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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(c(b(x46926))))
→ε b(a(c(b(a(c(b(x46926)))))))
→ε a(a(c(b(a(c(b(x46926)))))))
→1.1.1 a(a(c(a(a(c(b(x46926)))))))
→1.1.1 a(a(c(a(c(b(x46926))))))
→1.1.1 a(a(c(c(b(x46926)))))
→1.1 a(a(b(x46926)))
→1 a(b(a(c(b(a(x46926))))))
→1.1 a(b(c(b(a(x46926)))))
= t8
where t8 = t0σ and σ = {x46926/a(x46926)}