. ==[ start ]==> (((^a.a) a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (a (a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (a (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 52280/3813681. ------ 1. ==[ start ]==> ((a (a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 52281/3813699. ------ 1. ==[ start ]==> (((a a) a)((b a)(a a))) REDUCED to normal form. ------ 52282/3813726. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 52283/3813753. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (b (((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y) a))) 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. ------ 52284/3813780. ------ 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. ------ 52285/3813807. ------ 1. ==[ start ]==> (((a a) b)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 52286/3813834. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^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. ------ 52287/3813861. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(a b))) REDUCED to normal form. ------ 52288/3813888. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 52289/3813906. ------ 1. ==[ start ]==> ((a (^b.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 52290/3813942. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(b a))) 3. ==[ beta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 52291/3813978. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.y))) 3. ==[ beta ]==> ((a a)((b a)(^y.y))) 4. ==[ alpha ]==> ((a a)((b a)(^x.x))) REDUCED to normal form. ------ 52292/3814068. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(a (a a)))) 5. ==[ beta ]==> (a ((^y.b)(a (a a)))) 6. ==[ alpha ]==> (a ((^x.b)(a (a a)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 52293/3814149. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))(a b))) 3. ==[ beta ]==> ((a (^x.(x x)))((a b)(a b))) REDUCED to normal form. ------ 52294/3814167. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) 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. ------ 52295/3814248. ------ 1. ==[ start ]==> ((a (a (a a)))((b a) a)) REDUCED to normal form. ------ 52296/3814284. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 52297/3814338. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(z z)))) 7. ==[ beta ]==> ((^y.b)(^z.(z z))) 8. ==[ alpha ]==> ((^x.b)(^y.(y y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 52298/3814392. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52299/3814446. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 52300/3814473. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 52301/3814563. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 52302/3814572. ------ 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. ------ 52303/3814698. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(a b))) 3. ==[ beta ]==> (((a (a a)) b)(a (a b))) REDUCED to normal form. ------ 52304/3814725. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (a ((a (^y.y))((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((a (^x.x))((^y.y)(a a)))) 7. ==[ beta ]==> (a ((a (^x.x))(a a))) REDUCED to normal form. ------ 52305/3814743. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 52306/3814752. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 52307/3814824. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 52308/3814896. ------ 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.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 52309/3814950. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.b))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.b))) 7. ==[ beta ]==> ((a a)(a (^y.b))) 8. ==[ alpha ]==> ((a a)(a (^x.b))) REDUCED to normal form. ------ 52310/3814977. ------ 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. ------ 52311/3815031. ------ 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. ------ 52312/3815067. ------ 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))(^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. ------ 52313/3815121. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^z.a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52314/3815202. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.b))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 52315/3815229. ------ 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))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52316/3815238. ------ 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)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (a a))) REDUCED to normal form. ------ 52317/3815265. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 52318/3815292. ------ 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. ------ 52319/3815319. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52320/3815346. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(((a a) a) a)) REDUCED to normal form. ------ 52321/3815517. ------ 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. ------ 52322/3815544. ------ 1. ==[ start ]==> ((a (a b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 52323/3815553. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.b)(a (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52324/3815634. ------ 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))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))((^x1.x1)(^y1.y1)))) IRREDUCIBLE: cycle. ------ 52325/3815715. ------ 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 ((^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. ------ 52326/3815742. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.y))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 52327/3815769. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.b)(^a.(^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. ------ 52328/3815823. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^z.(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. ------ 52329/3815904. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 52330/3815913. ------ 1. ==[ start ]==> (((a b)(^a.a))(b (a b))) 2. ==[ alpha ]==> (((a b)(^x.x))(b (a b))) REDUCED to normal form. ------ 52331/3815931. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 52332/3815949. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a)) a)) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 52333/3815976. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.b) b)) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) b) REDUCED to normal form. ------ 52334/3816102. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.y))((a a) a))) 3. ==[ beta ]==> (b ((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a) a))) REDUCED to normal form. ------ 52335/3816147. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> ((^y.(a a))(a (^z.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(a (^y.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52336/3816174. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.b)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 5. ==[ beta ]==> ((^y.b)(a a)) 6. ==[ alpha ]==> ((^x.b)(a a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 52337/3816228. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2) 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. ------ 52338/3816309. ------ 1. ==[ start ]==> (((^a.b)(^a.(^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. ------ 52339/3816363. ------ 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))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 52340/3816390. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)(^a.(^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. ------ 52341/3816444. ------ 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 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 11. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 12. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 13. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 14. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 52342/3816507. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b ((a a) a))) REDUCED to normal form. ------ 52343/3816525. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (b ((^z.z)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.x)(^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 52344/3816534. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 52345/3816561. ------ 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. ------ 52346/3816597. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 52347/3816732. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a) a)(^y.y))) 3. ==[ beta ]==> ((((a a) a) a)(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 52348/3816759. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(^a.a))(^a.(^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. ------ 52349/3816786. ------ 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. ------ 52350/3816813. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 52351/3816849. ------ 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)((^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. ------ 52352/3816984. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52353/3816993. ------ 1. ==[ start ]==> (((a b) c)(c (a (a a)))) REDUCED to normal form. ------ 52354/3817020. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(b (^y.y))) 6. ==[ alpha ]==> (((a a) b)(b (^x.x))) REDUCED to normal form. ------ 52355/3817047. ------ 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. ------ 52356/3817101. ------ 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. ------ 52357/3817128. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.b))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.b))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 52358/3817182. ------ 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)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52359/3817227. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 52360/3817326. ------ 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)))) REDUCED to normal form. ------ 52361/3817353. ------ 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)(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) a)) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) a)) 7. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 52362/3817380. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (a a)) b)) 3. ==[ beta ]==> ((a (a b))((a (a a)) b)) REDUCED to normal form. ------ 52363/3817488. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 52364/3817515. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(z z)) b)) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z)) b)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y)) b)) 5. ==[ beta ]==> (((a a)(a (^x.x)))(b b)) REDUCED to normal form. ------ 52365/3817542. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 52366/3817659. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (b ((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52367/3817740. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 52368/3817803. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b a)) REDUCED to normal form. ------ 52369/3817911. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((a a) a)) REDUCED to normal form. ------ 52370/3817929. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(a (^y.(y y)))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.(y y)))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.(x x)))) REDUCED to normal form. ------ 52371/3817992. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 52372/3818010. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (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. ------ 52373/3818046. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (a a))) 3. ==[ beta ]==> (((a a)(^y.a))(c (a a))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (a a))) REDUCED to normal form. ------ 52374/3818073. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (a (^x1.x1)))) REDUCED to normal form. ------ 52375/3818136. ------ 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))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 52376/3818190. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))((a (^y.y))(^z.z))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 52377/3818217. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 52378/3818244. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z)) a)) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z)) a)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y)) a)) 5. ==[ beta ]==> (((a a) a)((a (^y.y)) a)) 6. ==[ alpha ]==> (((a a) a)((a (^x.x)) a)) REDUCED to normal form. ------ 52379/3818271. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a a) b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a a) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a) b)) REDUCED to normal form. ------ 52380/3818298. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 52381/3818325. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z) b)) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y) b)) 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. ------ 52382/3818352. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 52383/3818397. ------ 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 (a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52384/3818406. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z) a)) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 52385/3818415. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52386/3818432. ------ 1. ==[ start ]==> (^a.(b (b a))) 2. ==[ alpha ]==> (^x.(b (b x))) REDUCED to normal form. ------ 52387/3818433. ------ 1. ==[ start ]==> (a (b (b a))) REDUCED to normal form. ------ 52388/3818463. ------ 1. ==[ start ]==> ((^a.(a a))(^a.(a (^a.(^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 ]==> ((^x1.(x1 (^y1.(^z1.z1))))(^y.(^z.z))) 6. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(^y1.y1))) 7. ==[ beta ]==> ((^x1.(^y1.y1))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52389/3823188. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(x1 x1))) 3. ==[ beta ]==> ((^x1.(x1 x1))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 5. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52390/3823224. ------ 1. ==[ start ]==> ((^a.a)(b (b a))) 2. ==[ alpha ]==> ((^x.x)(b (b a))) 3. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 52391/3823245. ------ 1. ==[ start ]==> (((^a.a) a)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52392/3823251. ------ 1. ==[ start ]==> ((^a.(a a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 52393/3823254. ------ 1. ==[ start ]==> ((a (a a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 52394/3823278. ------ 1. ==[ start ]==> ((^a.b)((b a)(a a))) 2. ==[ alpha ]==> ((^x.b)((b a)(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52395/3823359. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a b)(a (a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 52396/3823719. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))(^z.b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 52397/3823812. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.(b a))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(y a))) 3. ==[ beta ]==> ((a a)(^y.(y a))) 4. ==[ alpha ]==> ((a a)(^x.(x a))) REDUCED to normal form. ------ 52398/3824091. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(b z))) 3. ==[ eta ]==> (((a (^x.x))((^y.y) a)) b) 4. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 52399/3824169. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52400/3824838. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52401/3824934. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.a) d)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a) d)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 52402/3825288. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 52403/3825297. ------ 1. ==[ start ]==> (((a b) a)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) a)(^x.(a a))) REDUCED to normal form. ------ 52404/3825522. ------ 1. ==[ start ]==> (((a a)(a b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> (((a a)(a b))(^x.(x x))) REDUCED to normal form. ------ 52405/3825708. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(a b))((a a)(a b)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a b))((a a)(a b)))) 5. