NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = c(a(a(b(a(a(a(x67)))))))
→ε a(a(b(a(c(c(a(a(b(a(a(x67)))))))))))
→1.1.1.1.1 a(a(b(a(c(a(a(b(a(c(c(a(a(b(a(x67)))))))))))))))
→1.1.1.1.1.1.1.1.1.1 a(a(b(a(c(a(a(b(a(c(a(a(b(a(c(c(a(a(b(x67)))))))))))))))))))
→1.1.1.1.1.1.1.1.1 a(a(b(a(c(a(a(b(a(a(a(b(a(c(c(a(a(b(c(c(a(a(b(x67)))))))))))))))))))))))
= t4
where t4 = C[t0σ] and σ = {x67/b(a(c(c(a(a(b(c(c(a(a(b(x67))))))))))))} and C = a(a(b(a(☐))))