MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(c(x0))) → Wait(Right1(x0))
Begin(c(x0)) → Wait(Right2(x0))
Begin(B(A(x0))) → Wait(Right3(x0))
Begin(A(x0)) → Wait(Right4(x0))
Begin(a(C(x0))) → Wait(Right5(x0))
Begin(C(x0)) → Wait(Right6(x0))
Begin(A(B(x0))) → Wait(Right7(x0))
Begin(B(x0)) → Wait(Right8(x0))
Begin(c(b(x0))) → Wait(Right9(x0))
Begin(b(x0)) → Wait(Right10(x0))
Begin(C(a(x0))) → Wait(Right11(x0))
Begin(a(x0)) → Wait(Right12(x0))
Begin(A(x0)) → Wait(Right13(x0))
Begin(a(x0)) → Wait(Right14(x0))
Begin(B(x0)) → Wait(Right15(x0))
Begin(b(x0)) → Wait(Right16(x0))
Begin(C(x0)) → Wait(Right17(x0))
Begin(c(x0)) → Wait(Right18(x0))
Right1(a(End(x0))) → Left(c(b(a(End(x0)))))
Right2(a(b(End(x0)))) → Left(c(b(a(End(x0)))))
Right3(C(End(x0))) → Left(A(B(C(End(x0)))))
Right4(C(B(End(x0)))) → Left(A(B(C(End(x0)))))
Right5(b(End(x0))) → Left(C(a(b(End(x0)))))
Right6(b(a(End(x0)))) → Left(C(a(b(End(x0)))))
Right7(c(End(x0))) → Left(B(A(c(End(x0)))))
Right8(c(A(End(x0)))) → Left(B(A(c(End(x0)))))
Right9(A(End(x0))) → Left(b(c(A(End(x0)))))
Right10(A(c(End(x0)))) → Left(b(c(A(End(x0)))))
Right11(B(End(x0))) → Left(a(C(B(End(x0)))))
Right12(B(C(End(x0)))) → Left(a(C(B(End(x0)))))
Right13(a(End(x0))) → Left(End(x0))
Right14(A(End(x0))) → Left(End(x0))
Right15(b(End(x0))) → Left(End(x0))
Right16(B(End(x0))) → Left(End(x0))
Right17(c(End(x0))) → Left(End(x0))
Right18(C(End(x0))) → Left(End(x0))
Right1(a(x0)) → Aa(Right1(x0))
Right2(a(x0)) → Aa(Right2(x0))
Right3(a(x0)) → Aa(Right3(x0))
Right4(a(x0)) → Aa(Right4(x0))
Right5(a(x0)) → Aa(Right5(x0))
Right6(a(x0)) → Aa(Right6(x0))
Right7(a(x0)) → Aa(Right7(x0))
Right8(a(x0)) → Aa(Right8(x0))
Right9(a(x0)) → Aa(Right9(x0))
Right10(a(x0)) → Aa(Right10(x0))
Right11(a(x0)) → Aa(Right11(x0))
Right12(a(x0)) → Aa(Right12(x0))
Right13(a(x0)) → Aa(Right13(x0))
Right14(a(x0)) → Aa(Right14(x0))
Right15(a(x0)) → Aa(Right15(x0))
Right16(a(x0)) → Aa(Right16(x0))
Right17(a(x0)) → Aa(Right17(x0))
Right18(a(x0)) → Aa(Right18(x0))
Right1(b(x0)) → Ab(Right1(x0))
Right2(b(x0)) → Ab(Right2(x0))
Right3(b(x0)) → Ab(Right3(x0))
Right4(b(x0)) → Ab(Right4(x0))
Right5(b(x0)) → Ab(Right5(x0))
Right6(b(x0)) → Ab(Right6(x0))
Right7(b(x0)) → Ab(Right7(x0))
Right8(b(x0)) → Ab(Right8(x0))
Right9(b(x0)) → Ab(Right9(x0))
Right10(b(x0)) → Ab(Right10(x0))
Right11(b(x0)) → Ab(Right11(x0))
Right12(b(x0)) → Ab(Right12(x0))
Right13(b(x0)) → Ab(Right13(x0))
Right14(b(x0)) → Ab(Right14(x0))
Right15(b(x0)) → Ab(Right15(x0))
Right16(b(x0)) → Ab(Right16(x0))
Right17(b(x0)) → Ab(Right17(x0))
Right18(b(x0)) → Ab(Right18(x0))
Right1(c(x0)) → Ac(Right1(x0))
Right2(c(x0)) → Ac(Right2(x0))
Right3(c(x0)) → Ac(Right3(x0))
