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))
Right1(b(End(x0))) → Left(a(b(End(x0))))
Right1(b(x0)) → Ab(Right1(x0))
Right1(a(x0)) → Aa(Right1(x0))
Ab(Left(x0)) → Left(b(x0))
Aa(Left(x0)) → Left(a(x0))
Wait(Left(x0)) → Begin(x0)
b(a(x0)) → a(b(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(a(b(End(x146))))
→ε Wait(Right1(b(End(x146))))
→1 Wait(Left(a(b(End(x146)))))
→ε Begin(a(b(End(x146))))
= t3
where t3 = t0σ and σ = {x146/x146}