NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(x0)) → Wait(Right1(x0))
Begin(a(x0)) → Wait(Right2(x0))
Begin(y(x0)) → Wait(Right3(x0))
Begin(q1(b(x0))) → Wait(Right4(x0))
Begin(b(x0)) → Wait(Right5(x0))
Begin(q2(a(x0))) → Wait(Right6(x0))
Begin(a(x0)) → Wait(Right7(x0))
Begin(q2(y(x0))) → Wait(Right8(x0))
Begin(y(x0)) → Wait(Right9(x0))
Begin(q1(b(x0))) → Wait(Right10(x0))
Begin(b(x0)) → Wait(Right11(x0))
Begin(q2(a(x0))) → Wait(Right12(x0))
Begin(a(x0)) → Wait(Right13(x0))
Begin(q2(y(x0))) → Wait(Right14(x0))
Begin(y(x0)) → Wait(Right15(x0))
Begin(x(x0)) → Wait(Right16(x0))
Begin(y(x0)) → Wait(Right17(x0))
Begin(y(x0)) → Wait(Right18(x0))
Begin(bl(x0)) → Wait(Right19(x0))
Right1(q0(End(x0))) → Left(x(q1(End(x0))))
Right2(q1(End(x0))) → Left(a(q1(End(x0))))
Right3(q1(End(x0))) → Left(y(q1(End(x0))))
Right4(a(End(x0))) → Left(q2(a(y(End(x0)))))
Right5(a(q1(End(x0)))) → Left(q2(a(y(End(x0)))))
Right6(a(End(x0))) → Left(q2(a(a(End(x0)))))
Right7(a(q2(End(x0)))) → Left(q2(a(a(End(x0)))))
Right8(a(End(x0))) → Left(q2(a(y(End(x0)))))
Right9(a(q2(End(x0)))) → Left(q2(a(y(End(x0)))))
Right10(y(End(x0))) → Left(q2(y(y(End(x0)))))
Right11(y(q1(End(x0)))) → Left(q2(y(y(End(x0)))))
Right12(y(End(x0))) → Left(q2(y(a(End(x0)))))
Right13(y(q2(End(x0)))) → Left(q2(y(a(End(x0)))))
Right14(y(End(x0))) → Left(q2(y(y(End(x0)))))
Right15(y(q2(End(x0)))) → Left(q2(y(y(End(x0)))))
Right16(q2(End(x0))) → Left(x(q0(End(x0))))
Right17(q0(End(x0))) → Left(y(q3(End(x0))))
Right18(q3(End(x0))) → Left(y(q3(End(x0))))
Right19(q3(End(x0))) → Left(bl(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))
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))
Right16(a(x0)) → Aa(Right16(x0))
Right17(a(x0)) → Aa(Right17(x0))
Right18(a(x0)) → Aa(Right18(x0))
Right19(a(x0)) → Aa(Right19(x0))
Right1(x(x0)) → Ax(Right1(x0))
Right2(x(x0)) → Ax(Right2(x0))
Right3(x(x0)) → Ax(Right3(x0))
Right4(x(x0)) → Ax(Right4(x0))
Right5(x(x0)) → Ax(Right5(x0))
Right6(x(x0)) → Ax(Right6(x0))
Right7(x(x0)) → Ax(Right7(x0))
Right8(x(x0)) → Ax(Right8(x0))
Right9(x(x0)) → Ax(Right9(x0))
Right10(x(x0)) → Ax(Right10(x0))
Right11(x(x0)) → Ax(Right11(x0))
Right12(x(x0)) → Ax(Right12(x0))
Right13(x(x0)) → Ax(Right13(x0))
Right14(x(x0)) → Ax(Right14(x0))
Right15(x(x0)) → Ax(Right15(x0))
Right16(x(x0)) → Ax(Right16(x0))
Right17(x(x0)) → Ax(Right17(x0))
Right18(x(x0)) → Ax(Right18(x0))
