NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(s(x0)) Wait(Right1(x0))
Begin(u(x0)) Wait(Right2(x0))
Begin(u(x0)) Wait(Right3(x0))
Begin(u(x0)) Wait(Right4(x0))
Begin(u(x0)) Wait(Right5(x0))
Begin(s(x0)) Wait(Right6(x0))
Begin(r(x0)) Wait(Right7(x0))
Begin(n(x0)) Wait(Right8(x0))
Right1(r(End(x0))) Left(s(r(End(x0))))
Right2(r(End(x0))) Left(u(r(End(x0))))
Right3(s(End(x0))) Left(u(s(End(x0))))
Right4(n(End(x0))) Left(u(n(End(x0))))
Right5(c(End(x0))) Left(u(c(End(x0))))
Right6(c(End(x0))) Left(s(c(End(x0))))
Right7(c(End(x0))) Left(r(c(End(x0))))
Right8(c(End(x0))) Left(n(c(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))
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))
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))
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))
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))
Ar(Left(x0)) Left(r(x0))
As(Left(x0)) Left(s(x0))
Au(Left(x0)) Left(u(x0))
An(Left(x0)) Left(n(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
r(s(x0)) s(r(x0))
r(u(x0)) u(r(x0))
s(u(x0)) u(s(x0))
n(u(x0)) u(n(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))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(s(r(End(x10929))))
ε Wait(Right1(r(End(x10929))))
1 Wait(Left(s(r(End(x10929)))))
ε Begin(s(r(End(x10929))))
= t3
where t3 = t0σ and σ = {x10929/x10929}