NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(r(x0)) Wait(Right1(x0))
Begin(s(x0)) Wait(Right2(x0))
Begin(n(x0)) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Begin(u(x0)) Wait(Right5(x0))
Begin(u(x0)) Wait(Right6(x0))
Begin(u(x0)) Wait(Right7(x0))
Begin(r(u(x0))) Wait(Right8(x0))
Begin(u(x0)) Wait(Right9(x0))
Begin(s(u(x0))) Wait(Right10(x0))
Begin(u(x0)) Wait(Right11(x0))
Begin(n(u(x0))) Wait(Right12(x0))
Begin(u(x0)) Wait(Right13(x0))
Begin(u(x0)) Wait(Right14(x0))
Begin(s(x0)) Wait(Right15(x0))
Begin(r(x0)) Wait(Right16(x0))
Begin(n(x0)) Wait(Right17(x0))
Begin(n(x0)) Wait(Right18(x0))
Right1(r(End(x0))) Left(s(r(End(x0))))
Right2(r(End(x0))) Left(s(r(End(x0))))
Right3(r(End(x0))) Left(s(r(End(x0))))
Right4(r(End(x0))) Left(u(s(b(End(x0)))))
Right5(r(End(x0))) Left(u(r(End(x0))))
Right6(s(End(x0))) Left(u(s(End(x0))))
Right7(n(End(x0))) Left(u(n(End(x0))))
Right8(t(End(x0))) Left(t(c(r(End(x0)))))
Right9(t(r(End(x0)))) Left(t(c(r(End(x0)))))
Right10(t(End(x0))) Left(t(c(r(End(x0)))))
Right11(t(s(End(x0)))) Left(t(c(r(End(x0)))))
Right12(t(End(x0))) Left(t(c(r(End(x0)))))
Right13(t(n(End(x0)))) Left(t(c(r(End(x0)))))
Right14(c(End(x0))) Left(u(c(End(x0))))
Right15(c(End(x0))) Left(s(c(End(x0))))
Right16(c(End(x0))) Left(r(c(End(x0))))
Right17(c(End(x0))) Left(n(c(End(x0))))
Right18(c(End(x0))) Left(n(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))
Right11(r(x0)) Ar(Right11(x0))
Right12(r(x0)) Ar(Right12(x0))
Right13(r(x0)) Ar(Right13(x0))
Right14(r(x0)) Ar(Right14(x0))
Right15(r(x0)) Ar(Right15(x0))
Right16(r(x0)) Ar(Right16(x0))
Right17(r(x0)) Ar(Right17(x0))
Right18(r(x0)) Ar(Right18(x0))
Right1(s(x0)) As(Right1(x0))
Right2(s(x0)) As(Right2(x0))
Right3(s(x0)) As(Right3(x0))
Right4(s(x0)) As(Right4(x0))
Right5(s(x0)) As(Right5(x0))
Right6(s(x0)) As(Right6(x0))
Right7(s(x0)) As(Right7(x0))
Right8(s(x0)) As(Right8(x0))
Right9(s(x0)) As(Right9(x0))
Right10(s(x0)) As(Right10(x0))
Right11(s(x0)) As(Right11(x0))
Right12(s(x0)) As(Right12(x0))
Right13(s(x0)) As(Right13(x0))
Right14(s(x0)) As(Right14(x0))
Right15(s(x0)) As(Right15(x0))
Right16(s(x0)) As(Right16(x0))
Right17(s(x0)) As(Right17(x0))
Right18(s(x0)) As(Right18(x0))
Right1(n(x0)) An(Right1(x0))
Right2(n(x0)) An(Right2(x0))
Right3(n(x0)) An(Right3(x0))
Right4(n(x0)) An(Right4(x0))
Right5(n(x0)) An(Right5(x0))
Right6(n(x0)) An(Right6(x0))
Right7(n(x0)) An(Right7(x0))
Right8(n(x0)) An(Right8(x0))
Right9(n(x0)) An(Right9(x0))
Right10(n(x0)) An(Right10(x0))
Right11(n(x0)) An(Right11(x0))
Right12(n(x0)) An(Right12(x0))
Right13(n(x0)) An(Right13(x0))
Right14(n(x0)) An(Right14(x0))
Right15(n(x0)) An(Right15(x0))
Right16(n(x0)) An(Right16(x0))
Right17(n(x0)) An(Right17(x0))
Right18(n(x0)) An(Right18(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))
Right1(u(x0)) Au(Right1(x0))
Right2(u(x0)) Au(Right2(x0))
Right3(u(x0)) Au(Right3(x0))
Right4(u(x0)) Au(Right4(x0))
Right5(u(x0)) Au(Right5(x0))
Right6(u(x0)) Au(Right6(x0))
Right7(u(x0)) Au(Right7(x0))
Right8(u(x0)) Au(Right8(x0))
Right9(u(x0)) Au(Right9(x0))
Right10(u(x0)) Au(Right10(x0))
Right11(u(x0)) Au(Right11(x0))
Right12(u(x0)) Au(Right12(x0))
Right13(u(x0)) Au(Right13(x0))
Right14(u(x0)) Au(Right14(x0))
Right15(u(x0)) Au(Right15(x0))
Right16(u(x0)) Au(Right16(x0))
Right17(u(x0)) Au(Right17(x0))
Right18(u(x0)) Au(Right18(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))
Right11(t(x0)) At(Right11(x0))
Right12(t(x0)) At(Right12(x0))
Right13(t(x0)) At(Right13(x0))
Right14(t(x0)) At(Right14(x0))
Right15(t(x0)) At(Right15(x0))
Right16(t(x0)) At(Right16(x0))
Right17(t(x0)) At(Right17(x0))
Right18(t(x0)) At(Right18(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))
Ar(Left(x0)) Left(r(x0))
As(Left(x0)) Left(s(x0))
An(Left(x0)) Left(n(x0))
Ab(Left(x0)) Left(b(x0))
Au(Left(x0)) Left(u(x0))
At(Left(x0)) Left(t(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
r(r(x0)) s(r(x0))
r(s(x0)) s(r(x0))
r(n(x0)) s(r(x0))
r(b(x0)) u(s(b(x0)))
r(u(x0)) u(r(x0))
s(u(x0)) u(s(x0))
n(u(x0)) u(n(x0))
t(r(u(x0))) t(c(r(x0)))
t(s(u(x0))) t(c(r(x0)))
t(n(u(x0))) t(c(r(x0)))
c(u(x0)) u(c(x0))
c(s(x0)) s(c(x0))
c(r(x0)) r(c(x0))
c(n(x0)) n(c(x0))
c(n(x0)) n(x0)

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(s(r(End(x81975))))
ε Wait(Right2(r(End(x81975))))
1 Wait(Left(s(r(End(x81975)))))
ε Begin(s(r(End(x81975))))
= t3
where t3 = t0σ and σ = {x81975/x81975}