Right4(c(x0)) → Ac(Right4(x0))
Right5(c(x0)) → Ac(Right5(x0))
Right6(c(x0)) → Ac(Right6(x0))
Right7(c(x0)) → Ac(Right7(x0))
Right8(c(x0)) → Ac(Right8(x0))
Right9(c(x0)) → Ac(Right9(x0))
Right10(c(x0)) → Ac(Right10(x0))
Right11(c(x0)) → Ac(Right11(x0))
Right12(c(x0)) → Ac(Right12(x0))
Right13(c(x0)) → Ac(Right13(x0))
Right14(c(x0)) → Ac(Right14(x0))
Right15(c(x0)) → Ac(Right15(x0))
Right16(c(x0)) → Ac(Right16(x0))
Right17(c(x0)) → Ac(Right17(x0))
Right18(c(x0)) → Ac(Right18(x0))
Right1(C(x0)) → AC(Right1(x0))
Right2(C(x0)) → AC(Right2(x0))
Right3(C(x0)) → AC(Right3(x0))
Right4(C(x0)) → AC(Right4(x0))
Right5(C(x0)) → AC(Right5(x0))
Right6(C(x0)) → AC(Right6(x0))
Right7(C(x0)) → AC(Right7(x0))
Right8(C(x0)) → AC(Right8(x0))
Right9(C(x0)) → AC(Right9(x0))
Right10(C(x0)) → AC(Right10(x0))
Right11(C(x0)) → AC(Right11(x0))
Right12(C(x0)) → AC(Right12(x0))
Right13(C(x0)) → AC(Right13(x0))
Right14(C(x0)) → AC(Right14(x0))
Right15(C(x0)) → AC(Right15(x0))
Right16(C(x0)) → AC(Right16(x0))
Right17(C(x0)) → AC(Right17(x0))
Right18(C(x0)) → AC(Right18(x0))
Right1(B(x0)) → AB(Right1(x0))
Right2(B(x0)) → AB(Right2(x0))
Right3(B(x0)) → AB(Right3(x0))
Right4(B(x0)) → AB(Right4(x0))
Right5(B(x0)) → AB(Right5(x0))
Right6(B(x0)) → AB(Right6(x0))
Right7(B(x0)) → AB(Right7(x0))
Right8(B(x0)) → AB(Right8(x0))
Right9(B(x0)) → AB(Right9(x0))
Right10(B(x0)) → AB(Right10(x0))
Right11(B(x0)) → AB(Right11(x0))
Right12(B(x0)) → AB(Right12(x0))
Right13(B(x0)) → AB(Right13(x0))
Right14(B(x0)) → AB(Right14(x0))
Right15(B(x0)) → AB(Right15(x0))
Right16(B(x0)) → AB(Right16(x0))
Right17(B(x0)) → AB(Right17(x0))
Right18(B(x0)) → AB(Right18(x0))
Right1(A(x0)) → AA(Right1(x0))
Right2(A(x0)) → AA(Right2(x0))
Right3(A(x0)) → AA(Right3(x0))
Right4(A(x0)) → AA(Right4(x0))
Right5(A(x0)) → AA(Right5(x0))
Right6(A(x0)) → AA(Right6(x0))
Right7(A(x0)) → AA(Right7(x0))
Right8(A(x0)) → AA(Right8(x0))
Right9(A(x0)) → AA(Right9(x0))
Right10(A(x0)) → AA(Right10(x0))
Right11(A(x0)) → AA(Right11(x0))
Right12(A(x0)) → AA(Right12(x0))
Right13(A(x0)) → AA(Right13(x0))
Right14(A(x0)) → AA(Right14(x0))
Right15(A(x0)) → AA(Right15(x0))
Right16(A(x0)) → AA(Right16(x0))
Right17(A(x0)) → AA(Right17(x0))
Right18(A(x0)) → AA(Right18(x0))
Aa(Left(x0)) → Left(a(x0))
Ab(Left(x0)) → Left(b(x0))
Ac(Left(x0)) → Left(c(x0))
AC(Left(x0)) → Left(C(x0))
AB(Left(x0)) → Left(B(x0))
AA(Left(x0)) → Left(A(x0))
Wait(Left(x0)) → Begin(x0)
a(b(c(x0))) → c(b(a(x0)))
C(B(A(x0))) → A(B(C(x0)))
b(a(C(x0))) → C(a(b(x0)))
c(A(B(x0))) → B(A(c(x0)))
A(c(b(x0))) → b(c(A(x0)))
B(C(a(x0))) → a(C(B(x0)))
a(A(x0)) → x0
A(a(x0)) → x0
b(B(x0)) → x0
B(b(x0)) → x0
c(C(x0)) → x0
C(c(x0)) → x0

