MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(c(x0)) → Wait(Right1(x0))
Begin(b(x0)) → Wait(Right2(x0))
Begin(B(x0)) → Wait(Right3(x0))
Begin(B(c(b(c(x0))))) → Wait(Right4(x0))
Begin(c(b(c(x0)))) → Wait(Right5(x0))
Begin(b(c(x0))) → Wait(Right6(x0))
Begin(c(x0)) → Wait(Right7(x0))
Begin(B(x0)) → Wait(Right8(x0))
Begin(b(x0)) → Wait(Right9(x0))
Begin(C(x0)) → Wait(Right10(x0))
Begin(c(x0)) → Wait(Right11(x0))
Right1(c(End(x0))) → Left(End(x0))
Right2(b(End(x0))) → Left(B(End(x0)))
Right3(B(End(x0))) → Left(b(End(x0)))
Right4(c(End(x0))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right5(c(B(End(x0)))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right6(c(B(c(End(x0))))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right7(c(B(c(b(End(x0)))))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right8(b(End(x0))) → Left(End(x0))
Right9(B(End(x0))) → Left(End(x0))
Right10(c(End(x0))) → Left(End(x0))
Right11(C(End(x0))) → Left(End(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))
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))
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))
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))
AC(Left(x0)) → Left(C(x0))
Ac(Left(x0)) → Left(c(x0))
Ab(Left(x0)) → Left(b(x0))
AB(Left(x0)) → Left(B(x0))
Wait(Left(x0)) → Begin(x0)
C(x0) → c(x0)
c(c(x0)) → x0
b(b(x0)) → B(x0)
B(B(x0)) → b(x0)
c(B(c(b(c(x0))))) → B(c(b(c(B(c(b(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(c(x0)) → Wait(Right1(x0))
Begin(b(x0)) → Wait(Right2(x0))
Begin(B(x0)) → Wait(Right3(x0))
Begin(B(c(b(c(x0))))) → Wait(Right4(x0))
Begin(c(b(c(x0)))) → Wait(Right5(x0))
Begin(b(c(x0))) → Wait(Right6(x0))
Begin(c(x0)) → Wait(Right7(x0))
Begin(B(x0)) → Wait(Right8(x0))
Begin(b(x0)) → Wait(Right9(x0))
Begin(C(x0)) → Wait(Right10(x0))
Begin(c(x0)) → Wait(Right11(x0))
Right1(c(End(x0))) → Left(End(x0))
Right2(b(End(x0))) → Left(B(End(x0)))
Right3(B(End(x0))) → Left(b(End(x0)))
Right4(c(End(x0))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right5(c(B(End(x0)))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right6(c(B(c(End(x0))))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right7(c(B(c(b(End(x0)))))) → Left(B(c(b(c(B(c(b(End(x0)))))))))
Right8(b(End(x0))) → Left(End(x0))
Right9(B(End(x0))) → Left(End(x0))
Right10(c(End(x0))) → Left(End(x0))
Right11(C(End(x0))) → Left(End(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))
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))
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))
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))
AC(Left(x0)) → Left(C(x0))
Ac(Left(x0)) → Left(c(x0))
Ab(Left(x0)) → Left(b(x0))
AB(Left(x0)) → Left(B(x0))
Wait(Left(x0)) → Begin(x0)
C(x0) → c(x0)
c(c(x0)) → x0
b(b(x0)) → B(x0)
B(B(x0)) → b(x0)
c(B(c(b(c(x0))))) → B(c(b(c(B(c(b(x0)))))))
b(B(x0)) → x0
B(b(x0)) → x0
c(C(x0)) → x0
C(c(x0)) → x0