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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(c(b(b(x51281)))))
→ε b(b(a(a(c(a(c(b(b(x51281)))))))))
→1.1.1.1.1 b(b(a(a(c(c(b(b(x51281))))))))
→1.1.1.1 b(b(a(a(b(b(x51281))))))
→1.1.1 b(b(a(b(b(a(a(c(a(b(x51281))))))))))
→1.1 b(b(b(b(a(a(c(a(b(a(a(c(a(b(x51281))))))))))))))
→1.1.1.1.1.1.1.1.1 b(b(b(b(a(a(c(a(b(a(c(a(b(x51281)))))))))))))
→1.1.1.1.1.1.1.1.1 b(b(b(b(a(a(c(a(b(c(a(b(x51281))))))))))))
→1.1.1.1.1.1.1.1.1.1 b(b(b(b(a(a(c(a(b(c(b(b(a(a(c(a(x51281))))))))))))))))
= t8
where t8 = C[t0σ] and σ = {x51281/a(a(c(a(x51281))))} and C = b(b(b(b(a(a(c(☐)))))))