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(a(a(b(a(a(b(x0)))))))) Wait(Right5(x0))
Begin(a(a(b(a(a(b(x0))))))) Wait(Right6(x0))
Begin(a(b(a(a(b(x0)))))) Wait(Right7(x0))
Begin(b(a(a(b(x0))))) Wait(Right8(x0))
Begin(a(a(b(x0)))) Wait(Right9(x0))
Begin(a(b(x0))) Wait(Right10(x0))
Begin(b(x0)) Wait(Right11(x0))
Begin(b(a(a(b(x0))))) Wait(Right12(x0))
Begin(a(a(b(x0)))) Wait(Right13(x0))
Begin(a(b(x0))) Wait(Right14(x0))
Begin(b(x0)) Wait(Right15(x0))
Right1(b(End(x0))) Left(b(a(b(a(a(b(End(x0))))))))
Right2(b(End(x0))) Left(b(a(b(b(End(x0))))))
Right3(b(b(End(x0)))) Left(b(a(b(b(End(x0))))))
Right4(b(b(a(End(x0))))) Left(b(a(b(b(End(x0))))))
Right5(b(End(x0))) Left(b(a(a(a(b(b(End(x0))))))))
Right6(b(a(End(x0)))) Left(b(a(a(a(b(b(End(x0))))))))
Right7(b(a(a(End(x0))))) Left(b(a(a(a(b(b(End(x0))))))))
Right8(b(a(a(a(End(x0)))))) Left(b(a(a(a(b(b(End(x0))))))))
Right9(b(a(a(a(b(End(x0))))))) Left(b(a(a(a(b(b(End(x0))))))))
Right10(b(a(a(a(b(a(End(x0)))))))) Left(b(a(a(a(b(b(End(x0))))))))
Right11(b(a(a(a(b(a(a(End(x0))))))))) Left(b(a(a(a(b(b(End(x0))))))))
Right12(b(End(x0))) Left(b(a(a(b(b(End(x0)))))))
Right13(b(b(End(x0)))) Left(b(a(a(b(b(End(x0)))))))
Right14(b(b(a(End(x0))))) Left(b(a(a(b(b(End(x0)))))))
Right15(b(b(a(a(End(x0)))))) Left(b(a(a(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))
Right12(b(x0)) Ab(Right12(x0))
Right13(b(x0)) Ab(Right13(x0))
Right14(b(x0)) Ab(Right14(x0))
Right15(b(x0)) Ab(Right15(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))
Right12(a(x0)) Aa(Right12(x0))
Right13(a(x0)) Aa(Right13(x0))
Right14(a(x0)) Aa(Right14(x0))
Right15(a(x0)) Aa(Right15(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Wait(Left(x0)) Begin(x0)
b(b(x0)) b(a(b(a(a(b(x0))))))
b(b(a(b(x0)))) b(a(b(b(x0))))
b(a(a(a(b(a(a(b(x0)))))))) b(a(a(a(b(b(x0))))))
b(b(a(a(b(x0))))) b(a(a(b(b(x0)))))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(b(a(b(b(End(x16365))))))
ε Wait(Right2(b(End(x16365))))
1 Wait(Left(b(a(b(b(End(x16365)))))))
ε Begin(b(a(b(b(End(x16365))))))
= t3
where t3 = t0σ and σ = {x16365/x16365}