NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = c(b(a(b(a(b(a(b(a(b(a(b(a(x82)))))))))))))
→ε a(b(a(b(a(b(c(b(c(b(a(b(a(b(a(b(a(x82)))))))))))))))))
→1.1.1.1.1.1.1.1 a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(c(b(a(b(a(x82)))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(c(x82)))))))))))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1.1.1 a(b(a(b(a(b(c(b(a(b(a(b(a(b(a(b(a(b(a(b(c(b(c(b(a(b(c(b(c(x82)))))))))))))))))))))))))))))
= t4
where t4 = C[t0σ] and σ = {x82/b(c(b(c(b(a(b(c(b(c(x82))))))))))} and C = a(b(a(b(a(b(☐))))))