MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(e(x0)) Wait(Right1(x0))
Begin(t(x0)) Wait(Right2(x0))
Begin(w(x0)) Wait(Right3(x0))
Begin(e(x0)) Wait(Right4(x0))
Begin(r(x0)) Wait(Right5(x0))
Begin(r(x0)) Wait(Right6(x0))
Begin(i(t(e(r(x0))))) Wait(Right7(x0))
Begin(t(e(r(x0)))) Wait(Right8(x0))
Begin(e(r(x0))) Wait(Right9(x0))
Begin(r(x0)) Wait(Right10(x0))
Right1(r(End(x0))) Left(w(r(End(x0))))
Right2(i(End(x0))) Left(e(r(End(x0))))
Right3(e(End(x0))) Left(r(i(End(x0))))
Right4(t(End(x0))) Left(r(e(End(x0))))
Right5(w(End(x0))) Left(i(t(End(x0))))
Right6(e(End(x0))) Left(e(w(End(x0))))
Right7(r(End(x0))) Left(e(w(r(i(t(e(End(x0))))))))
Right8(r(i(End(x0)))) Left(e(w(r(i(t(e(End(x0))))))))
Right9(r(i(t(End(x0))))) Left(e(w(r(i(t(e(End(x0))))))))
Right10(r(i(t(e(End(x0)))))) Left(e(w(r(i(t(e(End(x0))))))))
Right1(r(x0)) Ar(Right1(x0))
Right2(r(x0)) Ar(Right2(x0))
Right3(r(x0)) Ar(Right3(x0))
Right4(r(x0)) Ar(Right4(x0))
Right5(r(x0)) Ar(Right5(x0))
Right6(r(x0)) Ar(Right6(x0))
Right7(r(x0)) Ar(Right7(x0))
Right8(r(x0)) Ar(Right8(x0))
Right9(r(x0)) Ar(Right9(x0))
Right10(r(x0)) Ar(Right10(x0))
Right1(e(x0)) Ae(Right1(x0))
Right2(e(x0)) Ae(Right2(x0))
Right3(e(x0)) Ae(Right3(x0))
Right4(e(x0)) Ae(Right4(x0))
Right5(e(x0)) Ae(Right5(x0))
Right6(e(x0)) Ae(Right6(x0))
Right7(e(x0)) Ae(Right7(x0))
Right8(e(x0)) Ae(Right8(x0))
Right9(e(x0)) Ae(Right9(x0))
Right10(e(x0)) Ae(Right10(x0))
Right1(w(x0)) Aw(Right1(x0))
Right2(w(x0)) Aw(Right2(x0))
Right3(w(x0)) Aw(Right3(x0))
Right4(w(x0)) Aw(Right4(x0))
Right5(w(x0)) Aw(Right5(x0))
Right6(w(x0)) Aw(Right6(x0))
Right7(w(x0)) Aw(Right7(x0))
Right8(w(x0)) Aw(Right8(x0))
Right9(w(x0)) Aw(Right9(x0))
Right10(w(x0)) Aw(Right10(x0))
Right1(i(x0)) Ai(Right1(x0))
Right2(i(x0)) Ai(Right2(x0))
Right3(i(x0)) Ai(Right3(x0))
Right4(i(x0)) Ai(Right4(x0))
Right5(i(x0)) Ai(Right5(x0))
Right6(i(x0)) Ai(Right6(x0))
Right7(i(x0)) Ai(Right7(x0))
Right8(i(x0)) Ai(Right8(x0))
Right9(i(x0)) Ai(Right9(x0))
Right10(i(x0)) Ai(Right10(x0))
Right1(t(x0)) At(Right1(x0))
Right2(t(x0)) At(Right2(x0))
Right3(t(x0)) At(Right3(x0))
Right4(t(x0)) At(Right4(x0))
Right5(t(x0)) At(Right5(x0))
Right6(t(x0)) At(Right6(x0))
Right7(t(x0)) At(Right7(x0))
Right8(t(x0)) At(Right8(x0))
Right9(t(x0)) At(Right9(x0))
Right10(t(x0)) At(Right10(x0))
Ar(Left(x0)) Left(r(x0))
Ae(Left(x0)) Left(e(x0))
Aw(Left(x0)) Left(w(x0))
Ai(Left(x0)) Left(i(x0))
At(Left(x0)) Left(t(x0))
Wait(Left(x0)) Begin(x0)
r(e(x0)) w(r(x0))
i(t(x0)) e(r(x0))
e(w(x0)) r(i(x0))
t(e(x0)) r(e(x0))
w(r(x0)) i(t(x0))
e(r(x0)) e(w(x0))
