NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a34(x0)) Wait(Right1(x0))
Begin(a45(x0)) Wait(Right2(x0))
Begin(a56(x0)) Wait(Right3(x0))
Begin(a45(x0)) Wait(Right4(x0))
Begin(a56(x0)) Wait(Right5(x0))
Begin(a56(x0)) Wait(Right6(x0))
Right1(a12(End(x0))) Left(a34(a12(End(x0))))
Right2(a12(End(x0))) Left(a45(a12(End(x0))))
Right3(a12(End(x0))) Left(a56(a12(End(x0))))
Right4(a23(End(x0))) Left(a45(a23(End(x0))))
Right5(a23(End(x0))) Left(a56(a23(End(x0))))
Right6(a34(End(x0))) Left(a56(a34(End(x0))))
Right1(a12(x0)) Aa12(Right1(x0))
Right2(a12(x0)) Aa12(Right2(x0))
Right3(a12(x0)) Aa12(Right3(x0))
Right4(a12(x0)) Aa12(Right4(x0))
Right5(a12(x0)) Aa12(Right5(x0))
Right6(a12(x0)) Aa12(Right6(x0))
Right1(a34(x0)) Aa34(Right1(x0))
Right2(a34(x0)) Aa34(Right2(x0))
Right3(a34(x0)) Aa34(Right3(x0))
Right4(a34(x0)) Aa34(Right4(x0))
Right5(a34(x0)) Aa34(Right5(x0))
Right6(a34(x0)) Aa34(Right6(x0))
Right1(a45(x0)) Aa45(Right1(x0))
Right2(a45(x0)) Aa45(Right2(x0))
Right3(a45(x0)) Aa45(Right3(x0))
Right4(a45(x0)) Aa45(Right4(x0))
Right5(a45(x0)) Aa45(Right5(x0))
Right6(a45(x0)) Aa45(Right6(x0))
Right1(a56(x0)) Aa56(Right1(x0))
Right2(a56(x0)) Aa56(Right2(x0))
Right3(a56(x0)) Aa56(Right3(x0))
Right4(a56(x0)) Aa56(Right4(x0))
Right5(a56(x0)) Aa56(Right5(x0))
Right6(a56(x0)) Aa56(Right6(x0))
Right1(a23(x0)) Aa23(Right1(x0))
Right2(a23(x0)) Aa23(Right2(x0))
Right3(a23(x0)) Aa23(Right3(x0))
Right4(a23(x0)) Aa23(Right4(x0))
Right5(a23(x0)) Aa23(Right5(x0))
Right6(a23(x0)) Aa23(Right6(x0))
Aa12(Left(x0)) Left(a12(x0))
Aa34(Left(x0)) Left(a34(x0))
Aa45(Left(x0)) Left(a45(x0))
Aa56(Left(x0)) Left(a56(x0))
Aa23(Left(x0)) Left(a23(x0))
Wait(Left(x0)) Begin(x0)
a12(a34(x0)) a34(a12(x0))
a12(a45(x0)) a45(a12(x0))
a12(a56(x0)) a56(a12(x0))
a23(a45(x0)) a45(a23(x0))
a23(a56(x0)) a56(a23(x0))
a34(a56(x0)) a56(a34(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(a34(a12(End(x6487))))
ε Wait(Right1(a12(End(x6487))))
1 Wait(Left(a34(a12(End(x6487)))))
ε Begin(a34(a12(End(x6487))))
= t3
where t3 = t0σ and σ = {x6487/x6487}