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(y(x0)) Wait(Right2(x0))
Begin(q2(a(x0))) Wait(Right3(x0))
Begin(a(x0)) Wait(Right4(x0))
Begin(q2(y(x0))) Wait(Right5(x0))
Begin(y(x0)) Wait(Right6(x0))
Begin(q2(a(x0))) Wait(Right7(x0))
Begin(a(x0)) Wait(Right8(x0))
Begin(q2(y(x0))) Wait(Right9(x0))
Begin(y(x0)) Wait(Right10(x0))
Begin(y(x0)) Wait(Right11(x0))
Right1(q1(End(x0))) Left(a(q1(End(x0))))
Right2(q1(End(x0))) Left(y(q1(End(x0))))
Right3(a(End(x0))) Left(q2(a(a(End(x0)))))
Right4(a(q2(End(x0)))) Left(q2(a(a(End(x0)))))
Right5(a(End(x0))) Left(q2(a(y(End(x0)))))
Right6(a(q2(End(x0)))) Left(q2(a(y(End(x0)))))
Right7(y(End(x0))) Left(q2(y(a(End(x0)))))
Right8(y(q2(End(x0)))) Left(q2(y(a(End(x0)))))
Right9(y(End(x0))) Left(q2(y(y(End(x0)))))
Right10(y(q2(End(x0)))) Left(q2(y(y(End(x0)))))
Right11(q3(End(x0))) Left(y(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(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))
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))
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))
Aa(Left(x0)) Left(a(x0))
Ay(Left(x0)) Left(y(x0))
Aq2(Left(x0)) Left(q2(x0))
Aq3(Left(x0)) Left(q3(x0))
Wait(Left(x0)) Begin(x0)
q1(a(x0)) a(q1(x0))
q1(y(x0)) y(q1(x0))
a(q2(a(x0))) q2(a(a(x0)))
a(q2(y(x0))) q2(a(y(x0)))
y(q2(a(x0))) q2(y(a(x0)))
y(q2(y(x0))) q2(y(y(x0)))
q3(y(x0)) y(q3(x0))

Proof

1 Loop

The following loop proves nontermination.

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