MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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