NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(s(x0)) Wait(Right1(x0))
Begin(a(b(s(x0)))) Wait(Right2(x0))
Begin(b(s(x0))) Wait(Right3(x0))
Begin(s(x0)) Wait(Right4(x0))
Begin(a(b(b(x0)))) Wait(Right5(x0))
Begin(b(b(x0))) Wait(Right6(x0))
Begin(b(x0)) Wait(Right7(x0))
Begin(s(x0)) Wait(Right8(x0))
Begin(b(a(a(x0)))) Wait(Right9(x0))
Begin(a(a(x0))) Wait(Right10(x0))
Begin(a(x0)) Wait(Right11(x0))
Right1(a(End(x0))) Left(s(a(End(x0))))
Right2(b(End(x0))) Left(a(b(s(a(End(x0))))))
Right3(b(a(End(x0)))) Left(a(b(s(a(End(x0))))))
Right4(b(a(b(End(x0))))) Left(a(b(s(a(End(x0))))))
Right5(b(End(x0))) Left(c(s(End(x0))))
Right6(b(a(End(x0)))) Left(c(s(End(x0))))
Right7(b(a(b(End(x0))))) Left(c(s(End(x0))))
Right8(c(End(x0))) Left(a(b(a(b(End(x0))))))
Right9(a(End(x0))) Left(b(a(b(a(End(x0))))))
Right10(a(b(End(x0)))) Left(b(a(b(a(End(x0))))))
Right11(a(b(a(End(x0))))) Left(b(a(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))
Right8(a(x0)) Aa(Right8(x0))
Right9(a(x0)) Aa(Right9(x0))
Right10(a(x0)) Aa(Right10(x0))
Right11(a(x0)) Aa(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(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(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(x0))
Right5(c(x0)) Ac(Right5(x0))
Right6(c(x0)) Ac(Right6(x0))
Right7(c(x0)) Ac(Right7(x0))
Right8(c(x0)) Ac(Right8(x0))
Right9(c(x0)) Ac(Right9(x0))
Right10(c(x0)) Ac(Right10(x0))
Right11(c(x0)) Ac(Right11(x0))
Aa(Left(x0)) Left(a(x0))
As(Left(x0)) Left(s(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
a(s(x0)) s(a(x0))
b(a(b(s(x0)))) a(b(s(a(x0))))
b(a(b(b(x0)))) c(s(x0))
c(s(x0)) a(b(a(b(x0))))
a(b(a(a(x0)))) b(a(b(a(x0))))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(s(a(End(x14756))))
ε Wait(Right1(a(End(x14756))))
1 Wait(Left(s(a(End(x14756)))))
ε Begin(s(a(End(x14756))))
= t3
where t3 = t0σ and σ = {x14756/x14756}