MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(a(b(b(x0))))) Wait(Right1(x0))
Begin(a(b(b(x0)))) Wait(Right2(x0))
Begin(b(b(x0))) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Begin(a(b(b(x0)))) Wait(Right5(x0))
Begin(b(b(x0))) Wait(Right6(x0))
Begin(b(x0)) Wait(Right7(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right8(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right9(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right10(x0))
Begin(a(a(a(b(x0))))) Wait(Right11(x0))
Begin(a(a(b(x0)))) Wait(Right12(x0))
Begin(a(b(x0))) Wait(Right13(x0))
Begin(b(x0)) Wait(Right14(x0))
Begin(a(a(b(a(a(a(a(b(x0))))))))) Wait(Right15(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right16(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right17(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right18(x0))
Begin(a(a(a(b(x0))))) Wait(Right19(x0))
Begin(a(a(b(x0)))) Wait(Right20(x0))
Begin(a(b(x0))) Wait(Right21(x0))
Begin(b(x0)) Wait(Right22(x0))
Begin(a(a(a(b(a(a(a(a(b(x0)))))))))) Wait(Right23(x0))
Begin(a(a(b(a(a(a(a(b(x0))))))))) Wait(Right24(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right25(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right26(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right27(x0))
Begin(a(a(a(b(x0))))) Wait(Right28(x0))
Begin(a(a(b(x0)))) Wait(Right29(x0))
Begin(a(b(x0))) Wait(Right30(x0))
Begin(b(x0)) Wait(Right31(x0))
Right1(b(End(x0))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right2(b(a(End(x0)))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right3(b(a(a(End(x0))))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right4(b(a(a(b(End(x0)))))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right5(b(End(x0))) Left(b(b(End(x0))))
Right6(b(a(End(x0)))) Left(b(b(End(x0))))
Right7(b(a(b(End(x0))))) Left(b(b(End(x0))))
Right8(b(End(x0))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right9(b(a(End(x0)))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right10(b(a(b(End(x0))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right11(b(a(b(a(End(x0)))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right12(b(a(b(a(a(End(x0))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right13(b(a(b(a(a(a(End(x0)))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right14(b(a(b(a(a(a(a(End(x0))))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right15(b(End(x0))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right16(b(a(End(x0)))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right17(b(a(a(End(x0))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right18(b(a(a(b(End(x0)))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right19(b(a(a(b(a(End(x0))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right20(b(a(a(b(a(a(End(x0)))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right21(b(a(a(b(a(a(a(End(x0))))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right22(b(a(a(b(a(a(a(a(End(x0)))))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right23(b(End(x0))) Left(b(End(x0)))
Right24(b(a(End(x0)))) Left(b(End(x0)))
Right25(b(a(a(End(x0))))) Left(b(End(x0)))
Right26(b(a(a(a(End(x0)))))) Left(b(End(x0)))
Right27(b(a(a(a(b(End(x0))))))) Left(b(End(x0)))
Right28(b(a(a(a(b(a(End(x0)))))))) Left(b(End(x0)))
Right29(b(a(a(a(b(a(a(End(x0))))))))) Left(b(End(x0)))
Right30(b(a(a(a(b(a(a(a(End(x0)))))))))) Left(b(End(x0)))
Right31(b(a(a(a(b(a(a(a(a(End(x0))))))))))) Left(b(End(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))
Right19(b(x0)) Ab(Right19(x0))
Right20(b(x0)) Ab(Right20(x0))
Right21(b(x0)) Ab(Right21(x0))
Right22(b(x0)) Ab(Right22(x0))
Right23(b(x0)) Ab(Right23(x0))
Right24(b(x0)) Ab(Right24(x0))
Right25(b(x0)) Ab(Right25(x0))
Right26(b(x0)) Ab(Right26(x0))
Right27(b(x0)) Ab(Right27(x0))
Right28(b(x0)) Ab(Right28(x0))
Right29(b(x0)) Ab(Right29(x0))
Right30(b(x0)) Ab(Right30(x0))
Right31(b(x0)) Ab(Right31(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))
Right19(a(x0)) Aa(Right19(x0))
Right20(a(x0)) Aa(Right20(x0))
Right21(a(x0)) Aa(Right21(x0))
Right22(a(x0)) Aa(Right22(x0))
Right23(a(x0)) Aa(Right23(x0))
Right24(a(x0)) Aa(Right24(x0))
Right25(a(x0)) Aa(Right25(x0))
Right26(a(x0)) Aa(Right26(x0))
Right27(a(x0)) Aa(Right27(x0))
Right28(a(x0)) Aa(Right28(x0))
Right29(a(x0)) Aa(Right29(x0))
Right30(a(x0)) Aa(Right30(x0))
Right31(a(x0)) Aa(Right31(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Wait(Left(x0)) Begin(x0)
b(a(a(b(b(x0))))) b(a(a(a(a(b(b(x0)))))))
b(a(b(b(x0)))) b(b(x0))
b(a(b(a(a(a(a(b(x0)))))))) b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x0))))))))) b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x0)))))))))) b(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(a(a(b(b(x0))))) Wait(Right1(x0))
