NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(b(x0))) Wait(Right1(x0))
Begin(b(x0)) Wait(Right2(x0))
Begin(c(x0)) Wait(Right3(x0))
Right1(a(End(x0))) Left(b(b(a(b(c(a(End(x0))))))))
Right2(a(b(End(x0)))) Left(b(b(a(b(c(a(End(x0))))))))
Right3(b(End(x0))) Left(End(x0))
Right1(a(x0)) Aa(Right1(x0))
Right2(a(x0)) Aa(Right2(x0))
Right3(a(x0)) Aa(Right3(x0))
Right1(b(x0)) Ab(Right1(x0))
Right2(b(x0)) Ab(Right2(x0))
Right3(b(x0)) Ab(Right3(x0))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
a(x0) x0
a(b(b(x0))) b(b(a(b(c(a(x0))))))
b(c(x0)) x0

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(b(b(a(End(x41034)))))
ε Wait(Right1(a(End(x41034))))
1 Wait(Left(b(b(a(b(c(a(End(x41034)))))))))
ε Begin(b(b(a(b(c(a(End(x41034))))))))
1.1.1 Begin(b(b(b(c(a(End(x41034)))))))
1.1.1 Begin(b(b(a(End(x41034)))))
= t5
where t5 = t0σ and σ = {x41034/x41034}