NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(f(x0)) Wait(Right1(x0))
Begin(f(x0)) Wait(Right2(x0))
Begin(f(x0)) Wait(Right3(x0))
Begin(s(x0)) Wait(Right4(x0))
Begin(s(x0)) Wait(Right5(x0))
Begin(f(x0)) Wait(Right6(x0))
Begin(n(x0)) Wait(Right7(x0))
Begin(o(x0)) Wait(Right8(x0))
Begin(o(x0)) Wait(Right9(x0))
Right1(t(End(x0))) Left(t(c(n(End(x0)))))
Right2(n(End(x0))) Left(f(n(End(x0))))
Right3(o(End(x0))) Left(f(o(End(x0))))
Right4(n(End(x0))) Left(f(s(End(x0))))
Right5(o(End(x0))) Left(f(s(End(x0))))
Right6(c(End(x0))) Left(f(c(End(x0))))
Right7(c(End(x0))) Left(n(c(End(x0))))
Right8(c(End(x0))) Left(o(c(End(x0))))
Right9(c(End(x0))) Left(o(End(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))
Right1(f(x0)) Af(Right1(x0))
Right2(f(x0)) Af(Right2(x0))
Right3(f(x0)) Af(Right3(x0))
Right4(f(x0)) Af(Right4(x0))
Right5(f(x0)) Af(Right5(x0))
Right6(f(x0)) Af(Right6(x0))
Right7(f(x0)) Af(Right7(x0))
Right8(f(x0)) Af(Right8(x0))
Right9(f(x0)) Af(Right9(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))
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))
Right1(o(x0)) Ao(Right1(x0))
Right2(o(x0)) Ao(Right2(x0))
Right3(o(x0)) Ao(Right3(x0))
Right4(o(x0)) Ao(Right4(x0))
Right5(o(x0)) Ao(Right5(x0))
Right6(o(x0)) Ao(Right6(x0))
Right7(o(x0)) Ao(Right7(x0))
Right8(o(x0)) Ao(Right8(x0))
Right9(o(x0)) Ao(Right9(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))
At(Left(x0)) Left(t(x0))
Af(Left(x0)) Left(f(x0))
Ac(Left(x0)) Left(c(x0))
An(Left(x0)) Left(n(x0))
Ao(Left(x0)) Left(o(x0))
As(Left(x0)) Left(s(x0))
Wait(Left(x0)) Begin(x0)
t(f(x0)) t(c(n(x0)))
n(f(x0)) f(n(x0))
o(f(x0)) f(o(x0))
n(s(x0)) f(s(x0))
o(s(x0)) f(s(x0))
c(f(x0)) f(c(x0))
c(n(x0)) n(c(x0))
c(o(x0)) o(c(x0))
c(o(x0)) o(x0)

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(f(n(End(x19371))))
ε Wait(Right2(n(End(x19371))))
1 Wait(Left(f(n(End(x19371)))))
ε Begin(f(n(End(x19371))))
= t3
where t3 = t0σ and σ = {x19371/x19371}