Certification Problem

Input (TPDB SRS_Standard/Trafo_06/un04)

The rewrite relation of the following TRS is considered.

b(a(b(a(a(b(x1)))))) → b(b(a(b(a(b(x1)))))) (1)
b(a(b(b(x1)))) → b(b(a(a(b(a(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 = b(a(b(b(a(a(b(b(a(b(a(b(b(a(b(a(b(a(b(x1)))))))))))))))))))
→ b(a(b(b(a(a(b(b(a(b(b(a(a(b(a(b(a(b(a(b(a(b(x1))))))))))))))))))))))
→ b(a(b(b(a(a(b(b(b(a(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))
→ b(a(b(b(a(a(b(b(b(a(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))
→ b(b(a(a(b(a(b(a(a(b(b(b(a(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1))))))))))))))))))))))))))))
→ b(b(a(a(b(b(a(b(a(b(b(b(a(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1))))))))))))))))))))))))))))
→ b(b(a(a(b(b(a(b(b(a(a(b(a(b(b(a(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))))))))
→ b(b(a(a(b(b(a(b(b(a(a(b(b(a(a(b(a(b(a(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1))))))))))))))))))))))))))))))))))
→ b(b(a(a(b(b(a(b(b(a(a(b(b(a(a(b(b(a(b(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1))))))))))))))))))))))))))))))))))
→ b(b(a(a(b(b(b(a(a(b(a(b(a(a(b(b(a(a(b(b(a(b(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))))))))))))))
→ b(b(a(a(b(b(b(a(a(b(b(a(b(a(b(b(a(a(b(b(a(b(a(b(b(a(b(a(b(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))))))))))))))
= t10
where t10 = C[t0σ] and σ = {x1/a(b(a(b(a(b(x1))))))} and C = b(b(a(a(b(b(b(a(a(b(b(a(☐))))))))))))