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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(c(b(x33260))))
→ε b(a(c(b(c(c(b(x33260)))))))
→ε a(a(c(b(c(c(b(x33260)))))))
→1.1.1 a(a(c(a(c(c(b(x33260)))))))
→1.1.1.1 a(a(c(a(b(x33260)))))
→1.1.1 a(a(c(b(a(c(b(c(x33260))))))))
→1.1.1 a(a(c(a(a(c(b(c(x33260))))))))
→1.1.1 a(a(c(a(c(b(c(x33260)))))))
→1.1.1 a(a(c(c(b(c(x33260))))))
→1.1 a(a(b(c(x33260))))
→1 a(b(a(c(b(c(c(x33260)))))))
→1.1 a(b(c(b(c(c(x33260))))))
= t11
where t11 = t0σ and σ = {x33260/c(c(x33260))}