NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(0(x0)) → Wait(Right1(x0))
Begin(0(x0)) → Wait(Right2(x0))
Begin(1'(x0)) → Wait(Right3(x0))
Begin(q1(1(x0))) → Wait(Right4(x0))
Begin(1(x0)) → Wait(Right5(x0))
Begin(q1(1(x0))) → Wait(Right6(x0))
Begin(1(x0)) → Wait(Right7(x0))
Begin(q1(1(x0))) → Wait(Right8(x0))
Begin(1(x0)) → Wait(Right9(x0))
Begin(q2(0(x0))) → Wait(Right10(x0))
Begin(0(x0)) → Wait(Right11(x0))
Begin(q2(0(x0))) → Wait(Right12(x0))
Begin(0(x0)) → Wait(Right13(x0))
Begin(q2(0(x0))) → Wait(Right14(x0))
Begin(0(x0)) → Wait(Right15(x0))
Begin(q2(1'(x0))) → Wait(Right16(x0))
Begin(1'(x0)) → Wait(Right17(x0))
Begin(q2(1'(x0))) → Wait(Right18(x0))
Begin(1'(x0)) → Wait(Right19(x0))
Begin(q2(1'(x0))) → Wait(Right20(x0))
Begin(1'(x0)) → Wait(Right21(x0))
Begin(0'(x0)) → Wait(Right22(x0))
Begin(1'(x0)) → Wait(Right23(x0))
Begin(1'(x0)) → Wait(Right24(x0))
Begin(b(x0)) → Wait(Right25(x0))
Right1(q0(End(x0))) → Left(0'(q1(End(x0))))
Right2(q1(End(x0))) → Left(0(q1(End(x0))))
Right3(q1(End(x0))) → Left(1'(q1(End(x0))))
Right4(0(End(x0))) → Left(q2(0(1'(End(x0)))))
Right5(0(q1(End(x0)))) → Left(q2(0(1'(End(x0)))))
Right6(0'(End(x0))) → Left(q2(0'(1'(End(x0)))))
Right7(0'(q1(End(x0)))) → Left(q2(0'(1'(End(x0)))))
Right8(1'(End(x0))) → Left(q2(1'(1'(End(x0)))))
Right9(1'(q1(End(x0)))) → Left(q2(1'(1'(End(x0)))))
Right10(0(End(x0))) → Left(q2(0(0(End(x0)))))
Right11(0(q2(End(x0)))) → Left(q2(0(0(End(x0)))))
Right12(0'(End(x0))) → Left(q2(0'(0(End(x0)))))
Right13(0'(q2(End(x0)))) → Left(q2(0'(0(End(x0)))))
Right14(1'(End(x0))) → Left(q2(1'(0(End(x0)))))
Right15(1'(q2(End(x0)))) → Left(q2(1'(0(End(x0)))))
Right16(0(End(x0))) → Left(q2(0(1'(End(x0)))))
Right17(0(q2(End(x0)))) → Left(q2(0(1'(End(x0)))))
Right18(0'(End(x0))) → Left(q2(0'(1'(End(x0)))))
Right19(0'(q2(End(x0)))) → Left(q2(0'(1'(End(x0)))))
Right20(1'(End(x0))) → Left(q2(1'(1'(End(x0)))))
Right21(1'(q2(End(x0)))) → Left(q2(1'(1'(End(x0)))))
Right22(q2(End(x0))) → Left(0'(q0(End(x0))))
Right23(q0(End(x0))) → Left(1'(q3(End(x0))))
Right24(q3(End(x0))) → Left(1'(q3(End(x0))))
Right25(q3(End(x0))) → Left(b(q4(End(x0))))
Right1(q0(x0)) → Aq0(Right1(x0))
Right2(q0(x0)) → Aq0(Right2(x0))
Right3(q0(x0)) → Aq0(Right3(x0))
Right4(q0(x0)) → Aq0(Right4(x0))
Right5(q0(x0)) → Aq0(Right5(x0))
