NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(l(x0)) → Wait(Right1(x0))
Begin(c(x0)) → Wait(Right2(x0))
Begin(a(r(x0))) → Wait(Right3(x0))
Begin(r(x0)) → Wait(Right4(x0))
Begin(r(a(x0))) → Wait(Right5(x0))
Begin(a(x0)) → Wait(Right6(x0))
Right1(a(End(x0))) → Left(l(a(End(x0))))
Right2(a(End(x0))) → Left(c(a(End(x0))))
Right3(c(End(x0))) → Left(r(a(End(x0))))
Right4(c(a(End(x0)))) → Left(r(a(End(x0))))
Right5(l(End(x0))) → Left(a(l(c(c(r(End(x0)))))))
Right6(l(r(End(x0)))) → Left(a(l(c(c(r(End(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))
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))
Right1(c(x0)) → Ac(Right1(x0))
Right2(c(x0)) → Ac(Right2(x0))
Right3(c(x0)) → Ac(Right3(x0))
Right4(c(x0)) → Ac(Right4(x0))
Right5(c(x0)) → Ac(Right5(x0))
Right6(c(x0)) → Ac(Right6(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))
Aa(Left(x0)) → Left(a(x0))
Al(Left(x0)) → Left(l(x0))
Ac(Left(x0)) → Left(c(x0))
Ar(Left(x0)) → Left(r(x0))
Wait(Left(x0)) → Begin(x0)
a(l(x0)) → l(a(x0))
a(c(x0)) → c(a(x0))
c(a(r(x0))) → r(a(x0))
l(r(a(x0))) → a(l(c(c(r(x0)))))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(l(a(End(x5002))))
→ε Wait(Right1(a(End(x5002))))
→1 Wait(Left(l(a(End(x5002)))))
→ε Begin(l(a(End(x5002))))
= t3
where t3 = t0σ and σ = {x5002/x5002}