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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(c(b(x16562))))
→ε b(a(a(c(b(a(c(b(x16562))))))))
→1.1.1.1 b(a(a(c(a(c(b(x16562)))))))
→1.1.1.1 b(a(a(c(c(b(x16562))))))
→1.1.1 b(a(a(b(x16562))))
→1.1 b(a(b(a(a(c(b(a(x16562))))))))
→1.1.1 b(a(b(a(c(b(a(x16562)))))))
→1.1.1 b(a(b(c(b(a(x16562))))))
= t7
where t7 = C[t0σ] and σ = {x16562/a(x16562)} and C = b(☐)