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 52406/3825918. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(a y))) 3. ==[ eta ]==> ((((^x.x)(a a)) a) a) 4. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 52407/3826107. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 52408/3826620. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.a))) REDUCED to normal form. ------ 52409/3827061. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^a.((^a.a)(^a.a)))) 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)(^x.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 52410/3827139. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))((^z.z) a))) 3. ==[ eta ]==> (b ((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 52411/3827511. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(z z)))) REDUCED to normal form. ------ 52412/3827583. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.(^b.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. ------ 52413/3827592. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 52414/3827688. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52415/3827871. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 52416/3827970. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.(^a.a))) 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. ------ 52417/3827976. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((^x.(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. ------ 52418/3827979. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 52419/3827988. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52420/3828018. ------ 1. ==[ start ]==> ((a a)(b (b a))) REDUCED to normal form. ------ 52421/3828036. ------ 1. ==[ start ]==> (((^a.a) a)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52422/3828045. ------ 1. ==[ start ]==> ((a (a a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 52423/3828054. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^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. ------ 52424/3828072. ------ 1. ==[ start ]==> ((a b)((b a)(a a))) REDUCED to normal form. ------ 52425/3828126. ------ 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. ------ 52426/3828153. ------ 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. ------ 52427/3828288. ------ 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)(^z.z)))) REDUCED to normal form. ------ 52428/3828315. ------ 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. ------ 52429/3828351. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.z))) 3. ==[ beta ]==> ((^y.a)((b a)(^z.z))) 4. ==[ alpha ]==> ((^x.a)((b a)(^y.y))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 52430/3828378. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((a 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. ------ 52431/3828387. ------ 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 (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 52432/3828414. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a a)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 52433/3828432. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) a)((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(^y.(y y)))) 5. ==[ beta ]==> (a ((a b)(^y.(y y)))) 6. ==[ alpha ]==> (a ((a b)(^x.(x x)))) REDUCED to normal form. ------ 52434/3828441. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 52435/3828459. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 52436/3828495. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 52437/3828513. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.b))) REDUCED to normal form. ------ 52438/3828603. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(b a))) 3. ==[ beta ]==> ((a a)((^y.y)(b a))) 4. ==[ alpha ]==> ((a a)((^x.x)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 52439/3828621. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a) a)) 3. ==[ beta ]==> ((^y.(y y))((b a) a)) 4. ==[ alpha ]==> ((^x.(x x))((b a) a)) 5. ==[ beta ]==> (((b a) a)((b a) a)) REDUCED to normal form. ------ 52440/3828648. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((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. ------ 52441/3828684. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(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. ------ 52442/3828711. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 52443/3828765. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 52444/3828792. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.b)(^x1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 52445/3828819. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.a)(^b.(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. ------ 52446/3828855. ------ 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. ------ 52447/3828882. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(a (b a))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (b a))) REDUCED to normal form. ------ 52448/3828909. ------ 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))) REDUCED to normal form. ------ 52449/3828936. ------ 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. ------ 52450/3828963. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))((a b)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))((a b) a)) REDUCED to normal form. ------ 52451/3829116. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 52452/3829170. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(^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)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 52453/3829188. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 52454/3829197. ------ 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 a)) REDUCED to normal form. ------ 52455/3829224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z) a))) 7. ==[ beta ]==> ((^y.b)((^z.z) a)) 8. ==[ alpha ]==> ((^x.b)((^y.y) a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 52456/3829431. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(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. ------ 52457/3829521. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(^a.a))(^b.(^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. ------ 52458/3829602. ------ 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))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 52459/3829728. ------ 1. ==[ start ]==> ((a (^a.b))((^c.a) d)) 2. ==[ alpha ]==> ((a (^x.b))((^y.a) d)) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 52460/3829746. ------ 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. ------ 52461/3829773. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (a a))(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.z))) REDUCED to normal form. ------ 52462/3829800. ------ 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. ------ 52463/3829827. ------ 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))) 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. ------ 52464/3829854. ------ 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 (^x.x))((a a)(a a))) REDUCED to normal form. ------ 52465/3829899. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))(a a))) 3. ==[ beta ]==> (b ((^y.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 52466/3829917. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52467/3829998. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.(^x1.x1)))) IRREDUCIBLE: cycle. ------ 52468/3830061. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 52469/3830079. ------ 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 ((a a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 52470/3830088. ------ 1. ==[ start ]==> (((a b) a)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)((^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. ------ 52471/3830106. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((a b)(((^y.y)(a a)) a)) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a)) a)) 5. ==[ beta ]==> ((a b)((a a) a)) REDUCED to normal form. ------ 52472/3830115. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 52473/3830133. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((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. ------ 52474/3830169. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 52475/3830196. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(^x1.(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. ------ 52476/3830223. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 52477/3830250. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 52478/3830277. ------ 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. ------ 52479/3830313. ------ 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. ------ 52480/3830340. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a b)(a a))) REDUCED to normal form. ------ 52481/3830367. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 52482/3830394. ------ 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. ------ 52483/3830421. ------ 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. ------ 52484/3830448. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 52485/3830466. ------ 1. ==[ start ]==> (((^a.b) b)(c (^c.a))) 2. ==[ alpha ]==> (((^x.b) b)(c (^y.a))) 3. ==[ beta ]==> (b (c (^y.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 52486/3830475. ------ 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. ------ 52487/3830502. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)(a b))) 3. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 52488/3830538. ------ 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. ------ 52489/3830592. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 52490/3830673. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 52491/3830682. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 52492/3830709. ------ 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))) 5. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 52493/3830727. ------ 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. ------ 52494/3830736. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 52495/3830754. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a) a) b)) 3. ==[ beta ]==> ((^y.y)(((a a) a) b)) 4. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 52496/3830763. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)(^a.(^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. ------ 52497/3830817. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 52498/3830844. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.a)(^z.(^x1.x1)))((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((^x.a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 9. ==[ beta ]==> (a ((^x1.a)(^y1.(^z1.z1)))) 10. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52499/3830871. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^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. ------ 52500/3830898. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 52501/3830961. ------ 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)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((^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. ------ 52502/3830988. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (a a))((^y.y) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a (a a)) a)) REDUCED to normal form. ------ 52503/3831015. ------ 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. ------ 52504/3831042. ------ 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.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 52505/3831069. ------ 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. ------ 52506/3831114. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)(a a))) 3. ==[ beta ]==> (b ((^y.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52507/3831213. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (^x1.x1))(^y1.(^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. ------ 52508/3831357. ------ 1. ==[ start ]==> (((a b) c)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(y y)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 52509/3831384. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^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. ------ 52510/3831456. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^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. ------ 52511/3831546. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52512/3831591. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^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. ------ 52513/3831600. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 52514/3831627. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^x1.x1))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 52515/3831654. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 52516/3831825. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 52517/3831852. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(a ((^a.a)(^a.a)))) 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)))) 5. ==[ beta ]==> (((a b) a)(a (^y.y))) 6. ==[ alpha ]==> (((a b) a)(a (^x.x))) REDUCED to normal form. ------ 52518/3831879. ------ 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. ------ 52519/3831906. ------ 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 (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (a (^y.y)))) REDUCED to normal form. ------ 52520/3831933. ------ 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. ------ 52521/3832023. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 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. ------ 52522/3832104. ------ 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 ((a (a a)) a)) REDUCED to normal form. ------ 52523/3832167. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 52524/3832212. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y)) a)) 3. ==[ beta ]==> ((b a)((^y.(y y)) a)) 4. ==[ alpha ]==> ((b a)((^x.(x x)) a)) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 52525/3832239. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 52526/3832275. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b (^z.a))) 3. ==[ beta ]==> ((a (^y.(a a)))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.a))) REDUCED to normal form. ------ 52527/3832302. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.(y y)))) REDUCED to normal form. ------ 52528/3832356. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^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)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 52529/3832374. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a a)(^y.a))) 3. ==[ beta ]==> (b ((a a)(^y.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 52530/3832383. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) a)) 5. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 52531/3832410. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 52532/3832437. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^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. ------ 52533/3832482. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 52534/3832500. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(a a))) REDUCED to normal form. ------ 52535/3832527. ------ 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 (^z.z)))) REDUCED to normal form. ------ 52536/3832581. ------ 1. ==[ start ]==> (((a (a a))(a b))(b b)) REDUCED to normal form. ------ 52537/3832635. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b (a a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b (a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (a a))) REDUCED to normal form. ------ 52538/3832662. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 52539/3832689. ------ 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. ------ 52540/3832716. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(b a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b a)) REDUCED to normal form. ------ 52541/3832761. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a)(^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. ------ 52542/3832770. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 52543/3832779. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52544/3832836. ------ 1. ==[ start ]==> ((^a.(a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52545/3833133. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52546/3833403. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^b.(b a))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y a))) 3. ==[ beta ]==> ((^y.(y a))((^y.(y a))(^y.(y a)))) 4. ==[ alpha ]==> ((^x.(x a))((^y.(y a))(^z.(z a)))) 5. ==[ beta ]==> (((^y.(y a))(^z.(z a))) a) 6. ==[ alpha ]==> (((^x.(x a))(^y.(y 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. ------ 52547/3834186. ------ 1. ==[ start ]==> ((^a.((a a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.((a a)(^z.z)))(^y.((a a)(^z.z))))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.((a a)(^y.y)))(^z.((a a)(^x1.x1))))(^y1.((a a)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^y1.((a a)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 52548/3837273. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> ((^x.(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52549/3837561. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.(^a.a))) 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. ------ 52550/3837615. ------ 1. ==[ start ]==> ((^a.(^a.a))(b (b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52551/3837633. ------ 1. ==[ start ]==> ((^a.(a a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52552/3837636. ------ 1. ==[ start ]==> ((a (a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52553/3837645. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(y (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(x (^y.(^z.z)))) REDUCED to normal form. ------ 52554/3837696. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52555/3837858. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) 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 ]==> (^x.(a ((^z.z)(a a)))) 6. ==[ alpha ]==> (^x.(a ((^y.y)(a a)))) 7. ==[ beta ]==> (^x.(a (a a))) REDUCED to normal form. ------ 52556/3837930. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52557/3837933. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52558/3838200. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(b a))) 3. ==[ beta ]==> (((^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)))) 5. ==[ beta ]==> ((b a)(((^y.y)(b a))((^z.z)(b a)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(b a))((^y.y)(b a)))) 7. ==[ beta ]==> ((b a)((b a)((^y.y)(b a)))) 8. ==[ alpha ]==> ((b a)((b a)((^x.x)(b a)))) 9. ==[ beta ]==> ((b a)((b a)(b a))) REDUCED to normal form. ------ 52559/3838203. ------ 1. ==[ start ]==> ((a (a (a a)))(^b.(b a))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(x a))) REDUCED to normal form. ------ 52560/3838425. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52561/3838983. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y)((a a)(^z.z)))((^y.y)((a a)(^z.z))))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x)((a a)(^y.y)))((^z.z)((a a)(^x1.x1))))((^y1.y1)((a a)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^y.y))((^z.z)((a a)(^x1.x1))))((^y1.y1)((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)((a a)(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)((a a)(^x1.x1)))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^x1.x1))) 10. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 52562/3838986. ------ 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. ------ 52563/3839238. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.((z z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.((y y)(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.((y y)(^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 52564/3839316. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 52565/3839496. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((^y.(a a))(a a)) b) 4. ==[ alpha ]==> (((^x.(a a))(a a)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 52566/3839679. ------ 1. ==[ start ]==> (((a b) a)(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 52567/3839883. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(b (a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(b (a b))) 3. ==[ beta ]==> (^y.((b (a b))(b (a b)))) 4. ==[ alpha ]==> (^x.((b (a b))(b (a b)))) REDUCED to normal form. ------ 52568/3839904. ------ 1. ==[ start ]==> (((a a)(a b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 52569/3840090. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b (^z.b))) 3. ==[ beta ]==> ((^y.y)((b (^z.b))(b (^z.b)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.b))(b (^z.b)))) 5. ==[ beta ]==> ((b (^y.b))(b (^z.b))) 6. ==[ alpha ]==> ((b (^x.b))(b (^y.b))) REDUCED to normal form. ------ 52570/3840102. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(a b))) 3. ==[ beta ]==> ((^y.(a a))(^z.(a b))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(a b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52571/3840687. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.(^z.b))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(^z.b))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.b))) REDUCED to normal form. ------ 52572/3840765. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((((^z.(z z))((^x1.x1) a))((^z.(z z))((^x1.x1) a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))((^y.y) a))((^z.(z z))((^x1.x1) a)))(^y1.y1)) 5. ==[ beta ]==> (((((^y.y) a)((^y.y) a))((^z.(z z))((^x1.x1) a)))(^y1.y1)) 6. ==[ alpha ]==> (((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) a)))(^y1.y1)) 7. ==[ beta ]==> (((a ((^y.y) a))((^z.(z z))((^x1.x1) a)))(^y1.y1)) 8. ==[ alpha ]==> (((a ((^x.x) a))((^y.(y y))((^z.z) a)))(^x1.x1)) 9. ==[ beta ]==> (((a a)((^y.(y y))((^z.z) a)))(^x1.x1)) 10. ==[ alpha ]==> (((a a)((^x.(x x))((^y.y) a)))(^z.z)) 11. ==[ beta ]==> (((a a)(((^y.y) a)((^y.y) a)))(^z.z)) 12. ==[ alpha ]==> (((a a)(((^x.x) a)((^y.y) a)))(^z.z)) 13. ==[ beta ]==> (((a a)(a ((^y.y) a)))(^z.z)) 14. ==[ alpha ]==> (((a a)(a ((^x.x) a)))(^y.y)) 15. ==[ beta ]==> (((a a)(a a))(^y.y)) 16. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 52573/3841020. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.((z z) z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((z z) z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((y y) y))) REDUCED to normal form. ------ 52574/3841308. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.((^a.a)(^a.a)))) 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))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 52575/3841443. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52576/3841521. ------ 1. ==[ start ]==> ((^a.(b a))(c (^b.a))) 2. ==[ alpha ]==> ((^x.(b x))(c (^y.a))) 3. ==[ eta ]==> (b (c (^y.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 52577/3841803. ------ 1. ==[ start ]==> (((^a.a)(b a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(y (y y)))) 3. ==[ beta ]==> ((b a)(^y.(y (y y)))) 4. ==[ alpha ]==> ((b a)(^x.(x (x x)))) REDUCED to normal form. ------ 52578/3841884. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)(a b))(^y.((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y) a))) 5. ==[ beta ]==> (((a b)(a b))(^x.a)) REDUCED to normal form. ------ 52579/3841974. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 52580/3842070. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52581/3842073. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 52582/3842145. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.y))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.y))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.x))) REDUCED to normal form. ------ 52583/3842199. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(a (^a.a)))) 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)))) REDUCED to normal form. ------ 52584/3842253. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52585/3842307. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 52586/3842358. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.a)(^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. ------ 52587/3842361. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 52588/3842370. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52589/3842418. ------ 1. ==[ start ]==> ((a (^a.a))(b (b a))) 2. ==[ alpha ]==> ((a (^x.x))(b (b a))) REDUCED to normal form. ------ 52590/3842436. ------ 1. ==[ start ]==> ((a (a a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52591/3842445. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(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. ------ 52592/3842454. ------ 1. ==[ start ]==> (((a a) a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 52593/3842472. ------ 1. ==[ start ]==> (((^a.a)(a a))((b a)(a a))) 2. ==[ alpha ]==> (((^x.x)(a a))((b a)(a a))) 3. ==[ beta ]==> ((a a)((b a)(a a))) REDUCED to normal form. ------ 52594/3842499. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 52595/3842508. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(^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)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 52596/3842553. ------ 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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52597/3842580. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) 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. ------ 52598/3842607. ------ 1. ==[ start ]==> (((^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))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((a a) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((a a) a))) 7. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 52599/3842634. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a b))) 5. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 52600/3842661. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.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. ------ 52601/3842733. ------ 1. ==[ start ]==> ((a ((^a.a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 52602/3842778. ------ 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)))) REDUCED to normal form. ------ 52603/3842805. ------ 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. ------ 52604/3842832. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.(y y)))) REDUCED to normal form. ------ 52605/3842859. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 52606/3842922. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(a b))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(a b))) 5. ==[ beta ]==> (((a a) a)((a b)(a b))) REDUCED to normal form. ------ 52607/3842949. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 52608/3842976. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 52609/3843003. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(b a))) 3. ==[ beta ]==> ((a (a (a a)))(b a)) REDUCED to normal form. ------ 52610/3843075. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((a b)(((^y.y)(a a)) c)) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a)) c)) 5. ==[ beta ]==> ((a b)((a a) c)) REDUCED to normal form. ------ 52611/3843228. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(c ((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 52612/3843318. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 52613/3843363. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52614/3843390. ------ 1. ==[ start ]==> (((^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 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. ------ 52615/3843444. ------ 1. ==[ start ]==> (((^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) 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. ------ 52616/3843498. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 9. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 52617/3843525. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)((a a)(^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. ------ 52618/3843561. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 52619/3843588. ------ 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.(^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. ------ 52620/3843615. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 7. ==[ beta ]==> ((a b)(^y.a)) 8. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 52621/3843678. ------ 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.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. ------ 52622/3843705. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((a a)((^y.(y y))((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((a a) a))) 7. ==[ beta ]==> ((a a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 52623/3843732. ------ 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. ------ 52624/3843759. ------ 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)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 52625/3843786. ------ 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. ------ 52626/3844038. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a ((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(a ((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)(a ((a a)(^y.y)))) 8. ==[ alpha ]==> ((a a)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 52627/3844047. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 52628/3844074. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52629/3844101. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b) c)) 3. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 52630/3844119. ------ 1. ==[ start ]==> ((a (^a.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((a (^x.b))(((a a) a) a)) REDUCED to normal form. ------ 52631/3844245. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 52632/3844290. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 52633/3844299. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(a a))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 52634/3844452. ------ 1. ==[ start ]==> ((((a a) a) b)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) b)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 52635/3844479. ------ 1. ==[ start ]==> (((a b) a)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 52636/3844506. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a a)(^x.b))((a a) a)) REDUCED to normal form. ------ 52637/3844560. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a) c)) REDUCED to normal form. ------ 52638/3844659. ------ 1. ==[ start ]==> (((^a.b)(a a))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(c ((a a) a))) 3. ==[ beta ]==> (b (c ((a a) a))) REDUCED to normal form. ------ 52639/3844686. ------ 1. ==[ start ]==> ((a (^b.(a a)))(b (a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(b (a b))) REDUCED to normal form. ------ 52640/3844704. ------ 1. ==[ start ]==> (((a a)(a b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(^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. ------ 52641/3844866. ------ 1. ==[ start ]==> (((a b)(a a))(c (^c.a))) 2. ==[ alpha ]==> (((a b)(a a))(c (^x.a))) REDUCED to normal form. ------ 52642/3844893. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (^y.b))) 3. ==[ beta ]==> ((a (a a))(b (^y.b))) 4. ==[ alpha ]==> ((a (a a))(b (^x.b))) REDUCED to normal form. ------ 52643/3844902. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(a b))) 3. ==[ beta ]==> ((^y.(a a))((a a)(a b))) 4. ==[ alpha ]==> ((^x.(a a))((a a)(a b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52644/3845073. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 52645/3845100. ------ 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. ------ 52646/3845127. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b) a)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b) a)) REDUCED to normal form. ------ 52647/3845154. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a) a) b)) REDUCED to normal form. ------ 52648/3845280. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 52649/3845316. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.b) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b) a)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 52650/3845460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(b (^z.a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(b (^z.a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(b (^y.a))) 5. ==[ beta ]==> ((a (a a))(b (^y.a))) 6. ==[ alpha ]==> ((a (a a))(b (^x.a))) REDUCED to normal form. ------ 52651/3845487. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(a (^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 52652/3845505. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)(((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. ------ 52653/3845514. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(a a))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 52654/3845541. ------ 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 (^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)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 52655/3845568. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 52656/3845748. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a) d)) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a) d)) 3. ==[ beta ]==> (((a b) c)(a d)) REDUCED to normal form. ------ 52657/3845820. ------ 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. ------ 52658/3845847. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.y)(((^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. ------ 52659/3845856. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1)) 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. ------ 52660/3845883. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(z z)) c)) 3. ==[ beta ]==> ((a (^y.b))((^z.(z z)) c)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(y y)) c)) 5. ==[ beta ]==> ((a (^x.b))(c c)) REDUCED to normal form. ------ 52661/3845901. ------ 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)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) 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. ------ 52662/3845991. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 52663/3846018. ------ 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.(^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. ------ 52664/3846045. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 52665/3846081. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 52666/3846108. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 8. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 52667/3846135. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^a.a))(^a.a))) 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. ------ 52668/3846162. ------ 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))(^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. ------ 52669/3846189. ------ 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)(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.a))) 7. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 8. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 9. ==[ beta ]==> ((^y.a)(^z.a)) 10. ==[ alpha ]==> ((^x.a)(^y.a)) 11. ==[ beta ]==> a REDUCED to normal form. ------ 52670/3846216. ------ 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)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 52671/3846243. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.a)(^b.(^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. ------ 52672/3846324. ------ 1. ==[ start ]==> ((a (b a))(c (^b.a))) 2. ==[ alpha ]==> ((a (b a))(c (^x.a))) REDUCED to normal form. ------ 52673/3846558. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y)) c)) REDUCED to normal form. ------ 52674/3846603. ------ 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. ------ 52675/3846630. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) a)(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. ------ 52676/3846666. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 52677/3846684. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b))((a a)((^y.y) a))) 4. ==[ alpha ]==> (((a b)(a b))((a a)((^x.x) a))) 5. ==[ beta ]==> (((a b)(a b))((a a) a)) REDUCED to normal form. ------ 52678/3846747. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 52679/3846765. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 52680/3846774. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.a))) REDUCED to normal form. ------ 52681/3846801. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) 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. ------ 52682/3846828. ------ 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)) REDUCED to normal form. ------ 52683/3846873. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 52684/3846891. ------ 1. ==[ start ]==> (((a a)(b a))(c (^a.a))) 2. ==[ alpha ]==> (((a a)(b a))(c (^x.x))) REDUCED to normal form. ------ 52685/3846918. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 52686/3846945. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(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))) 5. ==[ beta ]==> ((a (a a))(a (^y.a))) 6. ==[ alpha ]==> ((a (a a))(a (^x.a))) REDUCED to normal form. ------ 52687/3846972. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^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. ------ 52688/3846999. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^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. ------ 52689/3847026. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.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. ------ 52690/3847053. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 52691/3847080. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(b (^z.z))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b (^z.z))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.y))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 52692/3847107. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 52693/3847152. ------ 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 a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52694/3847161. ------ 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. ------ 52695/3847170. ------ 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. ------ 52696/3851673. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52697/3852054. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^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. ------ 52698/3852063. ------ 1. ==[ start ]==> (((a a) a)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 52699/3852069. ------ 1. ==[ start ]==> ((^a.b)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52700/3852351. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 52701/3852510. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^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. ------ 52702/3852621. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z a))) 3. ==[ beta ]==> ((^y.(y y))(^z.(z a))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(y a))) 5. ==[ beta ]==> ((^y.(y a))(^y.(y a))) 6. ==[ alpha ]==> ((^x.(x a))(^y.(y a))) 7. ==[ beta ]==> ((^y.(y a)) a) 8. ==[ alpha ]==> ((^x.(x a)) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52703/3852834. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52704/3852960. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52705/3853647. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52706/3853656. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 52707/3853905. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((((^y.y)(a a))(^z.z)) b) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.y)) b) 5. ==[ beta ]==> (((a a)(^y.y)) b) 6. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 52708/3854106. ------ 1. ==[ start ]==> (((^a.a)(a b))(^b.((^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)(^x.(a a))) REDUCED to normal form. ------ 52709/3854292. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.b))((^z.(^x1.x1))(^y1.b)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.b))((^y1.(^z1.z1))(^x2.b)))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(^x2.b)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.b)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.b))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.b))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52710/3854538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 5. ==[ beta ]==> (^y.(^z.(y y))) 6. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 52711/3854727. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(a z))) 3. ==[ eta ]==> (((^x.x)((^y.y)(a a))) a) 4. ==[ beta ]==> (((^y.y)(a a)) a) 5. ==[ alpha ]==> (((^x.x)(a a)) a) 6. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 52712/3854925. ------ 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))) REDUCED to normal form. ------ 52713/3855174. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> ((((a (a a))(^z.a))((a (a a))(^z.a)))(^y.y)) 4. ==[ alpha ]==> ((((a (a a))(^x.a))((a (a a))(^y.a)))(^z.z)) REDUCED to normal form. ------ 52714/3855429. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 52715/3855591. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^a.(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.z))) 3. ==[ beta ]==> (b (^z.(^x1.z))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 52716/3855930. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a) c)) 2. ==[ alpha ]==> ((^x.(b x))((^y.a) c)) 3. ==[ eta ]==> (b ((^y.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52717/3856104. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^b.(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)))) REDUCED to normal form. ------ 52718/3856212. ------ 1. ==[ start ]==> (((^a.a)(b a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b a)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(y y)))) REDUCED to normal form. ------ 52719/3856302. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^y.a)) REDUCED to normal form. ------ 52720/3856479. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 52721/3856482. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.a))) REDUCED to normal form. ------ 52722/3856554. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.c)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.c)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.c)) 5. ==[ beta ]==> ((a (a a))(^y.c)) 6. ==[ alpha ]==> ((a (a a))(^x.c)) REDUCED to normal form. ------ 52723/3856662. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.b)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.b)) REDUCED to normal form. ------ 52724/3856716. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 52725/3856761. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 52726/3856767. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((^x.(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. ------ 52727/3856779. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52728/3856845. ------ 1. ==[ start ]==> (((^a.a) a)(b (b a))) 2. ==[ alpha ]==> (((^x.x) a)(b (b a))) 3. ==[ beta ]==> (a (b (b a))) REDUCED to normal form. ------ 52729/3856863. ------ 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 ]==> ((^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. ------ 52730/3856872. ------ 1. ==[ start ]==> (((a a) a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 52731/3856881. ------ 1. ==[ start ]==> ((a b)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 52732/3856899. ------ 1. ==[ start ]==> (((a a)(^a.a))((b a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(a a))) REDUCED to normal form. ------ 52733/3856926. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 52734/3856953. ------ 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. ------ 52735/3856980. ------ 1. ==[ start ]==> (((a a) b)((a b)(a (a a)))) REDUCED to normal form. ------ 52736/3857007. ------ 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)))) 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. ------ 52737/3857034. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^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. ------ 52738/3857061. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(a b))) REDUCED to normal form. ------ 52739/3857115. ------ 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)((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. ------ 52740/3857160. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 52741/3857241. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (a ((^y.(a a))((^z.z) a))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y) a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 52742/3857268. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 52743/3857322. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^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)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52744/3857340. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a a))(^y.b))) 3. ==[ beta ]==> (((a a) a)((a (a a))(^y.b))) 4. ==[ alpha ]==> (((a a) a)((a (a a))(^x.b))) REDUCED to normal form. ------ 52745/3857367. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 52746/3857430. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(b a))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(b a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(b a))) 5. ==[ beta ]==> (((^y.y)(b a))((^y.y)(b a))) 6. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(b a))) 7. ==[ beta ]==> ((b a)((^y.y)(b a))) 8. ==[ alpha ]==> ((b a)((^x.x)(b a))) 9. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 52747/3857511. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 7. ==[ beta ]==> ((^y.(a a))(^z.a)) 8. ==[ alpha ]==> ((^x.(a a))(^y.a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52748/3857538. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 52749/3857619. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 52750/3857646. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 52751/3857736. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 52752/3857772. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a)) c)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 52753/3857871. ------ 1. ==[ start ]==> (((a (a a)) b)((a (a a))((a a) a))) REDUCED to normal form. ------ 52754/3857898. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) a)(a b))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(a b))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(a b))) 5. ==[ beta ]==> (a (((^y.y) a)(a b))) 6. ==[ alpha ]==> (a (((^x.x) a)(a b))) 7. ==[ beta ]==> (a (a (a b))) REDUCED to normal form. ------ 52755/3857925. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 52756/3857943. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 52757/3857952. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 52758/3858069. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 52759/3858096. ------ 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)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^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. ------ 52760/3858150. ------ 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. ------ 52761/3858177. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 52762/3858240. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(^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)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52763/3858294. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.b)(^x1.a))) 5. ==[ beta ]==> (a ((^z.b)(^x1.a))) 6. ==[ alpha ]==> (a ((^x.b)(^y.a))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 52764/3858402. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.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. ------ 52765/3858411. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (a b))) REDUCED to normal form. ------ 52766/3858438. ------ 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)))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (a a))) REDUCED to normal form. ------ 52767/3858465. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 52768/3858492. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(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. ------ 52769/3858519. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)(a (^y.y)))) REDUCED to normal form. ------ 52770/3858717. ------ 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. ------ 52771/3858726. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(a a))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(a a))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(a a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52772/3858807. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) IRREDUCIBLE: cycle. ------ 52773/3858888. ------ 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 ((^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. ------ 52774/3858915. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 52775/3858942. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((^y.