NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(p(x0)) Wait(Right1(x0))
Begin(r(x0)) Wait(Right2(x0))
Begin(P(P(x0))) Wait(Right3(x0))
Begin(P(x0)) Wait(Right4(x0))
Begin(P(x0)) Wait(Right5(x0))
Begin(p(x0)) Wait(Right6(x0))
Begin(R(x0)) Wait(Right7(x0))
Begin(r(x0)) Wait(Right8(x0))
Right1(r(End(x0))) Left(p(p(r(P(End(x0))))))
Right2(r(End(x0))) Left(End(x0))
Right3(r(End(x0))) Left(P(P(r(End(x0)))))
Right4(r(P(End(x0)))) Left(P(P(r(End(x0)))))
Right5(p(End(x0))) Left(End(x0))
Right6(P(End(x0))) Left(End(x0))
Right7(r(End(x0))) Left(End(x0))
Right8(R(End(x0))) Left(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(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(p(x0)) Ap(Right1(x0))
Right2(p(x0)) Ap(Right2(x0))
Right3(p(x0)) Ap(Right3(x0))
Right4(p(x0)) Ap(Right4(x0))
Right5(p(x0)) Ap(Right5(x0))
Right6(p(x0)) Ap(Right6(x0))
Right7(p(x0)) Ap(Right7(x0))
Right8(p(x0)) Ap(Right8(x0))
Right1(P(x0)) AP(Right1(x0))
Right2(P(x0)) AP(Right2(x0))
Right3(P(x0)) AP(Right3(x0))
Right4(P(x0)) AP(Right4(x0))
Right5(P(x0)) AP(Right5(x0))
Right6(P(x0)) AP(Right6(x0))
Right7(P(x0)) AP(Right7(x0))
Right8(P(x0)) AP(Right8(x0))
AR(Left(x0)) Left(R(x0))
Ar(Left(x0)) Left(r(x0))
Ap(Left(x0)) Left(p(x0))
AP(Left(x0)) Left(P(x0))
Wait(Left(x0)) Begin(x0)
R(x0) r(x0)
r(p(x0)) p(p(r(P(x0))))
r(r(x0)) x0
r(P(P(x0))) P(P(r(x0)))
p(P(x0)) x0
P(p(x0)) x0
r(R(x0)) x0
R(r(x0)) x0

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(P(P(r(End(x9893)))))
ε Wait(Right3(r(End(x9893))))
1 Wait(Left(P(P(r(End(x9893))))))
ε Begin(P(P(r(End(x9893)))))
= t3
where t3 = t0σ and σ = {x9893/x9893}