Certification Problem

Input (TPDB SRS_Standard/Waldmann_19/random-400)

The rewrite relation of the following TRS is considered.

b(b(a(b(x1)))) → a(a(a(a(x1)))) (1)
a(b(a(a(x1)))) → a(b(b(b(x1)))) (2)
a(b(a(a(x1)))) → b(a(b(b(x1)))) (3)

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(a(b(a(a(a(a(b(a(a(a(a(x1)))))))))))))))
→ a(a(b(b(a(b(a(a(a(b(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(b(a(b(b(b(a(b(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(b(a(b(a(a(a(a(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(b(b(a(b(b(a(a(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(a(a(a(a(b(a(a(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(a(a(a(b(a(b(b(a(b(b(a(a(x1)))))))))))))))
→ a(a(b(a(a(a(b(a(a(a(a(a(b(a(a(x1)))))))))))))))
→ a(a(b(a(a(a(b(a(a(a(a(a(b(b(b(x1)))))))))))))))
→ a(a(b(a(a(b(a(b(b(a(a(a(b(b(b(x1)))))))))))))))
→ a(b(a(b(b(b(a(b(b(a(a(a(b(b(b(x1)))))))))))))))
→ a(b(a(b(a(a(a(a(b(a(a(a(b(b(b(x1)))))))))))))))
→ a(b(a(b(a(a(a(b(a(b(b(a(b(b(b(x1)))))))))))))))
→ a(b(a(b(a(a(a(b(a(a(a(a(a(b(b(x1)))))))))))))))
→ a(b(a(b(a(a(b(a(b(b(a(a(a(b(b(x1)))))))))))))))
→ a(b(b(a(b(b(b(a(b(b(a(a(a(b(b(x1)))))))))))))))
→ a(b(b(a(b(a(a(a(a(b(a(a(a(b(b(x1)))))))))))))))
→ a(b(b(a(b(a(a(a(a(b(b(b(a(b(b(x1)))))))))))))))
→ a(b(b(a(b(a(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
→ a(b(b(a(b(a(a(a(b(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(b(a(b(b(b(a(b(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(b(a(b(a(a(a(a(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(b(b(a(b(b(a(a(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(a(a(a(a(b(a(a(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(a(a(a(b(a(b(b(a(b(b(a(a(b(x1)))))))))))))))
→ a(b(a(a(a(b(a(a(a(a(a(b(a(a(b(x1)))))))))))))))
→ a(b(a(a(a(b(a(a(a(a(a(b(b(b(b(x1)))))))))))))))
→ a(b(a(a(b(a(b(b(a(a(a(b(b(b(b(x1)))))))))))))))
→ b(a(b(b(b(a(b(b(a(a(a(b(b(b(b(x1)))))))))))))))
→ b(a(b(a(a(a(a(b(a(a(a(b(b(b(b(x1)))))))))))))))
→ b(a(b(a(a(a(b(a(b(b(a(b(b(b(b(x1)))))))))))))))
→ b(a(b(a(a(a(b(a(a(a(a(a(b(b(b(x1)))))))))))))))
→ b(a(b(a(a(b(a(b(b(a(a(a(b(b(b(x1)))))))))))))))
→ b(b(a(b(b(b(a(b(b(a(a(a(b(b(b(x1)))))))))))))))
→ b(b(a(b(a(a(a(a(b(a(a(a(b(b(b(x1)))))))))))))))
→ b(b(a(b(a(a(a(b(a(b(b(a(b(b(b(x1)))))))))))))))
→ b(b(a(b(a(a(a(b(a(a(a(a(a(b(b(x1)))))))))))))))
→ b(b(a(b(a(a(b(a(b(b(a(a(a(b(b(x1)))))))))))))))
→ b(b(a(b(b(b(b(a(b(b(a(a(a(b(b(x1)))))))))))))))
→ b(b(a(b(b(a(a(a(a(b(a(a(a(b(b(x1)))))))))))))))
→ b(b(a(b(b(a(a(a(b(a(b(b(a(b(b(x1)))))))))))))))
→ b(b(a(b(b(a(a(a(b(a(a(a(a(a(b(x1)))))))))))))))
→ b(b(a(b(b(a(a(b(a(b(b(a(a(a(b(x1)))))))))))))))
→ a(a(a(a(b(a(a(b(a(b(b(a(a(a(b(x1)))))))))))))))
→ a(a(a(b(a(b(b(b(a(b(b(a(a(a(b(x1)))))))))))))))
→ a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x1)))))))))))))))
→ a(a(a(b(a(b(a(a(a(b(a(b(b(a(b(x1)))))))))))))))
→ a(a(a(b(a(b(a(a(a(b(a(a(a(a(a(x1)))))))))))))))
→ a(a(a(b(a(b(a(a(b(a(b(b(a(a(a(x1)))))))))))))))
→ a(a(a(b(b(a(b(b(b(a(b(b(a(a(a(x1)))))))))))))))
→ a(a(a(b(b(a(b(a(a(a(a(b(a(a(a(x1)))))))))))))))
→ a(a(a(b(b(a(b(a(a(a(b(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(b(a(b(b(b(a(b(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(b(a(b(a(a(a(a(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(b(b(a(b(b(a(a(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(a(a(a(a(b(a(a(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(a(a(a(b(a(b(b(a(b(b(a(x1)))))))))))))))
→ a(a(a(b(a(a(a(b(a(a(a(a(a(b(a(x1)))))))))))))))
→ a(a(a(b(a(a(b(a(b(b(a(a(a(b(a(x1)))))))))))))))
→ a(a(b(a(b(b(b(a(b(b(a(a(a(b(a(x1)))))))))))))))
→ a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(x1)))))))))))))))
→ a(a(b(a(b(a(a(a(b(a(b(b(a(b(a(x1)))))))))))))))
→ a(a(b(a(b(a(a(a(b(a(a(a(a(a(a(x1)))))))))))))))
→ a(a(b(a(b(a(a(b(a(b(b(a(a(a(a(x1)))))))))))))))
→ a(a(b(b(a(b(b(b(a(b(b(a(a(a(a(x1)))))))))))))))
→ a(a(b(b(a(b(a(a(a(a(b(a(a(a(a(x1)))))))))))))))
= t65
where t65 = t0σ and σ = {x1/x1}