r(i(t(e(r(x0))))) e(w(r(i(t(e(x0))))))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(e(x0)) Wait(Right1(x0))
Begin(t(x0)) Wait(Right2(x0))
Begin(w(x0)) Wait(Right3(x0))
Begin(e(x0)) Wait(Right4(x0))
Begin(r(x0)) Wait(Right5(x0))
Begin(r(x0)) Wait(Right6(x0))
Begin(i(t(e(r(x0))))) Wait(Right7(x0))
Begin(t(e(r(x0)))) Wait(Right8(x0))
Begin(e(r(x0))) Wait(Right9(x0))
Begin(r(x0)) Wait(Right10(x0))
Right1(r(End(x0))) Left(w(r(End(x0))))
Right2(i(End(x0))) Left(e(r(End(x0))))
Right3(e(End(x0))) Left(r(i(End(x0))))
Right4(t(End(x0))) Left(r(e(End(x0))))
Right5(w(End(x0))) Left(i(t(End(x0))))
Right6(e(End(x0))) Left(e(w(End(x0))))
Right7(r(End(x0))) Left(e(w(r(i(t(e(End(x0))))))))
Right8(r(i(End(x0)))) Left(e(w(r(i(t(e(End(x0))))))))
Right9(r(i(t(End(x0))))) Left(e(w(r(i(t(e(End(x0))))))))
Right10(r(i(t(e(End(x0)))))) Left(e(w(r(i(t(e(End(x0))))))))
Right1(r(x0)) Ar(Right1(x0))
Right2(r(x0)) Ar(Right2(x0))
Right3(r(x0)) Ar(Right3(x0))
Right4(r(x0)) Ar(Right4(x0))
Right5(r(x0)) Ar(Right5(x0))
Right6(r(x0)) Ar(Right6(x0))
Right7(r(x0)) Ar(Right7(x0))
Right8(r(x0)) Ar(Right8(x0))
Right9(r(x0)) Ar(Right9(x0))
Right10(r(x0)) Ar(Right10(x0))
Right1(e(x0)) Ae(Right1(x0))
Right2(e(x0)) Ae(Right2(x0))
Right3(e(x0)) Ae(Right3(x0))
Right4(e(x0)) Ae(Right4(x0))
Right5(e(x0)) Ae(Right5(x0))
Right6(e(x0)) Ae(Right6(x0))
Right7(e(x0)) Ae(Right7(x0))
Right8(e(x0)) Ae(Right8(x0))
Right9(e(x0)) Ae(Right9(x0))
Right10(e(x0)) Ae(Right10(x0))
Right1(w(x0)) Aw(Right1(x0))
Right2(w(x0)) Aw(Right2(x0))
Right3(w(x0)) Aw(Right3(x0))
Right4(w(x0)) Aw(Right4(x0))
Right5(w(x0)) Aw(Right5(x0))
Right6(w(x0)) Aw(Right6(x0))
Right7(w(x0)) Aw(Right7(x0))
Right8(w(x0)) Aw(Right8(x0))
Right9(w(x0)) Aw(Right9(x0))
Right10(w(x0)) Aw(Right10(x0))
Right1(i(x0)) Ai(Right1(x0))
Right2(i(x0)) Ai(Right2(x0))
Right3(i(x0)) Ai(Right3(x0))
Right4(i(x0)) Ai(Right4(x0))
Right5(i(x0)) Ai(Right5(x0))
Right6(i(x0)) Ai(Right6(x0))
Right7(i(x0)) Ai(Right7(x0))
Right8(i(x0)) Ai(Right8(x0))
Right9(i(x0)) Ai(Right9(x0))
Right10(i(x0)) Ai(Right10(x0))
Right1(t(x0)) At(Right1(x0))
Right2(t(x0)) At(Right2(x0))
Right3(t(x0)) At(Right3(x0))
Right4(t(x0)) At(Right4(x0))
Right5(t(x0)) At(Right5(x0))
Right6(t(x0)) At(Right6(x0))
Right7(t(x0)) At(Right7(x0))
Right8(t(x0)) At(Right8(x0))
Right9(t(x0)) At(Right9(x0))
Right10(t(x0)) At(Right10(x0))
Ar(Left(x0)) Left(r(x0))
Ae(Left(x0)) Left(e(x0))
Aw(Left(x0)) Left(w(x0))
Ai(Left(x0)) Left(i(x0))
At(Left(x0)) Left(t(x0))
Wait(Left(x0)) Begin(x0)
r(e(x0)) w(r(x0))
i(t(x0)) e(r(x0))
e(w(x0)) r(i(x0))
t(e(x0)) r(e(x0))
w(r(x0)) i(t(x0))
e(r(x0)) e(w(x0))
r(i(t(e(r(x0))))) e(w(r(i(t(e(x0))))))