NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(1(1(x0))) Wait(Right1(x0))
Begin(1(x0)) Wait(Right2(x0))
Begin(1(h(b(x0)))) Wait(Right3(x0))
Begin(h(b(x0))) Wait(Right4(x0))
Begin(b(x0)) Wait(Right5(x0))
Begin(s(x0)) Wait(Right6(x0))
Begin(s(x0)) Wait(Right7(x0))
Begin(1(b(x0))) Wait(Right8(x0))
Begin(b(x0)) Wait(Right9(x0))
Begin(t(x0)) Wait(Right10(x0))
Begin(t(x0)) Wait(Right11(x0))
Right1(h(End(x0))) Left(1(h(End(x0))))
Right2(h(1(End(x0)))) Left(1(h(End(x0))))
Right3(1(End(x0))) Left(1(1(s(b(End(x0))))))
Right4(1(1(End(x0)))) Left(1(1(s(b(End(x0))))))
Right5(1(1(h(End(x0))))) Left(1(1(s(b(End(x0))))))
Right6(1(End(x0))) Left(s(1(End(x0))))
Right7(b(End(x0))) Left(b(h(End(x0))))
Right8(h(End(x0))) Left(t(1(1(b(End(x0))))))
Right9(h(1(End(x0)))) Left(t(1(1(b(End(x0))))))
Right10(1(End(x0))) Left(t(1(1(1(End(x0))))))
Right11(b(End(x0))) Left(b(h(End(x0))))
Right1(h(x0)) Ah(Right1(x0))
Right2(h(x0)) Ah(Right2(x0))
Right3(h(x0)) Ah(Right3(x0))
Right4(h(x0)) Ah(Right4(x0))
Right5(h(x0)) Ah(Right5(x0))
Right6(h(x0)) Ah(Right6(x0))
Right7(h(x0)) Ah(Right7(x0))
Right8(h(x0)) Ah(Right8(x0))
Right9(h(x0)) Ah(Right9(x0))
Right10(h(x0)) Ah(Right10(x0))
Right11(h(x0)) Ah(Right11(x0))
Right1(1(x0)) A1(Right1(x0))
Right2(1(x0)) A1(Right2(x0))
Right3(1(x0)) A1(Right3(x0))
Right4(1(x0)) A1(Right4(x0))
Right5(1(x0)) A1(Right5(x0))
Right6(1(x0)) A1(Right6(x0))
Right7(1(x0)) A1(Right7(x0))
Right8(1(x0)) A1(Right8(x0))
Right9(1(x0)) A1(Right9(x0))
Right10(1(x0)) A1(Right10(x0))
Right11(1(x0)) A1(Right11(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))
Right8(b(x0)) Ab(Right8(x0))
Right9(b(x0)) Ab(Right9(x0))
Right10(b(x0)) Ab(Right10(x0))
Right11(b(x0)) Ab(Right11(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))
Right9(s(x0)) As(Right9(x0))
Right10(s(x0)) As(Right10(x0))
Right11(s(x0)) As(Right11(x0))
Right1(t(x0)) At(Right1(x0))
Right2(t(x0)) At(Right2(x0))
Right3(t(x0)) At(Right3(x0))
Right4(t(x0)) At(Right4(x0))
Right5(t(x0)) At(Right5(x0))
Right6(t(x0)) At(Right6(x0))
Right7(t(x0)) At(Right7(x0))
Right8(t(x0)) At(Right8(x0))
Right9(t(x0)) At(Right9(x0))
Right10(t(x0)) At(Right10(x0))
Right11(t(x0)) At(Right11(x0))
Ah(Left(x0)) Left(h(x0))
A1(Left(x0)) Left(1(x0))
Ab(Left(x0)) Left(b(x0))
As(Left(x0)) Left(s(x0))
At(Left(x0)) Left(t(x0))
Wait(Left(x0)) Begin(x0)
h(1(1(x0))) 1(h(x0))
1(1(h(b(x0)))) 1(1(s(b(x0))))
1(s(x0)) s(1(x0))
b(s(x0)) b(h(x0))
h(1(b(x0))) t(1(1(b(x0))))
1(t(x0)) t(1(1(1(x0))))
b(t(x0)) b(h(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(s(1(End(x30257))))
ε Wait(Right6(1(End(x30257))))
1 Wait(Left(s(1(End(x30257)))))
ε Begin(s(1(End(x30257))))
= t3
where t3 = t0σ and σ = {x30257/x30257}