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(b(c(x0))) → Wait(Right1(x0))
Begin(c(x0)) → Wait(Right2(x0))
Begin(B(A(x0))) → Wait(Right3(x0))
Begin(A(x0)) → Wait(Right4(x0))
Begin(a(C(x0))) → Wait(Right5(x0))
Begin(C(x0)) → Wait(Right6(x0))
Begin(A(B(x0))) → Wait(Right7(x0))
Begin(B(x0)) → Wait(Right8(x0))
Begin(c(b(x0))) → Wait(Right9(x0))
Begin(b(x0)) → Wait(Right10(x0))
Begin(C(a(x0))) → Wait(Right11(x0))
Begin(a(x0)) → Wait(Right12(x0))
Begin(A(x0)) → Wait(Right13(x0))
Begin(a(x0)) → Wait(Right14(x0))
Begin(B(x0)) → Wait(Right15(x0))
Begin(b(x0)) → Wait(Right16(x0))
Begin(C(x0)) → Wait(Right17(x0))
Begin(c(x0)) → Wait(Right18(x0))
Right1(a(End(x0))) → Left(c(b(a(End(x0)))))
Right2(a(b(End(x0)))) → Left(c(b(a(End(x0)))))
Right3(C(End(x0))) → Left(A(B(C(End(x0)))))
Right4(C(B(End(x0)))) → Left(A(B(C(End(x0)))))
Right5(b(End(x0))) → Left(C(a(b(End(x0)))))
Right6(b(a(End(x0)))) → Left(C(a(b(End(x0)))))
Right7(c(End(x0))) → Left(B(A(c(End(x0)))))
Right8(c(A(End(x0)))) → Left(B(A(c(End(x0)))))
Right9(A(End(x0))) → Left(b(c(A(End(x0)))))
Right10(A(c(End(x0)))) → Left(b(c(A(End(x0)))))
Right11(B(End(x0))) → Left(a(C(B(End(x0)))))
Right12(B(C(End(x0)))) → Left(a(C(B(End(x0)))))
Right13(a(End(x0))) → Left(End(x0))
Right14(A(End(x0))) → Left(End(x0))
Right15(b(End(x0))) → Left(End(x0))
Right16(B(End(x0))) → Left(End(x0))
Right17(c(End(x0))) → Left(End(x0))
Right18(C(End(x0))) → Left(End(x0))
Right1(a(x0)) → Aa(Right1(x0))
Right2(a(x0)) → Aa(Right2(x0))
Right3(a(x0)) → Aa(Right3(x0))
Right4(a(x0)) → Aa(Right4(x0))
Right5(a(x0)) → Aa(Right5(x0))
Right6(a(x0)) → Aa(Right6(x0))
Right7(a(x0)) → Aa(Right7(x0))
Right8(a(x0)) → Aa(Right8(x0))
Right9(a(x0)) → Aa(Right9(x0))
Right10(a(x0)) → Aa(Right10(x0))
Right11(a(x0)) → Aa(Right11(x0))
Right12(a(x0)) → Aa(Right12(x0))
Right13(a(x0)) → Aa(Right13(x0))
Right14(a(x0)) → Aa(Right14(x0))
Right15(a(x0)) → Aa(Right15(x0))
Right16(a(x0)) → Aa(Right16(x0))
Right17(a(x0)) → Aa(Right17(x0))
Right18(a(x0)) → Aa(Right18(x0))
Right1(b(x0)) → Ab(Right1(x0))
Right2(b(x0)) → Ab(Right2(x0))
Right3(b(x0)) → Ab(Right3(x0))
Right4(b(x0)) → Ab(Right4(x0))
Right5(b(x0)) → Ab(Right5(x0))
Right6(b(x0)) → Ab(Right6(x0))
Right7(b(x0)) → Ab(Right7(x0))
Right8(b(x0)) → Ab(Right8(x0))
Right9(b(x0)) → Ab(Right9(x0))
Right10(b(x0)) → Ab(Right10(x0))
Right11(b(x0)) → Ab(Right11(x0))
Right12(b(x0)) → Ab(Right12(x0))
Right13(b(x0)) → Ab(Right13(x0))
Right14(b(x0)) → Ab(Right14(x0))
Right15(b(x0)) → Ab(Right15(x0))
Right16(b(x0)) → Ab(Right16(x0))
Right17(b(x0)) → Ab(Right17(x0))
Right18(b(x0)) → Ab(Right18(x0))
Right1(c(x0)) → Ac(Right1(x0))
Right2(c(x0)) → Ac(Right2(x0))
Right3(c(x0)) → Ac(Right3(x0))
