MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(x0)) → Wait(Right1(x0))
Begin(b(x0)) → Wait(Right2(x0))
Begin(a(a(x0))) → Wait(Right3(x0))
Begin(a(x0)) → Wait(Right4(x0))
Begin(a(b(x0))) → Wait(Right5(x0))
Begin(b(x0)) → Wait(Right6(x0))
Begin(b(a(x0))) → Wait(Right7(x0))
Begin(a(x0)) → Wait(Right8(x0))
Begin(b(b(x0))) → Wait(Right9(x0))
Begin(b(x0)) → Wait(Right10(x0))
Begin(a(x0)) → Wait(Right11(x0))
Begin(b(a(x0))) → Wait(Right12(x0))
Begin(a(x0)) → Wait(Right13(x0))
Begin(a(a(x0))) → Wait(Right14(x0))
Begin(a(x0)) → Wait(Right15(x0))
Begin(b(a(x0))) → Wait(Right16(x0))
Begin(a(x0)) → Wait(Right17(x0))
Right1(a(End(x0))) → Left(a(b(a(End(x0)))))
Right2(a(End(x0))) → Left(b(b(b(End(x0)))))
Right3(a(End(x0))) → Left(a(a(b(a(a(End(x0)))))))
Right4(a(a(End(x0)))) → Left(a(a(b(a(a(End(x0)))))))
Right5(a(End(x0))) → Left(a(b(b(a(b(End(x0)))))))
Right6(a(a(End(x0)))) → Left(a(b(b(a(b(End(x0)))))))
Right7(a(End(x0))) → Left(b(a(b(b(a(End(x0)))))))
Right8(a(b(End(x0)))) → Left(b(a(b(b(a(End(x0)))))))
Right9(a(End(x0))) → Left(b(b(b(b(b(End(x0)))))))
Right10(a(b(End(x0)))) → Left(b(b(b(b(b(End(x0)))))))
Right11(b(End(x0))) → Left(b(b(b(End(x0)))))
Right12(a(End(x0))) → Left(a(b(b(a(b(End(x0)))))))
Right13(a(b(End(x0)))) → Left(a(b(b(a(b(End(x0)))))))
Right14(b(End(x0))) → Left(b(a(b(b(a(End(x0)))))))
Right15(b(a(End(x0)))) → Left(b(a(b(b(a(End(x0)))))))
Right16(b(End(x0))) → Left(b(b(b(b(b(End(x0)))))))
Right17(b(b(End(x0)))) → Left(b(b(b(b(b(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))
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))
Aa(Left(x0)) → Left(a(x0))
Ab(Left(x0)) → Left(b(x0))
Wait(Left(x0)) → Begin(x0)
a(x0) → b(x0)
a(a(x0)) → a(b(a(x0)))
a(b(x0)) → b(b(b(x0)))
a(a(a(x0))) → a(a(b(a(a(x0)))))
a(a(b(x0))) → a(b(b(a(b(x0)))))
a(b(a(x0))) → b(a(b(b(a(x0)))))
a(b(b(x0))) → b(b(b(b(b(x0)))))
b(a(x0)) → b(b(b(x0)))
a(b(a(x0))) → a(b(b(a(b(x0)))))
b(a(a(x0))) → b(a(b(b(a(x0)))))
b(b(a(x0))) → b(b(b(b(b(x0)))))

Proof

1 Termination Assumption

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