Right19(x(x0)) → Ax(Right19(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))
Right1(y(x0)) → Ay(Right1(x0))
Right2(y(x0)) → Ay(Right2(x0))
Right3(y(x0)) → Ay(Right3(x0))
Right4(y(x0)) → Ay(Right4(x0))
Right5(y(x0)) → Ay(Right5(x0))
Right6(y(x0)) → Ay(Right6(x0))
Right7(y(x0)) → Ay(Right7(x0))
Right8(y(x0)) → Ay(Right8(x0))
Right9(y(x0)) → Ay(Right9(x0))
Right10(y(x0)) → Ay(Right10(x0))
Right11(y(x0)) → Ay(Right11(x0))
Right12(y(x0)) → Ay(Right12(x0))
Right13(y(x0)) → Ay(Right13(x0))
Right14(y(x0)) → Ay(Right14(x0))
Right15(y(x0)) → Ay(Right15(x0))
Right16(y(x0)) → Ay(Right16(x0))
Right17(y(x0)) → Ay(Right17(x0))
Right18(y(x0)) → Ay(Right18(x0))
Right19(y(x0)) → Ay(Right19(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))
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))
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))
Right1(bl(x0)) → Abl(Right1(x0))
Right2(bl(x0)) → Abl(Right2(x0))
Right3(bl(x0)) → Abl(Right3(x0))
Right4(bl(x0)) → Abl(Right4(x0))
Right5(bl(x0)) → Abl(Right5(x0))
Right6(bl(x0)) → Abl(Right6(x0))
Right7(bl(x0)) → Abl(Right7(x0))
Right8(bl(x0)) → Abl(Right8(x0))
Right9(bl(x0)) → Abl(Right9(x0))
Right10(bl(x0)) → Abl(Right10(x0))
Right11(bl(x0)) → Abl(Right11(x0))
Right12(bl(x0)) → Abl(Right12(x0))
Right13(bl(x0)) → Abl(Right13(x0))
Right14(bl(x0)) → Abl(Right14(x0))
Right15(bl(x0)) → Abl(Right15(x0))
Right16(bl(x0)) → Abl(Right16(x0))
Right17(bl(x0)) → Abl(Right17(x0))
Right18(bl(x0)) → Abl(Right18(x0))
Right19(bl(x0)) → Abl(Right19(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))
Aq0(Left(x0)) → Left(q0(x0))
Aa(Left(x0)) → Left(a(x0))
Ax(Left(x0)) → Left(x(x0))
Aq1(Left(x0)) → Left(q1(x0))
Ay(Left(x0)) → Left(y(x0))
Ab(Left(x0)) → Left(b(x0))
Aq2(Left(x0)) → Left(q2(x0))
Aq3(Left(x0)) → Left(q3(x0))
Abl(Left(x0)) → Left(bl(x0))
Aq4(Left(x0)) → Left(q4(x0))
Wait(Left(x0)) → Begin(x0)
q0(a(x0)) → x(q1(x0))
q1(a(x0)) → a(q1(x0))
q1(y(x0)) → y(q1(x0))
a(q1(b(x0))) → q2(a(y(x0)))
a(q2(a(x0))) → q2(a(a(x0)))
a(q2(y(x0))) → q2(a(y(x0)))
y(q1(b(x0))) → q2(y(y(x0)))
y(q2(a(x0))) → q2(y(a(x0)))
y(q2(y(x0))) → q2(y(y(x0)))
q2(x(x0)) → x(q0(x0))
q0(y(x0)) → y(q3(x0))
q3(y(x0)) → y(q3(x0))
q3(bl(x0)) → bl(q4(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(a(q1(End(x150465))))
→ε Wait(Right2(q1(End(x150465))))
→1 Wait(Left(a(q1(End(x150465)))))
→ε Begin(a(q1(End(x150465))))
= t3
where t3 = t0σ and σ = {x150465/x150465}