NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(b(c(a(c(c(b(b(c(x0))))))))))
→1.1.1.1 a(a(b(c(a(a(c(b(b(c(x0))))))))))
→ε b(b(c(a(c(c(a(a(c(b(b(c(x0))))))))))))
→1.1.1.1.1.1.1 b(b(c(a(c(c(a(a(a(b(b(c(x0))))))))))))
→1.1.1.1.1.1.1 b(b(c(a(c(c(a(b(b(c(a(c(b(c(x0))))))))))))))
→1.1.1 b(b(c(a(a(c(a(b(b(c(a(c(b(c(x0))))))))))))))
→1.1.1.1 b(b(c(a(a(a(a(b(b(c(a(c(b(c(x0))))))))))))))
→1.1.1.1.1 b(b(c(a(a(b(b(c(a(c(b(c(a(c(b(c(x0))))))))))))))))
→1.1.1.1.1.1.1.1 b(b(c(a(a(b(b(c(a(a(b(c(a(c(b(c(x0))))))))))))))))
→1.1.1 b(b(c(b(b(c(a(c(b(c(a(a(b(c(a(c(b(c(x0))))))))))))))))))
→1.1.1.1.1.1 b(b(c(b(b(c(a(a(b(c(a(a(b(c(a(c(b(c(x0))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(a(a(b(c(b(b(c(a(c(c(a(c(b(c(x0))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(a(a(b(c(b(b(c(a(c(c(a(a(b(c(x0))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(a(a(b(c(b(b(c(a(c(c(b(b(c(a(c(c(x0))))))))))))))))))))))
→1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(c(c(b(b(c(a(c(c(b(b(c(a(c(c(x0))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(a(c(b(b(c(a(c(c(b(b(c(a(c(c(x0))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(a(a(b(b(c(a(c(c(b(b(c(a(c(c(x0))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(b(b(c(a(c(b(c(a(c(c(b(b(c(a(c(c(x0))))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(b(b(c(a(c(b(c(a(c(c(b(b(c(a(a(c(x0))))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1 b(b(c(b(b(c(b(b(c(a(b(b(c(a(a(b(c(a(c(c(b(b(c(a(a(c(x0))))))))))))))))))))))))))
= t19
where t19 = C[t0σ] and σ = {x0/a(a(c(x0)))} and C = b(b(c(b(b(c(b(b(c(a(b(b(c(☐)))))))))))))