MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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