NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

a(x0) → x0
a(a(a(x0))) → b(x0)
b(c(x0)) → a(c(c(b(x0))))
c(x0) → x0

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(a(c(c(c(c(x69176)))))))
→ε b(c(c(c(c(x69176)))))
→ε a(c(c(b(c(c(c(x69176)))))))
→1 a(c(b(c(c(c(x69176))))))
→1 a(b(c(c(c(x69176)))))
→1 a(a(c(c(b(c(c(x69176)))))))
→1.1 a(a(c(b(c(c(x69176))))))
→1.1 a(a(b(c(c(x69176)))))
→1.1 a(a(a(c(c(b(c(x69176)))))))
→1.1.1.1.1 a(a(a(c(c(a(c(c(b(x69176)))))))))
→1.1.1.1.1 a(a(a(c(c(c(c(b(x69176))))))))
= t10
where t10 = t0σ and σ = {x69176/b(x69176)}