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(Q(Q(x0))) Wait(Right2(x0))
Begin(Q(x0)) Wait(Right3(x0))
Begin(p(q(x0))) Wait(Right4(x0))
Begin(q(x0)) Wait(Right5(x0))
Begin(q(p(x0))) Wait(Right6(x0))
Begin(p(x0)) Wait(Right7(x0))
Begin(Q(x0)) Wait(Right8(x0))
Begin(q(x0)) Wait(Right9(x0))
Begin(P(x0)) Wait(Right10(x0))
Begin(p(x0)) Wait(Right11(x0))
Right1(p(End(x0))) Left(q(q(End(x0))))
Right2(p(End(x0))) Left(Q(Q(p(End(x0)))))
Right3(p(Q(End(x0)))) Left(Q(Q(p(End(x0)))))
Right4(Q(End(x0))) Left(q(p(Q(End(x0)))))
Right5(Q(p(End(x0)))) Left(q(p(Q(End(x0)))))
Right6(q(End(x0))) Left(p(q(q(End(x0)))))
Right7(q(q(End(x0)))) Left(p(q(q(End(x0)))))
Right8(q(End(x0))) Left(End(x0))
Right9(Q(End(x0))) Left(End(x0))
Right10(p(End(x0))) Left(End(x0))
Right11(P(End(x0))) Left(End(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))
Right9(P(x0)) AP(Right9(x0))
Right10(P(x0)) AP(Right10(x0))
Right11(P(x0)) AP(Right11(x0))
Right1(Q(x0)) AQ(Right1(x0))
Right2(Q(x0)) AQ(Right2(x0))
Right3(Q(x0)) AQ(Right3(x0))
Right4(Q(x0)) AQ(Right4(x0))
Right5(Q(x0)) AQ(Right5(x0))
Right6(Q(x0)) AQ(Right6(x0))
Right7(Q(x0)) AQ(Right7(x0))
Right8(Q(x0)) AQ(Right8(x0))
Right9(Q(x0)) AQ(Right9(x0))
Right10(Q(x0)) AQ(Right10(x0))
Right11(Q(x0)) AQ(Right11(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))
Right9(p(x0)) Ap(Right9(x0))
Right10(p(x0)) Ap(Right10(x0))
Right11(p(x0)) Ap(Right11(x0))
Right1(q(x0)) Aq(Right1(x0))
Right2(q(x0)) Aq(Right2(x0))
Right3(q(x0)) Aq(Right3(x0))
Right4(q(x0)) Aq(Right4(x0))
Right5(q(x0)) Aq(Right5(x0))
Right6(q(x0)) Aq(Right6(x0))
Right7(q(x0)) Aq(Right7(x0))
Right8(q(x0)) Aq(Right8(x0))
Right9(q(x0)) Aq(Right9(x0))
Right10(q(x0)) Aq(Right10(x0))
Right11(q(x0)) Aq(Right11(x0))
AP(Left(x0)) Left(P(x0))
AQ(Left(x0)) Left(Q(x0))
Ap(Left(x0)) Left(p(x0))
Aq(Left(x0)) Left(q(x0))
Wait(Left(x0)) Begin(x0)
P(x0) Q(Q(p(x0)))
p(p(x0)) q(q(x0))
p(Q(Q(x0))) Q(Q(p(x0)))
Q(p(q(x0))) q(p(Q(x0)))
q(q(p(x0))) p(q(q(x0)))
q(Q(x0)) x0
Q(q(x0)) x0
p(P(x0)) x0
P(p(x0)) x0

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(Q(Q(p(End(x15613)))))
ε Wait(Right2(p(End(x15613))))
1 Wait(Left(Q(Q(p(End(x15613))))))
ε Begin(Q(Q(p(End(x15613)))))
= t3
where t3 = t0σ and σ = {x15613/x15613}