NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(2(1(x0))) → Wait(Right1(x0))
Begin(1(x0)) → Wait(Right2(x0))
Begin(2(1(x0))) → Wait(Right3(x0))
Begin(1(x0)) → Wait(Right4(x0))
Begin(2(1(x0))) → Wait(Right5(x0))
Begin(1(x0)) → Wait(Right6(x0))
Begin(2(0(x0))) → Wait(Right7(x0))
Begin(0(x0)) → Wait(Right8(x0))
Begin(2(R(x0))) → Wait(Right9(x0))
Begin(R(x0)) → Wait(Right10(x0))
Begin(2(0(x0))) → Wait(Right11(x0))
Begin(0(x0)) → Wait(Right12(x0))
Begin(2(0(x0))) → Wait(Right13(x0))
Begin(0(x0)) → Wait(Right14(x0))
Begin(2(R(x0))) → Wait(Right15(x0))
Begin(R(x0)) → Wait(Right16(x0))
Right1(1(End(x0))) → Left(2(0(2(End(x0)))))
Right2(1(2(End(x0)))) → Left(2(0(2(End(x0)))))
Right3(0(End(x0))) → Left(1(0(2(End(x0)))))
Right4(0(2(End(x0)))) → Left(1(0(2(End(x0)))))
Right5(L(End(x0))) → Left(L(1(0(2(End(x0))))))
Right6(L(2(End(x0)))) → Left(L(1(0(2(End(x0))))))
Right7(1(End(x0))) → Left(2(0(1(End(x0)))))
Right8(1(2(End(x0)))) → Left(2(0(1(End(x0)))))
Right9(1(End(x0))) → Left(2(0(1(R(End(x0))))))
Right10(1(2(End(x0)))) → Left(2(0(1(R(End(x0))))))
Right11(0(End(x0))) → Left(1(0(1(End(x0)))))
Right12(0(2(End(x0)))) → Left(1(0(1(End(x0)))))
Right13(L(End(x0))) → Left(L(1(0(1(End(x0))))))
Right14(L(2(End(x0)))) → Left(L(1(0(1(End(x0))))))
Right15(0(End(x0))) → Left(1(0(1(R(End(x0))))))
Right16(0(2(End(x0)))) → Left(1(0(1(R(End(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))
Right12(1(x0)) → A1(Right12(x0))
Right13(1(x0)) → A1(Right13(x0))
Right14(1(x0)) → A1(Right14(x0))
Right15(1(x0)) → A1(Right15(x0))
Right16(1(x0)) → A1(Right16(x0))
Right1(2(x0)) → A2(Right1(x0))
Right2(2(x0)) → A2(Right2(x0))
Right3(2(x0)) → A2(Right3(x0))
Right4(2(x0)) → A2(Right4(x0))
Right5(2(x0)) → A2(Right5(x0))
Right6(2(x0)) → A2(Right6(x0))
Right7(2(x0)) → A2(Right7(x0))
Right8(2(x0)) → A2(Right8(x0))
Right9(2(x0)) → A2(Right9(x0))
Right10(2(x0)) → A2(Right10(x0))
Right11(2(x0)) → A2(Right11(x0))
Right12(2(x0)) → A2(Right12(x0))
Right13(2(x0)) → A2(Right13(x0))
Right14(2(x0)) → A2(Right14(x0))
Right15(2(x0)) → A2(Right15(x0))
Right16(2(x0)) → A2(Right16(x0))
Right1(0(x0)) → A0(Right1(x0))
Right2(0(x0)) → A0(Right2(x0))
Right3(0(x0)) → A0(Right3(x0))
Right4(0(x0)) → A0(Right4(x0))
Right5(0(x0)) → A0(Right5(x0))
Right6(0(x0)) → A0(Right6(x0))
Right7(0(x0)) → A0(Right7(x0))
Right8(0(x0)) → A0(Right8(x0))
Right9(0(x0)) → A0(Right9(x0))
Right10(0(x0)) → A0(Right10(x0))
Right11(0(x0)) → A0(Right11(x0))
Right12(0(x0)) → A0(Right12(x0))
Right13(0(x0)) → A0(Right13(x0))
Right14(0(x0)) → A0(Right14(x0))
Right15(0(x0)) → A0(Right15(x0))
Right16(0(x0)) → A0(Right16(x0))
Right1(L(x0)) → AL(Right1(x0))
Right2(L(x0)) → AL(Right2(x0))
Right3(L(x0)) → AL(Right3(x0))
Right4(L(x0)) → AL(Right4(x0))
Right5(L(x0)) → AL(Right5(x0))
Right6(L(x0)) → AL(Right6(x0))
Right7(L(x0)) → AL(Right7(x0))
Right8(L(x0)) → AL(Right8(x0))
Right9(L(x0)) → AL(Right9(x0))
Right10(L(x0)) → AL(Right10(x0))
Right11(L(x0)) → AL(Right11(x0))
Right12(L(x0)) → AL(Right12(x0))
Right13(L(x0)) → AL(Right13(x0))
Right14(L(x0)) → AL(Right14(x0))
Right15(L(x0)) → AL(Right15(x0))
Right16(L(x0)) → AL(Right16(x0))
Right1(R(x0)) → AR(Right1(x0))
Right2(R(x0)) → AR(Right2(x0))
Right3(R(x0)) → AR(Right3(x0))
Right4(R(x0)) → AR(Right4(x0))
Right5(R(x0)) → AR(Right5(x0))
Right6(R(x0)) → AR(Right6(x0))
Right7(R(x0)) → AR(Right7(x0))
Right8(R(x0)) → AR(Right8(x0))
Right9(R(x0)) → AR(Right9(x0))
Right10(R(x0)) → AR(Right10(x0))
Right11(R(x0)) → AR(Right11(x0))
Right12(R(x0)) → AR(Right12(x0))
Right13(R(x0)) → AR(Right13(x0))
Right14(R(x0)) → AR(Right14(x0))
Right15(R(x0)) → AR(Right15(x0))
Right16(R(x0)) → AR(Right16(x0))
A1(Left(x0)) → Left(1(x0))
A2(Left(x0)) → Left(2(x0))
A0(Left(x0)) → Left(0(x0))
AL(Left(x0)) → Left(L(x0))
AR(Left(x0)) → Left(R(x0))
Wait(Left(x0)) → Begin(x0)
1(2(1(x0))) → 2(0(2(x0)))
0(2(1(x0))) → 1(0(2(x0)))
L(2(1(x0))) → L(1(0(2(x0))))
1(2(0(x0))) → 2(0(1(x0)))
1(2(R(x0))) → 2(0(1(R(x0))))
0(2(0(x0))) → 1(0(1(x0)))
L(2(0(x0))) → L(1(0(1(x0))))
0(2(R(x0))) → 1(0(1(R(x0))))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(1(0(2(End(x49034)))))
→ε Wait(Right4(0(2(End(x49034)))))
→1 Wait(Left(1(0(2(End(x49034))))))
→ε Begin(1(0(2(End(x49034)))))
= t3
where t3 = t0σ and σ = {x49034/x49034}