NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = b(b(b(b(c(a(a(c(a(b(x0))))))))))
→ε c(a(b(b(b(c(a(a(c(a(b(x0)))))))))))
→1.1.1.1.1.1.1.1 c(a(b(b(b(c(a(a(a(b(x0))))))))))
→1.1 c(a(c(a(b(b(c(a(a(a(b(x0)))))))))))
→1.1.1.1 c(a(c(a(c(a(b(c(a(a(a(b(x0))))))))))))
→1.1.1.1.1.1.1 c(a(c(a(c(a(b(a(a(a(b(x0)))))))))))
→1.1.1.1.1.1.1 c(a(c(a(c(a(b(b(b(c(a(a(b(x0)))))))))))))
→1.1 c(a(a(c(a(b(b(b(c(a(a(b(x0))))))))))))
→1.1.1.1.1 c(a(a(c(a(c(a(b(b(c(a(a(b(x0)))))))))))))
→1.1.1 c(a(a(a(c(a(b(b(c(a(a(b(x0))))))))))))
→1.1.1.1.1.1 c(a(a(a(c(a(c(a(b(c(a(a(b(x0)))))))))))))
→1.1.1.1 c(a(a(a(a(c(a(b(c(a(a(b(x0))))))))))))
→1 c(b(b(c(a(a(a(c(a(b(c(a(a(b(x0))))))))))))))
→1.1.1.1 c(b(b(c(b(b(c(a(a(c(a(b(c(a(a(b(x0))))))))))))))))
→1.1.1 c(b(b(b(b(c(a(a(c(a(b(c(a(a(b(x0)))))))))))))))
= t14
where t14 = C[t0σ] and σ = {x0/c(a(a(b(x0))))} and C = c(☐)