Right4(c(x0)) → Ac(Right4(x0))
Right5(c(x0)) → Ac(Right5(x0))
Right6(c(x0)) → Ac(Right6(x0))
Right7(c(x0)) → Ac(Right7(x0))
Right8(c(x0)) → Ac(Right8(x0))
Right9(c(x0)) → Ac(Right9(x0))
Right10(c(x0)) → Ac(Right10(x0))
Right11(c(x0)) → Ac(Right11(x0))
Right12(c(x0)) → Ac(Right12(x0))
Right13(c(x0)) → Ac(Right13(x0))
Right14(c(x0)) → Ac(Right14(x0))
Right15(c(x0)) → Ac(Right15(x0))
Right16(c(x0)) → Ac(Right16(x0))
Right17(c(x0)) → Ac(Right17(x0))
Right18(c(x0)) → Ac(Right18(x0))
Right1(C(x0)) → AC(Right1(x0))
Right2(C(x0)) → AC(Right2(x0))
Right3(C(x0)) → AC(Right3(x0))
Right4(C(x0)) → AC(Right4(x0))
Right5(C(x0)) → AC(Right5(x0))
Right6(C(x0)) → AC(Right6(x0))
Right7(C(x0)) → AC(Right7(x0))
Right8(C(x0)) → AC(Right8(x0))
Right9(C(x0)) → AC(Right9(x0))
Right10(C(x0)) → AC(Right10(x0))
Right11(C(x0)) → AC(Right11(x0))
Right12(C(x0)) → AC(Right12(x0))
Right13(C(x0)) → AC(Right13(x0))
Right14(C(x0)) → AC(Right14(x0))
Right15(C(x0)) → AC(Right15(x0))
Right16(C(x0)) → AC(Right16(x0))
Right17(C(x0)) → AC(Right17(x0))
Right18(C(x0)) → AC(Right18(x0))
Right1(B(x0)) → AB(Right1(x0))
Right2(B(x0)) → AB(Right2(x0))
Right3(B(x0)) → AB(Right3(x0))
Right4(B(x0)) → AB(Right4(x0))
Right5(B(x0)) → AB(Right5(x0))
Right6(B(x0)) → AB(Right6(x0))
Right7(B(x0)) → AB(Right7(x0))
Right8(B(x0)) → AB(Right8(x0))
Right9(B(x0)) → AB(Right9(x0))
Right10(B(x0)) → AB(Right10(x0))
Right11(B(x0)) → AB(Right11(x0))
Right12(B(x0)) → AB(Right12(x0))
Right13(B(x0)) → AB(Right13(x0))
Right14(B(x0)) → AB(Right14(x0))
Right15(B(x0)) → AB(Right15(x0))
Right16(B(x0)) → AB(Right16(x0))
Right17(B(x0)) → AB(Right17(x0))
Right18(B(x0)) → AB(Right18(x0))
Right1(A(x0)) → AA(Right1(x0))
Right2(A(x0)) → AA(Right2(x0))
Right3(A(x0)) → AA(Right3(x0))
Right4(A(x0)) → AA(Right4(x0))
Right5(A(x0)) → AA(Right5(x0))
Right6(A(x0)) → AA(Right6(x0))
Right7(A(x0)) → AA(Right7(x0))
Right8(A(x0)) → AA(Right8(x0))
Right9(A(x0)) → AA(Right9(x0))
Right10(A(x0)) → AA(Right10(x0))
Right11(A(x0)) → AA(Right11(x0))
Right12(A(x0)) → AA(Right12(x0))
Right13(A(x0)) → AA(Right13(x0))
Right14(A(x0)) → AA(Right14(x0))
Right15(A(x0)) → AA(Right15(x0))
Right16(A(x0)) → AA(Right16(x0))
Right17(A(x0)) → AA(Right17(x0))
Right18(A(x0)) → AA(Right18(x0))
Aa(Left(x0)) → Left(a(x0))
Ab(Left(x0)) → Left(b(x0))
Ac(Left(x0)) → Left(c(x0))
AC(Left(x0)) → Left(C(x0))
AB(Left(x0)) → Left(B(x0))
AA(Left(x0)) → Left(A(x0))
Wait(Left(x0)) → Begin(x0)
a(b(c(x0))) → c(b(a(x0)))
C(B(A(x0))) → A(B(C(x0)))
b(a(C(x0))) → C(a(b(x0)))
c(A(B(x0))) → B(A(c(x0)))
A(c(b(x0))) → b(c(A(x0)))
B(C(a(x0))) → a(C(B(x0)))
a(A(x0)) → x0
A(a(x0)) → x0
b(B(x0)) → x0
B(b(x0)) → x0
c(C(x0)) → x0
C(c(x0)) → x0