Right6(q0(x0)) → Aq0(Right6(x0))
Right7(q0(x0)) → Aq0(Right7(x0))
Right8(q0(x0)) → Aq0(Right8(x0))
Right9(q0(x0)) → Aq0(Right9(x0))
Right10(q0(x0)) → Aq0(Right10(x0))
Right11(q0(x0)) → Aq0(Right11(x0))
Right12(q0(x0)) → Aq0(Right12(x0))
Right13(q0(x0)) → Aq0(Right13(x0))
Right14(q0(x0)) → Aq0(Right14(x0))
Right15(q0(x0)) → Aq0(Right15(x0))
Right16(q0(x0)) → Aq0(Right16(x0))
Right17(q0(x0)) → Aq0(Right17(x0))
Right18(q0(x0)) → Aq0(Right18(x0))
Right19(q0(x0)) → Aq0(Right19(x0))
Right20(q0(x0)) → Aq0(Right20(x0))
Right21(q0(x0)) → Aq0(Right21(x0))
Right22(q0(x0)) → Aq0(Right22(x0))
Right23(q0(x0)) → Aq0(Right23(x0))
Right24(q0(x0)) → Aq0(Right24(x0))
Right25(q0(x0)) → Aq0(Right25(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))
Right17(0(x0)) → A0(Right17(x0))
Right18(0(x0)) → A0(Right18(x0))
Right19(0(x0)) → A0(Right19(x0))
Right20(0(x0)) → A0(Right20(x0))
Right21(0(x0)) → A0(Right21(x0))
Right22(0(x0)) → A0(Right22(x0))
Right23(0(x0)) → A0(Right23(x0))
Right24(0(x0)) → A0(Right24(x0))
Right25(0(x0)) → A0(Right25(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))
Right17(0'(x0)) → A0'(Right17(x0))
Right18(0'(x0)) → A0'(Right18(x0))
Right19(0'(x0)) → A0'(Right19(x0))
Right20(0'(x0)) → A0'(Right20(x0))
Right21(0'(x0)) → A0'(Right21(x0))
Right22(0'(x0)) → A0'(Right22(x0))
Right23(0'(x0)) → A0'(Right23(x0))
Right24(0'(x0)) → A0'(Right24(x0))
Right25(0'(x0)) → A0'(Right25(x0))
Right1(q1(x0)) → Aq1(Right1(x0))
Right2(q1(x0)) → Aq1(Right2(x0))
Right3(q1(x0)) → Aq1(Right3(x0))
Right4(q1(x0)) → Aq1(Right4(x0))
Right5(q1(x0)) → Aq1(Right5(x0))
Right6(q1(x0)) → Aq1(Right6(x0))
Right7(q1(x0)) → Aq1(Right7(x0))
Right8(q1(x0)) → Aq1(Right8(x0))
Right9(q1(x0)) → Aq1(Right9(x0))
Right10(q1(x0)) → Aq1(Right10(x0))
Right11(q1(x0)) → Aq1(Right11(x0))
Right12(q1(x0)) → Aq1(Right12(x0))
Right13(q1(x0)) → Aq1(Right13(x0))
Right14(q1(x0)) → Aq1(Right14(x0))
Right15(q1(x0)) → Aq1(Right15(x0))
Right16(q1(x0)) → Aq1(Right16(x0))
Right17(q1(x0)) → Aq1(Right17(x0))
Right18(q1(x0)) → Aq1(Right18(x0))
Right19(q1(x0)) → Aq1(Right19(x0))
Right20(q1(x0)) → Aq1(Right20(x0))
Right21(q1(x0)) → Aq1(Right21(x0))
Right22(q1(x0)) → Aq1(Right22(x0))
Right23(q1(x0)) → Aq1(Right23(x0))
Right24(q1(x0)) → Aq1(Right24(x0))
Right25(q1(x0)) → Aq1(Right25(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))