(a a))(^z.z)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52776/3859077. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52777/3859086. ------ 1. ==[ start ]==> (((a b)(^a.a))(c ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(c ((a a) a))) REDUCED to normal form. ------ 52778/3859104. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 52779/3859149. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 52780/3859176. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.b) b)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.b) b)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b) b)) 5. ==[ beta ]==> ((a (^y.y))((^z.b) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.b) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 52781/3859275. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y)(^z.z)))) 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. ------ 52782/3859320. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (^z.b))) 3. ==[ beta ]==> ((^y.(a a))(b (^z.b))) 4. ==[ alpha ]==> ((^x.(a a))(b (^y.b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52783/3859347. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(a (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 5. ==[ beta ]==> (a (^y.(a a))) 6. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 52784/3859401. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> ((^y.a)(a (^z.z))) 8. ==[ alpha ]==> ((^x.a)(a (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 52785/3859482. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52786/3859536. ------ 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))) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 52787/3859563. ------ 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)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 52788/3859617. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52789/3859680. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(c (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 52790/3859698. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^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. ------ 52791/3859707. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 52792/3859734. ------ 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. ------ 52793/3859797. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 52794/3859932. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 52795/3859959. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^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. ------ 52796/3859986. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 52797/3860022. ------ 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))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 52798/3860157. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52799/3860166. ------ 1. ==[ start ]==> (((a b) c)(d ((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)(d ((^x.x) a))) 3. ==[ beta ]==> (((a b) c)(d a)) REDUCED to normal form. ------ 52800/3860193. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c (a (a a)))) 3. ==[ beta ]==> (((a a) b)(c (a (a a)))) REDUCED to normal form. ------ 52801/3860220. ------ 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. ------ 52802/3860274. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 52803/3860301. ------ 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. ------ 52804/3860355. ------ 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 (^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(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. ------ 52805/3860382. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 52806/3860400. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(a (^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(a (^z.a))) 3. ==[ beta ]==> (b (a (^z.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 52807/3860499. ------ 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)))) REDUCED to normal form. ------ 52808/3860526. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 52809/3860553. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y)) a)) 5. ==[ beta ]==> ((a (a b))((^y.y) a)) 6. ==[ alpha ]==> ((a (a b))((^x.x) a)) 7. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 52810/3860580. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (a a)) b)) REDUCED to normal form. ------ 52811/3860688. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 52812/3860715. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b b)) REDUCED to normal form. ------ 52813/3860742. ------ 1. ==[ start ]==> ((a (b a))((^b.a) c)) 2. ==[ alpha ]==> ((a (b a))((^x.a) c)) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 52814/3860832. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(z z))(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(a a))) 5. ==[ beta ]==> (b ((^z.(z z))(a a))) 6. ==[ alpha ]==> (b ((^x.(x x))(a a))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 52815/3860913. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 52816/3860976. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (a (^y.y)))) REDUCED to normal form. ------ 52817/3861021. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((b a)(^y.(y y))) 6. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 52818/3861084. ------ 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 (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 52819/3861102. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b (^y.a))) 3. ==[ beta ]==> (((a b)(a b))(b (^y.a))) 4. ==[ alpha ]==> (((a b)(a b))(b (^x.a))) REDUCED to normal form. ------ 52820/3861111. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a) a)) REDUCED to normal form. ------ 52821/3861165. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c b)) REDUCED to normal form. ------ 52822/3861183. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^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. ------ 52823/3861192. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b c)) REDUCED to normal form. ------ 52824/3861291. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 52825/3861309. ------ 1. ==[ start ]==> (((a a)(b a))((^b.a) a)) 2. ==[ alpha ]==> (((a a)(b a))((^x.a) a)) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 52826/3861336. ------ 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)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 52827/3861390. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 52828/3861417. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 52829/3861444. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.z)) a)) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.z)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 52830/3861471. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a) b)) REDUCED to normal form. ------ 52831/3861498. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a) 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. ------ 52832/3861525. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 52833/3861570. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 52834/3861579. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 52835/3861588. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 52836/3861690. ------ 1. ==[ start ]==> ((^a.b)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52837/3866388. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.b)) 3. ==[ beta ]==> ((^x1.b)(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52838/3866478. ------ 1. ==[ start ]==> ((^a.(a a))(b (b a))) 2. ==[ alpha ]==> ((^x.(x x))(b (b a))) 3. ==[ beta ]==> ((b (b a))(b (b a))) REDUCED to normal form. ------ 52839/3866499. ------ 1. ==[ start ]==> (((a a) a)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52840/3866505. ------ 1. ==[ start ]==> ((^a.b)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(a (a (^y.(^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52841/3866508. ------ 1. ==[ start ]==> ((a b)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 52842/3866586. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((((^z.z)(a a))((^x1.x1) a))(^y.y)) 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. ------ 52843/3866775. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a a)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(b a))) 3. ==[ eta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 52844/3867345. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(b z))) 3. ==[ eta ]==> ((((^x.x) a)(a (^y.y))) b) 4. ==[ beta ]==> ((a (a (^y.y))) b) 5. ==[ alpha ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 52845/3867396. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52846/3868092. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 52847/3868161. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.b) c)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.b) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 52848/3868335. ------ 1. ==[ start ]==> (((^a.b) a)(^a.(^c.(^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. ------ 52849/3868542. ------ 1. ==[ start ]==> (((^a.a)(a b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 52850/3868551. ------ 1. ==[ start ]==> (((a a)(^a.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 52851/3868776. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 52852/3868935. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))((a a) a))((a (^z.z))((a a) a)))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))((a a) a))((a (^z.z))((a a) a)))) 5. ==[ beta ]==> (((a (^y.y))((a a) a))((a (^z.z))((a a) a))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 52853/3869172. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(a y))) 3. ==[ eta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 52854/3869361. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(^a.b))) 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. ------ 52855/3869550. ------ 1. ==[ start ]==> (((^a.b) c)(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.b))) 3. ==[ beta ]==> (b (^y.(^z.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 52856/3870036. ------ 1. ==[ start ]==> (((a b)(^b.a))(^a.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 52857/3870315. ------ 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.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)))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 52858/3870366. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(a (^z.z)))) 3. ==[ eta ]==> (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. ------ 52859/3870540. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 52860/3870648. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.d)) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.d)) 3. ==[ beta ]==> ((b a)(^y.d)) 4. ==[ alpha ]==> ((b a)(^x.d)) REDUCED to normal form. ------ 52861/3870846. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.a))(^y.a)) REDUCED to normal form. ------ 52862/3870936. ------ 1. ==[ start ]==> (((a a)(b a))(^a.((^a.a) a))) 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. ------ 52863/3871125. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(y (^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 52864/3871197. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) 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. ------ 52865/3871203. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a b)) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 52866/3871206. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 52867/3871299. ------ 1. ==[ start ]==> ((a (a a))(b (b a))) REDUCED to normal form. ------ 52868/3871317. ------ 1. ==[ start ]==> (((a a) a)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 52869/3871326. ------ 1. ==[ start ]==> ((a b)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 52870/3871335. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 52871/3871380. ------ 1. ==[ start ]==> (((a a)(a a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 52872/3871407. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (a (^x.x)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a) a)) REDUCED to normal form. ------ 52873/3871542. ------ 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.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (a a))) REDUCED to normal form. ------ 52874/3871560. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(c (^c.(^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. ------ 52875/3871569. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 52876/3871596. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a a)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(b a))) 3. ==[ beta ]==> ((a a)((a a)(b a))) REDUCED to normal form. ------ 52877/3871632. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((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. ------ 52878/3871686. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (a (((^y.y)(a a))(^z.a))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.a))) 7. ==[ beta ]==> (a ((a a)(^y.a))) 8. ==[ alpha ]==> (a ((a a)(^x.a))) REDUCED to normal form. ------ 52879/3871695. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(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. ------ 52880/3871713. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(y y))) 6. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 52881/3871722. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 52882/3871857. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 52883/3871902. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 52884/3871938. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 52885/3871965. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 52886/3871992. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 52887/3872019. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 52888/3872046. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(^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. ------ 52889/3872073. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 52890/3872136. ------ 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 (^x.x)) a)(b ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b ((a a)(^y.y)))) REDUCED to normal form. ------ 52891/3872163. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(a (b a))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (b a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (b a))) REDUCED to normal form. ------ 52892/3872190. ------ 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. ------ 52893/3872217. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 52894/3872226. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52895/3872370. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 52896/3872397. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 52897/3872442. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 52898/3872478. ------ 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 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52899/3872685. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^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. ------ 52900/3872739. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b) c)) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b) c)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b) c)) 5. ==[ beta ]==> (a ((a b) c)) REDUCED to normal form. ------ 52901/3872775. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 52902/3872802. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 52903/3872856. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 52904/3872883. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52905/3872910. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 52906/3872982. ------ 1. ==[ start ]==> ((a (^a.b))((^a.b) c)) 2. ==[ alpha ]==> ((a (^x.b))((^y.b) c)) 3. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 52907/3873000. ------ 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. ------ 52908/3873027. ------ 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)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (a a)))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 52909/3873054. ------ 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. ------ 52910/3873081. ------ 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. ------ 52911/3873108. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(a b))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a b))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 52912/3873135. ------ 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. ------ 52913/3873153. ------ 1. ==[ start ]==> (((^a.b) a)(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 52914/3873171. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 52915/3873252. ------ 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)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) IRREDUCIBLE: cycle. ------ 52916/3873315. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)((a a) a))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 52917/3873333. ------ 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 ((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 52918/3873342. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 52919/3873360. ------ 1. ==[ start ]==> (((^a.a)(a b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((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. ------ 52920/3873369. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 52921/3873387. ------ 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)(((^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. ------ 52922/3873423. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.b)(^a.(^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. ------ 52923/3873477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 52924/3873504. ------ 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.(^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. ------ 52925/3873531. ------ 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. ------ 52926/3873567. ------ 1. ==[ start ]==> (((a a)(a b))(b (a b))) REDUCED to normal form. ------ 52927/3873594. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 52928/3873621. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)(a a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)(a a))) 5. ==[ beta ]==> ((a (^y.y))((a b)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(a a))) REDUCED to normal form. ------ 52929/3873648. ------ 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. ------ 52930/3873675. ------ 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)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^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 ((^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. ------ 52931/3873702. ------ 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. ------ 52932/3873729. ------ 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))(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. ------ 52933/3873756. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 52934/3873846. ------ 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)(^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. ------ 52935/3873927. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 52936/3873936. ------ 1. ==[ start ]==> (((a b) b)((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 52937/3873963. ------ 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)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 52938/3873981. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(^z.b))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.b))) 5. ==[ beta ]==> ((a a)((a a)(^y.b))) 6. ==[ alpha ]==> ((a a)((a a)(^x.b))) REDUCED to normal form. ------ 52939/3873990. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(a b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a b)) REDUCED to normal form. ------ 52940/3874008. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a b) a)) 3. ==[ beta ]==> ((^y.y)((a b) a)) 4. ==[ alpha ]==> ((^x.x)((a b) a)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 52941/3874017. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 52942/3874071. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(^a.a))(^b.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. ------ 52943/3874098. ------ 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 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> (((^y.(y y))(^z.(z z)))((^y.(y y))(^z.(z z)))) 8. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) 9. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) 10. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 52944/3874125. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)(^b.(^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. ------ 52945/3874152. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 52946/3874179. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 52947/3874215. ------ 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. ------ 52948/3874242. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a b))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 52949/3874269. ------ 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. ------ 52950/3874296. ------ 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. ------ 52951/3874323. ------ 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. ------ 52952/3874350. ------ 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. ------ 52953/3874368. ------ 1. ==[ start ]==> (((^a.b) c)(a (^a.b))) 2. ==[ alpha ]==> (((^x.b) c)(a (^y.b))) 3. ==[ beta ]==> (b (a (^y.b))) 4. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 52954/3874467. ------ 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)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 52955/3874602. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a)) c)) 3. ==[ beta ]==> (b ((a (a a)) c)) REDUCED to normal form. ------ 52956/3874611. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a))(^b.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. ------ 52957/3874638. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 52958/3874665. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.a))(^b.(^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. ------ 52959/3874800. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c (^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(c (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52960/3874827. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 52961/3874854. ------ 1. ==[ start ]==> (((a b)(^b.a))(a (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (^y.a))) REDUCED to normal form. ------ 52962/3874881. ------ 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)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 52963/3874908. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 52964/3875106. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b (a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(b (a (a a)))) 3. ==[ beta ]==> (((a b) a)(b (a (a a)))) REDUCED to normal form. ------ 52965/3875133. ------ 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.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)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 52966/3875160. ------ 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. ------ 52967/3875187. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) 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. ------ 52968/3875277. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (a a))(^z.z))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))(^z.z))) 5. ==[ beta ]==> (b ((a (a a))(^z.z))) 6. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 52969/3875358. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 52970/3875421. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 52971/3875493. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 52972/3875529. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 52973/3875547. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 52974/3875556. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b (^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b (^y.a))) REDUCED to normal form. ------ 52975/3875610. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 52976/3875628. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))(^a.(^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. ------ 52977/3875637. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 52978/3875664. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 52979/3875691. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 52980/3875754. ------ 1. ==[ start ]==> (((a a)(b a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b a))(a ((^x.x) a))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 52981/3875781. ------ 1. ==[ start ]==> (((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 a))) REDUCED to normal form. ------ 52982/3875808. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a a)(a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x)(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. ------ 52983/3875835. ------ 1. ==[ start ]==> (((a (a a))(a b))(c a)) REDUCED to normal form. ------ 52984/3875862. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(b b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(b 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. ------ 52985/3875916. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b (a a))) REDUCED to normal form. ------ 52986/3875943. ------ 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. ------ 52987/3875970. ------ 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))) REDUCED to normal form. ------ 52988/3876015. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.x1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 52989/3876024. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 52990/3876033. ------ 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. ------ 52991/3876086. ------ 1. ==[ start ]==> (^a.((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.x)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^x.x) REDUCED to normal form. ------ 52992/3876087. ------ 1. ==[ start ]==> (a ((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52993/3876144. ------ 1. ==[ start ]==> ((^a.b)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52994/3877980. ------ 1. ==[ start ]==> ((^a.(a b))(^a.(^c.(^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. ------ 52995/3880842. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(a a))) 3. ==[ beta ]==> ((^x1.(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 52996/3880914. ------ 1. ==[ start ]==> ((^a.a)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 52997/3880968. ------ 1. ==[ start ]==> ((^a.b)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 52998/3880971. ------ 1. ==[ start ]==> ((a b)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 52999/3880980. ------ 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. ------ 53000/3881004. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53001/3881166. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a a))(a b))) 3. ==[ beta ]==> (^y.((a (a a))(a b))) 4. ==[ alpha ]==> (^x.((a (a a))(a b))) REDUCED to normal form. ------ 53002/3881250. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(b a))) 3. ==[ beta ]==> ((^y.a)(^z.(b a))) 4. ==[ alpha ]==> ((^x.a)(^y.(b a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 53003/3881508. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^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))))) 4. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.(^y1.y1))((a a)(^z1.z1)))((^x2.(^y2.y2))((a a)(^z2.z2))))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))((a a)(^z1.z1)))((^x2.(^y2.y2))((a a)(^z2.z2))))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2))))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 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. ------ 53004/3882291. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(a a))))((^x2.(^y2.y2))((^z2.z2)(a a)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))((^z1.z1)(a a))))((^x2.(^y2.y2))((^z2.z2)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1)(a a))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(a a)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53005/3882624. ------ 1. ==[ start ]==> ((^a.(^a.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a b)(a (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 53006/3882804. ------ 1. ==[ start ]==> ((^a.(a b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(a (^y.(^z.z)))) 3. ==[ beta ]==> ((a (^y.(^z.z))) b) 4. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 53007/3882807. ------ 1. ==[ start ]==> ((a (a b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53008/3883014. ------ 1. ==[ start ]==> (((a a)(^a.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 53009/3883191. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c ((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c ((a a) a))) 3. ==[ beta ]==> (^y.((c ((a a) a))(c ((a a) a)))) 4. ==[ alpha ]==> (^x.((c ((a a) a))(c ((a a) a)))) REDUCED to normal form. ------ 53010/3883239. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 53011/3883437. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(a b))) 3. ==[ beta ]==> ((^y.y)(^x1.(a b))) 4. ==[ alpha ]==> ((^x.x)(^y.(a b))) 5. ==[ beta ]==> (^y.(a b)) 6. ==[ alpha ]==> (^x.(a b)) REDUCED to normal form. ------ 53012/3883635. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 53013/3884022. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 53014/3884073. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1))(a (^y1.y1)))((^z.(^x1.x1))(a (^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1))))(^x2.x2)) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(a (^z1.z1))))(^x2.x2)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(a (^x1.x1))))(^y1.y1)) 7. ==[ beta ]==> (((^y.(^z.z))(a (^x1.x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1)) 9. ==[ beta ]==> ((^y.y)(^x1.x1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53015/3884355. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^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. ------ 53016/3884490. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.((^a.a)(^a.a)))) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 53017/3884643. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.((^a.a)(^a.a)))) 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))(^x.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 53018/3884778. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 53019/3885138. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 53020/3885309. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 53021/3885378. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 53022/3885399. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 53023/3885480. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.x))) REDUCED to normal form. ------ 53024/3885534. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(a (^a.a)))) 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)))) REDUCED to normal form. ------ 53025/3885588. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53026/3885666. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^x1.x1)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 53027/3885669. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 53028/3885678. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53029/3885744. ------ 1. ==[ start ]==> ((a a)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 53030/3885780. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(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. ------ 53031/3885798. ------ 1. ==[ start ]==> ((a b)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53032/3885807. ------ 1. ==[ start ]==> (((^a.a)(a a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 53033/3885816. ------ 1. ==[ start ]==> (((a a)(^a.a))((^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. ------ 53034/3885834. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(a a))) REDUCED to normal form. ------ 53035/3885888. ------ 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) 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. ------ 53036/3885915. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(a (a a)))) 5. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 53037/3885942. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 53038/3885969. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z)(^x1.x1))((a 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. ------ 53039/3885996. ------ 1. ==[ start ]==> ((a (^b.a))((a (a a))(a b))) 2. ==[ alpha ]==> ((a (^x.a))((a (a a))(a b))) REDUCED to normal form. ------ 53040/3886077. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(b a))) 3. ==[ beta ]==> ((^y.a)((a a)(b a))) 4. ==[ alpha ]==> ((^x.a)((a a)(b a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 53041/3886113. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)(^y.y))) REDUCED to normal form. ------ 53042/3886140. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 53043/3886167. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 53044/3886194. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 53045/3886221. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 53046/3886257. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(^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)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 53047/3886284. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a b)(a b))) REDUCED to normal form. ------ 53048/3886311. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 53049/3886338. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 53050/3886410. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a) b)(((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. ------ 53051/3886581. ------ 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. ------ 53052/3886698. ------ 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 (^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. ------ 53053/3886725. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 53054/3886779. ------ 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.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 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. ------ 53055/3886833. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a b))) 7. ==[ beta ]==> (((^y.y) a)(a b)) 8. ==[ alpha ]==> (((^x.x) a)(a b)) 9. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 53056/3886860. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 53057/3886923. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 53058/3886950. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 53059/3886986. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 53060/3887040. ------ 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.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 a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 53061/3887067. ------ 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. ------ 53062/3887094. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.a)(a b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(a b))) 5. ==[ beta ]==> ((a a)((^y.a)(a b))) 6. ==[ alpha ]==> ((a a)((^x.a)(a b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 53063/3887121. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 53064/3887373. ------ 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)))) 9. ==[ beta ]==> ((a a)(b (a a))) REDUCED to normal form. ------ 53065/3887436. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 53066/3887454. ------ 1. ==[ start ]==> ((a (^a.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a b)(a (^y.y)))) REDUCED to normal form. ------ 53067/3887607. ------ 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. ------ 53068/3887634. ------ 1. ==[ start ]==> ((a (a b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 53069/3887787. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) 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. ------ 53070/3887814. ------ 1. ==[ start ]==> (((a b) a)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b) a)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 53071/3887841. ------ 1. ==[ start ]==> (((a a)(^a.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 53072/3887895. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b) b)) REDUCED to normal form. ------ 53073/3888021. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c ((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c ((a a) a))) REDUCED to normal form. ------ 53074/3888039. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^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. ------ 53075/3888066. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(a a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(a a))) REDUCED to normal form. ------ 53076/3888237. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))((a a) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53077/3888264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 53078/3888408. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) 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. ------ 53079/3888462. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 53080/3888489. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b) a)) REDUCED to normal form. ------ 53081/3888543. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1) c)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) c)) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y))) c) REDUCED to normal form. ------ 53082/3888615. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 53083/3888822. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(b (^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(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. ------ 53084/3888849. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 53085/3888903. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 53086/3889083. ------ 1. ==[ start ]==> (((a b) c)((a (a a)) c)) REDUCED to normal form. ------ 53087/3889155. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 53088/3889182. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(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))) 4. ==[ alpha ]==> ((^x.x)(a ((a a) a))) 5. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 53089/3889191. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 53090/3889218. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 53091/3889236. ------ 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. ------ 53092/3889317. ------ 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 ((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. ------ 53093/3889353. ------ 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))(^z1.z1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^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. ------ 53094/3889380. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 53095/3889416. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 53096/3889443. ------ 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.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 53097/3889470. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a b))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a b))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a b))(^y.y)) 8. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 53098/3889497. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(^a.a))(^a.a))) 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. ------ 53099/3889524. ------ 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 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 11. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53100/3889551. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.a)(^b.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. ------ 53101/3889578. ------ 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)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 53102/3889605. ------ 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)(^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. ------ 53103/3889893. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a b)) REDUCED to normal form. ------ 53104/3889938. ------ 1. ==[ start ]==> (((^a.a)(b a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))(b ((^y.y) a))) 3. ==[ beta ]==> ((b a)(b ((^y.y) a))) 4. ==[ alpha ]==> ((b a)(b ((^x.x) a))) 5. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 53105/3889965. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(a (a (a a)))) 3. ==[ beta ]==> ((^y.y)(a (a (a a)))) 4. ==[ alpha ]==> ((^x.x)(a (a (a a)))) 5. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 53106/3890001. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a) b)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a) b)) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 53107/3890019. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 53108/3890028. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^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. ------ 53109/3890082. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) 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. ------ 53110/3890100. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c b)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(c b)) 3. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 53111/3890109. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 53112/3890136. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a)(^b.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. ------ 53113/3890163. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) 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. ------ 53114/3890208. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (a (^x1.x1)))) REDUCED to normal form. ------ 53115/3890226. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a a)(b a))(^y.a)) 4. ==[ alpha ]==> (((a a)(b a))(^x.a)) REDUCED to normal form. ------ 53116/3890280. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (^a.(^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. ------ 53117/3890307. ------ 1. ==[ start ]==> (((a (a a))(a b))(a (^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(a (^x.a))) REDUCED to normal form. ------ 53118/3890334. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a a))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 53119/3890361. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)(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. ------ 53120/3890388. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^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. ------ 53121/3890415. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.(^x1.x1)))) 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. ------ 53122/3890442. ------ 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. ------ 53123/3890487. ------ 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))((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. ------ 53124/3890496. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 53125/3890505. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53126/3895413. ------ 1. ==[ start ]==> ((^a.(^a.a))((^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. ------ 53127/3895470. ------ 1. ==[ start ]==> (((^a.a)(a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 53128/3895479. ------ 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. ------ 53129/3895767. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 53130/3896037. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 53131/3896223. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53132/3896316. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(b y))) 3. ==[ eta ]==> (((^x.(x x)) b) b) 4. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 53133/3896559. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 53134/3896781. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^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)))) 4. ==[ alpha ]==> ((((a (^x.x))(^y.(a a)))((a (^z.z))(^x1.(a a))))((a (^y1.y1))(^z1.(a a)))) REDUCED to normal form. ------ 53135/3896820. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((a a)(^z.z)))) 5. ==[ beta ]==> (^y.((a a)(^z.z))) 6. ==[ alpha ]==> (^x.((a a)(^y.y))) REDUCED to normal form. ------ 53136/3897072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((y1 y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((x1 x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53137/3897288. ------ 1. ==[ start ]==> (((^a.b) a)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (b (^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 53138/3897306. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^a.(^c.(^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. ------ 53139/3897522. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^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. ------ 53140/3897681. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.a))((^z.a)(^x1.a)))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.a))((^x1.a)(^y1.a)))) 5. ==[ beta ]==> (^x.(a ((^x1.a)(^y1.a)))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.a)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 53141/3898143. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(a z))) 3. ==[ eta ]==> (((^x.(^y.y))(a b)) a) 4. ==[ beta ]==> ((^y.y) a) 5. ==[ alpha ]==> ((^x.x) a) 6. ==[ beta ]==> a REDUCED to normal form. ------ 53142/3898503. ------ 1. ==[ start ]==> (((^a.b) c)(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)(^y.((a a) a))) 3. ==[ beta ]==> (b (^y.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 53143/3898563. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((((^z.z)(^x1.x1))(^y1.(^z1.z1)))(((^z.z)(^x1.x1))(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2))))(^z2.z2)) 5. ==[ beta ]==> ((((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2))))(^z2.z2)) 6. ==[ alpha ]==> ((((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))(^y2.y2)) 7. ==[ beta ]==> (((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))(^y2.y2)) 8. ==[ alpha ]==> (((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1))))(^x2.x2)) 9. ==[ beta ]==> ((^y.y)(^x2.x2)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53144/3898845. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^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. ------ 53145/3898854. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.((z z) z))) REDUCED to normal form. ------ 53146/3898989. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 53147/3899133. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53148/3899319. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y)) b)) 3. ==[ eta ]==> (b ((^y.(y y)) b)) 4. ==[ alpha ]==> (b ((^x.(x x)) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 53149/3899412. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53150/3899628. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(^y1.(y1 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. ------ 53151/3899868. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 53152/3899889. ------ 1. ==[ start ]==> (((a a)(b a))(^c.c)) 2. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 53153/3899970. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.c)) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.c)) REDUCED to normal form. ------ 53154/3900156. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a a)(^a.a))) 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. ------ 53155/3900168. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53156/3900252. ------ 1. ==[ start ]==> ((a (^a.a))((^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. ------ 53157/3900288. ------ 1. ==[ start ]==> (((a a) a)(b (b a))) REDUCED to normal form. ------ 53158/3900306. ------ 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))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 53159/3900315. ------ 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. ------ 53160/3900342. ------ 1. ==[ start ]==> (((^a.a) b)((b a)(a a))) 2. ==[ alpha ]==> (((^x.x) b)((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 53161/3900369. ------ 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. ------ 53162/3900396. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a a) b)((a a)((^y.y) a))) 4. ==[ alpha ]==> (((a a) b)((a a)((^x.x) a))) 5. ==[ beta ]==> (((a a) b)((a a) a)) REDUCED to normal form. ------ 53163/3900423. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a b)(a (a a)))) REDUCED to normal form. ------ 53164/3900450. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 53165/3900477. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))((a 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. ------ 53166/3900531. ------ 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)(((^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. ------ 53167/3900603. ------ 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)(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. ------ 53168/3900684. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53169/3900783. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))(^z.b))) REDUCED to normal form. ------ 53170/3900810. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) 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. ------ 53171/3900846. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z))((a a)(^x1.x1)))((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 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. ------ 53172/3900873. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^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. ------ 53173/3900954. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 53174/3900981. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 53175/3901035. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 53176/3901062. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 53177/3901152. ------ 1. ==[ start ]==> (((^a.(a a)) b)(a (b a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(a (b a))) 3. ==[ beta ]==> ((b b)(a (b a))) REDUCED to normal form. ------ 53178/3901287. ------ 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.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. ------ 53179/3901314. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (a a))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))((a a) a))) 5. ==[ beta ]==> (a ((a (a a))((a a) a))) REDUCED to normal form. ------ 53180/3901341. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 53181/3901368. ------ 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.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 53182/3901395. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.a))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 53183/3901485. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 53184/3901512. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 53185/3901539. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 53186/3901593. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.b))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.b))) 7. ==[ beta ]==> ((a a)(a (^y.b))) 8. ==[ alpha ]==> ((a a)(a (^x.b))) REDUCED to normal form. ------ 53187/3901620. ------ 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. ------ 53188/3901656. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 53189/3901710. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 53190/3901791. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^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)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 53191/3901872. ------ 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.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(a a)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 53192/3901881. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(b (a a))) REDUCED to normal form. ------ 53193/3901908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a ((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53194/3901935. ------ 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. ------ 53195/3901971. ------ 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. ------ 53196/3902124. ------ 1. ==[ start ]==> (((^a.b) a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) 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)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 53197/3902142. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(a (^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 53198/3902304. ------ 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 ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 53199/3902331. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 53200/3902358. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^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. ------ 53201/3902412. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 53202/3902493. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 53203/3902520. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 53204/3902592. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a)) a)) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a)) a)) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 53205/3902619. ------ 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. ------ 53206/3902691. ------ 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. ------ 53207/3902736. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.a))) 3. ==[ beta ]==> ((^y.(a a))(c (^z.a))) 4. ==[ alpha ]==> ((^x.(a a))(c (^y.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53208/3902763. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(b (^x1.b))) 3. ==[ beta ]==> ((^y.y)(b (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(b (^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 53209/3902817. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(a a))) 5. ==[ beta ]==> ((^y.y)((^y1.b)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 7. ==[ beta ]==> ((^y.b)(a a)) 8. ==[ alpha ]==> ((^x.b)(a a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 53210/3902898. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 53211/3902952. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a) a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 53212/3902979. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)(a b))) 3. ==[ beta ]==> ((^y.y)((^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. ------ 53213/3903114. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.a)(^b.(^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. ------ 53214/3903123. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(c (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 53215/3903150. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((a a) a))) REDUCED to normal form. ------ 53216/3903186. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b) a)) 3. ==[ beta ]==> (((a a)(a a))((^y.b) a)) 4. ==[ alpha ]==> (((a a)(a a))((^x.b) a)) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 53217/3903213. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a) b)) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 53218/3903240. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y)) c)) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 53219/3903339. ------ 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. ------ 53220/3903375. ------ 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. ------ 53221/3903402. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 53222/3903438. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 7. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53223/3903573. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(^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. ------ 53224/3903654. ------ 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))(^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. ------ 53225/3903690. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a ((a a) a))) REDUCED to normal form. ------ 53226/3903717. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 53227/3903771. ------ 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)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53228/3903798. ------ 1. ==[ start ]==> ((((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)))) REDUCED to normal form. ------ 53229/3903816. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 53230/3903825. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 53231/3903915. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 53232/3903942. ------ 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 (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 53233/3903969. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a b))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 53234/3903996. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a)(^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. ------ 53235/3904023. ------ 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. ------ 53236/3904131. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 53237/3904158. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (b a))((^x.(x x)) b)) 3. ==[ beta ]==> ((a (b a))(b b)) REDUCED to normal form. ------ 53238/3904248. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 53239/3904329. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(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. ------ 53240/3904437. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 53241/3904464. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)(^y1.(y1 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. ------ 53242/3904500. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(a a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (a a))) REDUCED to normal form. ------ 53243/3904518. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))(c (^x.(^y.y)))) REDUCED to normal form. ------ 53244/3904527. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 53245/3904599. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(a a))) 3. ==[ beta ]==> (b ((^y.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 53246/3904608. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c b)) REDUCED to normal form. ------ 53247/3904635. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b c)) 3. ==[ beta ]==> (((a a)(^y.a))(b c)) 4. ==[ alpha ]==> (((a a)(^x.a))(b c)) REDUCED to normal form. ------ 53248/3904707. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 53249/3904725. ------ 1. ==[ start ]==> (((a a)(b a))((a a) c)) REDUCED to normal form. ------ 53250/3904752. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 53251/3904779. ------ 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))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 53252/3904806. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a) c)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x) c)) 3. ==[ beta ]==> (((a (a a))(a b)) c) REDUCED to normal form. ------ 53253/3904833. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(^z.z))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 53254/3904860. ------ 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)(^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 53255/3904887. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 53256/3904914. ------ 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. ------ 53257/3904941. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 53258/3904986. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(b a)) 3. ==[ beta ]==> ((^y.(^z.z))(b a)) 4. ==[ alpha ]==> ((^x.(^y.y))(b a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53259/3904995. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 53260/3905004. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 53261/3906969. ------ 1. ==[ start ]==> ((^a.(a b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.((^z.z)(a a))) b) 4. ==[ alpha ]==> ((^x.((^y.y)(a a))) b) 5. ==[ beta ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53262/3909975. ------ 1. ==[ start ]==> ((^a.b)(b (b a))) 2. ==[ alpha ]==> ((^x.b)(b (b a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 53263/3909996. ------ 1. ==[ start ]==> (((a a)(^a.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 53264/3910011. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^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. ------ 53265/3910056. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^z.z))(a (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 53266/3910245. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ eta ]==> ((^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. ------ 53267/3910293. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 53268/3910416. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 53269/3910554. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^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. ------ 53270/3910842. ------ 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. ------ 53271/3910866. ------ 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)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53272/3911337. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 53273/3911589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53274/3911631. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a)) b)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 53275/3911811. ------ 1. ==[ start ]==> ((^a.(a b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a a)((^y.y)(a a)))) 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. ------ 53276/3911814. ------ 1. ==[ start ]==> ((a (a b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a b))(^x.((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a b))(^x.(a a))) REDUCED to normal form. ------ 53277/3912273. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(y y)))) 7. ==[ beta ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 53278/3912405. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)((^x1.x1)(^y1.y1)))(((^z.z) a)((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> ((((^y.y) a)((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> ((a (^x.x))(a ((^z.z)(^x1.x1)))) 12. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.z)))) 13. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 14. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 53279/3912660. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^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. ------ 53280/3912669. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(a z))) 3. ==[ eta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 53281/3912867. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(y b))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y b))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x b))) REDUCED to normal form. ------ 53282/3913020. ------ 1. ==[ start ]==> (((^a.b) c)(^d.(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 53283/3913029. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 53284/3913371. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.a))) REDUCED to normal form. ------ 53285/3913812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 53286/3913836. ------ 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. ------ 53287/3914262. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 53288/3914343. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.((^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)))(^x1.a)) REDUCED to normal form. ------ 53289/3914385. ------ 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. ------ 53290/3914433. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.((^x1.x1) 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. ------ 53291/3914487. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(a (^y.y)))) REDUCED to normal form. ------ 53292/3914568. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.c)) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.c)) REDUCED to normal form. ------ 53293/3914622. ------ 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)))) REDUCED to normal form. ------ 53294/3914667. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 53295/3914673. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b a)) 3. ==[ beta ]==> ((b a)(^y.(^z.z))) 4. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 53296/3914787. ------ 1. ==[ start ]==> (((^a.a) a)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (a ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 53297/3914823. ------ 1. ==[ start ]==> ((a b)(b (b a))) REDUCED to normal form. ------ 53298/3914841. ------ 1. ==[ start ]==> (((a a)(^a.a))((^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. ------ 53299/3914859. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 53300/3914877. ------ 1. ==[ start ]==> (((a a)(a a))((b a)(a a))) REDUCED to normal form. ------ 53301/3914904. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 53302/3915039. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a a))(a b))) REDUCED to normal form. ------ 53303/3915066. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) a)((^a.a)(