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(1'(x0)) → Wait(Right2(x0))
Begin(q2(0(x0))) → Wait(Right3(x0))
Begin(0(x0)) → Wait(Right4(x0))
Begin(q2(0(x0))) → Wait(Right5(x0))
Begin(0(x0)) → Wait(Right6(x0))
Begin(q2(1'(x0))) → Wait(Right7(x0))
Begin(1'(x0)) → Wait(Right8(x0))
Begin(q2(1'(x0))) → Wait(Right9(x0))
Begin(1'(x0)) → Wait(Right10(x0))
Begin(1'(x0)) → Wait(Right11(x0))
Right1(q1(End(x0))) → Left(0(q1(End(x0))))
Right2(q1(End(x0))) → Left(1'(q1(End(x0))))
Right3(0(End(x0))) → Left(q2(0(0(End(x0)))))
Right4(0(q2(End(x0)))) → Left(q2(0(0(End(x0)))))
Right5(1'(End(x0))) → Left(q2(1'(0(End(x0)))))
Right6(1'(q2(End(x0)))) → Left(q2(1'(0(End(x0)))))
Right7(0(End(x0))) → Left(q2(0(1'(End(x0)))))
Right8(0(q2(End(x0)))) → Left(q2(0(1'(End(x0)))))
Right9(1'(End(x0))) → Left(q2(1'(1'(End(x0)))))
Right10(1'(q2(End(x0)))) → Left(q2(1'(1'(End(x0)))))
Right11(q3(End(x0))) → Left(1'(q3(End(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))
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))
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))
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))
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))
Aq1(Left(x0)) → Left(q1(x0))
A0(Left(x0)) → Left(0(x0))
A1'(Left(x0)) → Left(1'(x0))
Aq2(Left(x0)) → Left(q2(x0))
Aq3(Left(x0)) → Left(q3(x0))
Wait(Left(x0)) → Begin(x0)
q1(0(x0)) → 0(q1(x0))
q1(1'(x0)) → 1'(q1(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)))
1'(q2(1'(x0))) → q2(1'(1'(x0)))
q3(1'(x0)) → 1'(q3(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(0(q1(End(x19272))))
→ε Wait(Right1(q1(End(x19272))))
→1 Wait(Left(0(q1(End(x19272)))))
→ε Begin(0(q1(End(x19272))))
= t3
where t3 = t0σ and σ = {x19272/x19272}