Right17(1'(x0)) → A1'(Right17(x0))
Right18(1'(x0)) → A1'(Right18(x0))
Right19(1'(x0)) → A1'(Right19(x0))
Right20(1'(x0)) → A1'(Right20(x0))
Right21(1'(x0)) → A1'(Right21(x0))
Right22(1'(x0)) → A1'(Right22(x0))
Right23(1'(x0)) → A1'(Right23(x0))
Right24(1'(x0)) → A1'(Right24(x0))
Right25(1'(x0)) → A1'(Right25(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))
Right17(1(x0)) → A1(Right17(x0))
Right18(1(x0)) → A1(Right18(x0))
Right19(1(x0)) → A1(Right19(x0))
Right20(1(x0)) → A1(Right20(x0))
Right21(1(x0)) → A1(Right21(x0))
Right22(1(x0)) → A1(Right22(x0))
Right23(1(x0)) → A1(Right23(x0))
Right24(1(x0)) → A1(Right24(x0))
Right25(1(x0)) → A1(Right25(x0))
Right1(q2(x0)) → Aq2(Right1(x0))
Right2(q2(x0)) → Aq2(Right2(x0))
Right3(q2(x0)) → Aq2(Right3(x0))
Right4(q2(x0)) → Aq2(Right4(x0))
Right5(q2(x0)) → Aq2(Right5(x0))
Right6(q2(x0)) → Aq2(Right6(x0))
Right7(q2(x0)) → Aq2(Right7(x0))
Right8(q2(x0)) → Aq2(Right8(x0))
Right9(q2(x0)) → Aq2(Right9(x0))
Right10(q2(x0)) → Aq2(Right10(x0))
Right11(q2(x0)) → Aq2(Right11(x0))
Right12(q2(x0)) → Aq2(Right12(x0))
Right13(q2(x0)) → Aq2(Right13(x0))
Right14(q2(x0)) → Aq2(Right14(x0))
Right15(q2(x0)) → Aq2(Right15(x0))
Right16(q2(x0)) → Aq2(Right16(x0))
Right17(q2(x0)) → Aq2(Right17(x0))
Right18(q2(x0)) → Aq2(Right18(x0))
Right19(q2(x0)) → Aq2(Right19(x0))
Right20(q2(x0)) → Aq2(Right20(x0))
Right21(q2(x0)) → Aq2(Right21(x0))
Right22(q2(x0)) → Aq2(Right22(x0))
Right23(q2(x0)) → Aq2(Right23(x0))
Right24(q2(x0)) → Aq2(Right24(x0))
Right25(q2(x0)) → Aq2(Right25(x0))
Right1(q3(x0)) → Aq3(Right1(x0))
Right2(q3(x0)) → Aq3(Right2(x0))
Right3(q3(x0)) → Aq3(Right3(x0))
Right4(q3(x0)) → Aq3(Right4(x0))
Right5(q3(x0)) → Aq3(Right5(x0))
Right6(q3(x0)) → Aq3(Right6(x0))
Right7(q3(x0)) → Aq3(Right7(x0))
Right8(q3(x0)) → Aq3(Right8(x0))
Right9(q3(x0)) → Aq3(Right9(x0))
Right10(q3(x0)) → Aq3(Right10(x0))
Right11(q3(x0)) → Aq3(Right11(x0))
Right12(q3(x0)) → Aq3(Right12(x0))
Right13(q3(x0)) → Aq3(Right13(x0))
Right14(q3(x0)) → Aq3(Right14(x0))
Right15(q3(x0)) → Aq3(Right15(x0))
Right16(q3(x0)) → Aq3(Right16(x0))
Right17(q3(x0)) → Aq3(Right17(x0))
Right18(q3(x0)) → Aq3(Right18(x0))
Right19(q3(x0)) → Aq3(Right19(x0))
Right20(q3(x0)) → Aq3(Right20(x0))
Right21(q3(x0)) → Aq3(Right21(x0))
Right22(q3(x0)) → Aq3(Right22(x0))
