NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(b(b(x125299))))
→ε b(b(a(c(c(a(b(b(x125299))))))))
→1.1.1.1.1 b(b(a(c(c(b(b(a(c(c(a(b(x125299))))))))))))
→1.1.1.1 b(b(a(c(b(a(c(c(a(b(x125299))))))))))
→1.1.1 b(b(a(a(c(c(a(b(x125299))))))))
→1.1.1.1.1.1 b(b(a(a(c(c(b(b(a(c(c(a(x125299))))))))))))
→1.1.1.1.1 b(b(a(a(c(b(a(c(c(a(x125299))))))))))
→1.1.1.1 b(b(a(a(a(c(c(a(x125299))))))))
→1.1.1.1 b(b(a(a(b(c(c(a(x125299))))))))
→1.1.1 b(b(a(b(b(a(c(c(a(c(c(a(x125299))))))))))))
→1.1.1.1.1 b(b(a(b(b(b(c(c(a(c(c(a(x125299))))))))))))
= t10
where t10 = C[t0σ] and σ = {x125299/c(c(a(c(c(a(x125299))))))} and C = b(b(☐))