Begin(a(b(b(x0)))) Wait(Right2(x0))
Begin(b(b(x0))) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Begin(a(b(b(x0)))) Wait(Right5(x0))
Begin(b(b(x0))) Wait(Right6(x0))
Begin(b(x0)) Wait(Right7(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right8(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right9(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right10(x0))
Begin(a(a(a(b(x0))))) Wait(Right11(x0))
Begin(a(a(b(x0)))) Wait(Right12(x0))
Begin(a(b(x0))) Wait(Right13(x0))
Begin(b(x0)) Wait(Right14(x0))
Begin(a(a(b(a(a(a(a(b(x0))))))))) Wait(Right15(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right16(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right17(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right18(x0))
Begin(a(a(a(b(x0))))) Wait(Right19(x0))
Begin(a(a(b(x0)))) Wait(Right20(x0))
Begin(a(b(x0))) Wait(Right21(x0))
Begin(b(x0)) Wait(Right22(x0))
Begin(a(a(a(b(a(a(a(a(b(x0)))))))))) Wait(Right23(x0))
Begin(a(a(b(a(a(a(a(b(x0))))))))) Wait(Right24(x0))
Begin(a(b(a(a(a(a(b(x0)))))))) Wait(Right25(x0))
Begin(b(a(a(a(a(b(x0))))))) Wait(Right26(x0))
Begin(a(a(a(a(b(x0)))))) Wait(Right27(x0))
Begin(a(a(a(b(x0))))) Wait(Right28(x0))
Begin(a(a(b(x0)))) Wait(Right29(x0))
Begin(a(b(x0))) Wait(Right30(x0))
Begin(b(x0)) Wait(Right31(x0))
Right1(b(End(x0))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right2(b(a(End(x0)))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right3(b(a(a(End(x0))))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right4(b(a(a(b(End(x0)))))) Left(b(a(a(a(a(b(b(End(x0)))))))))
Right5(b(End(x0))) Left(b(b(End(x0))))
Right6(b(a(End(x0)))) Left(b(b(End(x0))))
Right7(b(a(b(End(x0))))) Left(b(b(End(x0))))
Right8(b(End(x0))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right9(b(a(End(x0)))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right10(b(a(b(End(x0))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right11(b(a(b(a(End(x0)))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right12(b(a(b(a(a(End(x0))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right13(b(a(b(a(a(a(End(x0)))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right14(b(a(b(a(a(a(a(End(x0))))))))) Left(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(End(x0))))))))))))))))))))))))
Right15(b(End(x0))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right16(b(a(End(x0)))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right17(b(a(a(End(x0))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right18(b(a(a(b(End(x0)))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right19(b(a(a(b(a(End(x0))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right20(b(a(a(b(a(a(End(x0)))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right21(b(a(a(b(a(a(a(End(x0))))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right22(b(a(a(b(a(a(a(a(End(x0)))))))))) Left(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(End(x0)))))))))))))))))
Right23(b(End(x0))) Left(b(End(x0)))
Right24(b(a(End(x0)))) Left(b(End(x0)))
Right25(b(a(a(End(x0))))) Left(b(End(x0)))
Right26(b(a(a(a(End(x0)))))) Left(b(End(x0)))
Right27(b(a(a(a(b(End(x0))))))) Left(b(End(x0)))
Right28(b(a(a(a(b(a(End(x0)))))))) Left(b(End(x0)))
Right29(b(a(a(a(b(a(a(End(x0))))))))) Left(b(End(x0)))
Right30(b(a(a(a(b(a(a(a(End(x0)))))))))) Left(b(End(x0)))
Right31(b(a(a(a(b(a(a(a(a(End(x0))))))))))) Left(b(End(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))
Right19(b(x0)) Ab(Right19(x0))
Right20(b(x0)) Ab(Right20(x0))
Right21(b(x0)) Ab(Right21(x0))
Right22(b(x0)) Ab(Right22(x0))
Right23(b(x0)) Ab(Right23(x0))
Right24(b(x0)) Ab(Right24(x0))
Right25(b(x0)) Ab(Right25(x0))
Right26(b(x0)) Ab(Right26(x0))
Right27(b(x0)) Ab(Right27(x0))
Right28(b(x0)) Ab(Right28(x0))
Right29(b(x0)) Ab(Right29(x0))
Right30(b(x0)) Ab(Right30(x0))
Right31(b(x0)) Ab(Right31(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))
Right19(a(x0)) Aa(Right19(x0))
Right20(a(x0)) Aa(Right20(x0))
Right21(a(x0)) Aa(Right21(x0))
Right22(a(x0)) Aa(Right22(x0))
Right23(a(x0)) Aa(Right23(x0))
Right24(a(x0)) Aa(Right24(x0))
Right25(a(x0)) Aa(Right25(x0))
Right26(a(x0)) Aa(Right26(x0))
Right27(a(x0)) Aa(Right27(x0))
Right28(a(x0)) Aa(Right28(x0))
Right29(a(x0)) Aa(Right29(x0))
Right30(a(x0)) Aa(Right30(x0))
Right31(a(x0)) Aa(Right31(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Wait(Left(x0)) Begin(x0)
b(a(a(b(b(x0))))) b(a(a(a(a(b(b(x0)))))))
b(a(b(b(x0)))) b(b(x0))
b(a(b(a(a(a(a(b(x0)))))))) b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x0))))))))) b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x0)))))))))) b(x0)