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(a(a(x0)))) Wait(Right11(x0))
Begin(a(a(x0))) Wait(Right12(x0))
Begin(a(x0)) Wait(Right13(x0))
Begin(a(a(b(x0)))) Wait(Right14(x0))
Begin(a(b(x0))) Wait(Right15(x0))
Begin(b(x0)) Wait(Right16(x0))
Begin(a(b(a(x0)))) Wait(Right17(x0))
Begin(b(a(x0))) Wait(Right18(x0))
Begin(a(x0)) Wait(Right19(x0))
Begin(a(b(b(x0)))) Wait(Right20(x0))
Begin(b(b(x0))) Wait(Right21(x0))
Begin(b(x0)) Wait(Right22(x0))
Begin(b(a(a(x0)))) Wait(Right23(x0))
Begin(a(a(x0))) Wait(Right24(x0))
Begin(a(x0)) Wait(Right25(x0))
Begin(b(a(b(x0)))) Wait(Right26(x0))
Begin(a(b(x0))) Wait(Right27(x0))
Begin(b(x0)) Wait(Right28(x0))
Begin(b(b(a(x0)))) Wait(Right29(x0))
Begin(b(a(x0))) Wait(Right30(x0))
Begin(a(x0)) Wait(Right31(x0))
Begin(b(b(b(x0)))) Wait(Right32(x0))
Begin(b(b(x0))) Wait(Right33(x0))
Begin(b(x0)) Wait(Right34(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(a(End(x0))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right12(a(a(End(x0)))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right13(a(a(a(End(x0))))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right14(a(End(x0))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right15(a(a(End(x0)))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right16(a(a(a(End(x0))))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right17(a(End(x0))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right18(a(a(End(x0)))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right19(a(a(b(End(x0))))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right20(a(End(x0))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right21(a(a(End(x0)))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right22(a(a(b(End(x0))))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right23(a(End(x0))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right24(a(b(End(x0)))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right25(a(b(a(End(x0))))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right26(a(End(x0))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right27(a(b(End(x0)))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right28(a(b(a(End(x0))))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right29(a(End(x0))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right30(a(b(End(x0)))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right31(a(b(b(End(x0))))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right32(a(End(x0))) Left(b(b(b(b(b(b(b(End(x0)))))))))
Right33(a(b(End(x0)))) Left(b(b(b(b(b(b(b(End(x0)))))))))
Right34(a(b(b(End(x0))))) Left(b(b(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))
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))
Right32(a(x0)) Aa(Right32(x0))
Right33(a(x0)) Aa(Right33(x0))
Right34(a(x0)) Aa(Right34(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))
Right32(b(x0)) Ab(Right32(x0))
Right33(b(x0)) Ab(Right33(x0))
Right34(b(x0)) Ab(Right34(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)))))
a(a(a(a(x0)))) a(a(a(b(a(a(a(x0)))))))
a(a(a(b(x0)))) a(a(b(b(a(a(b(x0)))))))
a(a(b(a(x0)))) a(b(a(b(a(b(a(x0)))))))
a(a(b(b(x0)))) a(b(b(b(a(b(b(x0)))))))
a(b(a(a(x0)))) b(a(a(b(b(a(a(x0)))))))
a(b(a(b(x0)))) b(a(b(b(b(a(b(x0)))))))
a(b(b(a(x0)))) b(b(a(b(b(b(a(x0)))))))
a(b(b(b(x0)))) b(b(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(a(a(x0)))) Wait(Right11(x0))
Begin(a(a(x0))) Wait(Right12(x0))
Begin(a(x0)) Wait(Right13(x0))
Begin(a(a(b(x0)))) Wait(Right14(x0))
Begin(a(b(x0))) Wait(Right15(x0))
Begin(b(x0)) Wait(Right16(x0))
Begin(a(b(a(x0)))) Wait(Right17(x0))
Begin(b(a(x0))) Wait(Right18(x0))
Begin(a(x0)) Wait(Right19(x0))
Begin(a(b(b(x0)))) Wait(Right20(x0))
Begin(b(b(x0))) Wait(Right21(x0))
Begin(b(x0)) Wait(Right22(x0))
Begin(b(a(a(x0)))) Wait(Right23(x0))
Begin(a(a(x0))) Wait(Right24(x0))
Begin(a(x0)) Wait(Right25(x0))
Begin(b(a(b(x0)))) Wait(Right26(x0))
Begin(a(b(x0))) Wait(Right27(x0))
Begin(b(x0)) Wait(Right28(x0))
Begin(b(b(a(x0)))) Wait(Right29(x0))
Begin(b(a(x0))) Wait(Right30(x0))
Begin(a(x0)) Wait(Right31(x0))
Begin(b(b(b(x0)))) Wait(Right32(x0))
Begin(b(b(x0))) Wait(Right33(x0))
Begin(b(x0)) Wait(Right34(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(a(End(x0))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right12(a(a(End(x0)))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right13(a(a(a(End(x0))))) Left(a(a(a(b(a(a(a(End(x0)))))))))
Right14(a(End(x0))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right15(a(a(End(x0)))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right16(a(a(a(End(x0))))) Left(a(a(b(b(a(a(b(End(x0)))))))))
Right17(a(End(x0))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right18(a(a(End(x0)))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right19(a(a(b(End(x0))))) Left(a(b(a(b(a(b(a(End(x0)))))))))
Right20(a(End(x0))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right21(a(a(End(x0)))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right22(a(a(b(End(x0))))) Left(a(b(b(b(a(b(b(End(x0)))))))))
Right23(a(End(x0))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right24(a(b(End(x0)))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right25(a(b(a(End(x0))))) Left(b(a(a(b(b(a(a(End(x0)))))))))
Right26(a(End(x0))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right27(a(b(End(x0)))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right28(a(b(a(End(x0))))) Left(b(a(b(b(b(a(b(End(x0)))))))))
Right29(a(End(x0))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right30(a(b(End(x0)))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right31(a(b(b(End(x0))))) Left(b(b(a(b(b(b(a(End(x0)))))))))
Right32(a(End(x0))) Left(b(b(b(b(b(b(b(End(x0)))))))))
Right33(a(b(End(x0)))) Left(b(b(b(b(b(b(b(End(x0)))))))))
Right34(a(b(b(End(x0))))) Left(b(b(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))
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))
Right32(a(x0)) Aa(Right32(x0))
Right33(a(x0)) Aa(Right33(x0))
Right34(a(x0)) Aa(Right34(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))
Right32(b(x0)) Ab(Right32(x0))
Right33(b(x0)) Ab(Right33(x0))
Right34(b(x0)) Ab(Right34(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)))))
a(a(a(a(x0)))) a(a(a(b(a(a(a(x0)))))))
a(a(a(b(x0)))) a(a(b(b(a(a(b(x0)))))))
a(a(b(a(x0)))) a(b(a(b(a(b(a(x0)))))))
a(a(b(b(x0)))) a(b(b(b(a(b(b(x0)))))))
a(b(a(a(x0)))) b(a(a(b(b(a(a(x0)))))))
a(b(a(b(x0)))) b(a(b(b(b(a(b(x0)))))))
a(b(b(a(x0)))) b(b(a(b(b(b(a(x0)))))))
a(b(b(b(x0)))) b(b(b(b(b(b(b(x0)))))))