NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(b(x0))) Wait(Right1(x0))
Begin(b(x0)) Wait(Right2(x0))
Begin(P(x0)) Wait(Right3(x0))
Begin(x(x0)) Wait(Right4(x0))
Begin(P(x0)) Wait(Right5(x0))
Begin(x(x0)) Wait(Right6(x0))
Begin(a(x0)) Wait(Right7(x0))
Right1(a(End(x0))) Left(P(a(b(End(x0)))))
Right2(a(b(End(x0)))) Left(P(a(b(End(x0)))))
Right3(a(End(x0))) Left(P(a(x(End(x0)))))
Right4(a(End(x0))) Left(x(a(End(x0))))
Right5(b(End(x0))) Left(b(Q(End(x0))))
Right6(Q(End(x0))) Left(a(Q(End(x0))))
Right7(Q(End(x0))) Left(b(b(a(End(x0)))))
Right1(a(x0)) Aa(Right1(x0))
Right2(a(x0)) Aa(Right2(x0))
Right3(a(x0)) Aa(Right3(x0))
Right4(a(x0)) Aa(Right4(x0))
Right5(a(x0)) Aa(Right5(x0))
Right6(a(x0)) Aa(Right6(x0))
Right7(a(x0)) Aa(Right7(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))
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))
Right1(x(x0)) Ax(Right1(x0))
Right2(x(x0)) Ax(Right2(x0))
Right3(x(x0)) Ax(Right3(x0))
Right4(x(x0)) Ax(Right4(x0))
Right5(x(x0)) Ax(Right5(x0))
Right6(x(x0)) Ax(Right6(x0))
Right7(x(x0)) Ax(Right7(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))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
AP(Left(x0)) Left(P(x0))
Ax(Left(x0)) Left(x(x0))
AQ(Left(x0)) Left(Q(x0))
Wait(Left(x0)) Begin(x0)
a(b(b(x0))) P(a(b(x0)))
a(P(x0)) P(a(x(x0)))
a(x(x0)) x(a(x0))
b(P(x0)) b(Q(x0))
Q(x(x0)) a(Q(x0))
Q(a(x0)) b(b(a(x0)))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(x(a(End(x12943))))
ε Wait(Right4(a(End(x12943))))
1 Wait(Left(x(a(End(x12943)))))
ε Begin(x(a(End(x12943))))
= t3
where t3 = t0σ and σ = {x12943/x12943}