Right23(q3(x0)) → Aq3(Right23(x0))
Right24(q3(x0)) → Aq3(Right24(x0))
Right25(q3(x0)) → Aq3(Right25(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))
Right16(b(x0)) → Ab(Right16(x0))
Right17(b(x0)) → Ab(Right17(x0))
Right18(b(x0)) → Ab(Right18(x0))
Right19(b(x0)) → Ab(Right19(x0))
Right20(b(x0)) → Ab(Right20(x0))
Right21(b(x0)) → Ab(Right21(x0))
Right22(b(x0)) → Ab(Right22(x0))
Right23(b(x0)) → Ab(Right23(x0))
Right24(b(x0)) → Ab(Right24(x0))
Right25(b(x0)) → Ab(Right25(x0))
Right1(q4(x0)) → Aq4(Right1(x0))
Right2(q4(x0)) → Aq4(Right2(x0))
Right3(q4(x0)) → Aq4(Right3(x0))
Right4(q4(x0)) → Aq4(Right4(x0))
Right5(q4(x0)) → Aq4(Right5(x0))
Right6(q4(x0)) → Aq4(Right6(x0))
Right7(q4(x0)) → Aq4(Right7(x0))
Right8(q4(x0)) → Aq4(Right8(x0))
Right9(q4(x0)) → Aq4(Right9(x0))
Right10(q4(x0)) → Aq4(Right10(x0))
Right11(q4(x0)) → Aq4(Right11(x0))
Right12(q4(x0)) → Aq4(Right12(x0))
Right13(q4(x0)) → Aq4(Right13(x0))
Right14(q4(x0)) → Aq4(Right14(x0))
Right15(q4(x0)) → Aq4(Right15(x0))
Right16(q4(x0)) → Aq4(Right16(x0))
Right17(q4(x0)) → Aq4(Right17(x0))
Right18(q4(x0)) → Aq4(Right18(x0))
Right19(q4(x0)) → Aq4(Right19(x0))
Right20(q4(x0)) → Aq4(Right20(x0))
Right21(q4(x0)) → Aq4(Right21(x0))
Right22(q4(x0)) → Aq4(Right22(x0))
Right23(q4(x0)) → Aq4(Right23(x0))
Right24(q4(x0)) → Aq4(Right24(x0))
Right25(q4(x0)) → Aq4(Right25(x0))
Aq0(Left(x0)) → Left(q0(x0))
A0(Left(x0)) → Left(0(x0))
A0'(Left(x0)) → Left(0'(x0))
Aq1(Left(x0)) → Left(q1(x0))
A1'(Left(x0)) → Left(1'(x0))
A1(Left(x0)) → Left(1(x0))
Aq2(Left(x0)) → Left(q2(x0))
Aq3(Left(x0)) → Left(q3(x0))
Ab(Left(x0)) → Left(b(x0))
Aq4(Left(x0)) → Left(q4(x0))
Wait(Left(x0)) → Begin(x0)
q0(0(x0)) → 0'(q1(x0))
q1(0(x0)) → 0(q1(x0))
q1(1'(x0)) → 1'(q1(x0))
0(q1(1(x0))) → q2(0(1'(x0)))
0'(q1(1(x0))) → q2(0'(1'(x0)))
1'(q1(1(x0))) → q2(1'(1'(x0)))
0(q2(0(x0))) → q2(0(0(x0)))
0'(q2(0(x0))) → q2(0'(0(x0)))
1'(q2(0(x0))) → q2(1'(0(x0)))
0(q2(1'(x0))) → q2(0(1'(x0)))
0'(q2(1'(x0))) → q2(0'(1'(x0)))
1'(q2(1'(x0))) → q2(1'(1'(x0)))
q2(0'(x0)) → 0'(q0(x0))
q0(1'(x0)) → 1'(q3(x0))
q3(1'(x0)) → 1'(q3(x0))
q3(b(x0)) → b(q4(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(0(q1(End(x251163))))
→ε Wait(Right2(q1(End(x251163))))
→1 Wait(Left(0(q1(End(x251163)))))
→ε Begin(0(q1(End(x251163))))
= t3
where t3 = t0σ and σ = {x251163/x251163}