Certification Problem

Input (TPDB SRS_Standard/Zantema_06/loop1)

The rewrite relation of the following TRS is considered.

a(b(b(x1))) → b(b(a(a(x1)))) (1)
a(a(x1)) → b(x1) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(a(b(b(b(b(x1))))))
→ a(b(b(a(a(b(b(x1)))))))
→ a(b(b(a(b(b(a(a(x1))))))))
→ a(b(b(a(b(b(b(x1)))))))
→ a(b(b(b(b(a(a(b(x1))))))))
→ a(b(b(b(b(b(b(x1)))))))
→ b(b(a(a(b(b(b(b(x1))))))))
= t6
where t6 = C[t0σ] and σ = {x1/x1} and C = b(b(☐))