NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(b(a(b(b(End(x276076))))))
ε Wait(Right2(b(End(x276076))))
1 Wait(Left(b(a(b(a(a(b(b(End(x276076))))))))))
ε Begin(b(a(b(a(a(b(b(End(x276076)))))))))
1.1.1.1.1.1 Begin(b(a(b(a(a(b(a(b(End(x276076))))))))))
1.1.1 Begin(b(a(b(b(End(x276076))))))
= t5
where t5 = t0σ and σ = {x276076/x276076}