Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-20)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = b(b(a(a(a(a(a(a(b(a(b(x1)))))))))))
→ b(b(a(a(a(a(b(a(b(a(a(b(x1))))))))))))
→ b(b(a(a(b(a(b(a(a(b(a(a(b(x1)))))))))))))
→ b(b(b(a(b(a(a(b(a(a(b(a(a(b(x1))))))))))))))
→ a(a(b(a(a(b(a(a(b(a(a(b(x1))))))))))))
→ a(a(b(b(a(b(a(a(a(b(a(a(b(x1)))))))))))))
→ a(a(b(b(b(a(a(a(b(a(a(b(x1))))))))))))
→ a(a(a(a(a(a(b(a(a(b(x1))))))))))
→ a(a(a(a(b(a(b(a(a(a(b(x1)))))))))))
→ a(a(b(a(b(a(a(b(a(a(a(b(x1))))))))))))
→ b(a(b(a(a(b(a(a(b(a(a(a(b(x1)))))))))))))
→ b(b(a(a(b(a(a(b(a(a(a(b(x1))))))))))))
→ b(b(b(a(b(a(a(a(b(a(a(a(b(x1)))))))))))))
→ a(a(b(a(a(a(b(a(a(a(b(x1)))))))))))
→ a(a(b(a(b(a(b(a(a(a(a(b(x1))))))))))))
→ b(a(b(a(a(b(a(b(a(a(a(a(b(x1)))))))))))))
→ b(a(b(b(a(b(a(a(b(a(a(a(a(b(x1))))))))))))))
→ b(a(b(b(b(a(a(b(a(a(a(a(b(x1)))))))))))))
→ b(a(a(a(a(b(a(a(a(a(b(x1)))))))))))
→ b(a(a(b(a(b(a(a(a(a(a(b(x1))))))))))))
→ b(b(a(b(a(a(b(a(a(a(a(a(b(x1)))))))))))))
→ b(b(a(b(b(a(b(a(a(a(a(a(a(b(x1))))))))))))))
→ b(b(a(b(b(b(a(a(a(a(a(a(b(x1)))))))))))))
→ b(b(a(a(a(a(a(a(a(a(b(x1)))))))))))
→ b(b(a(a(a(a(a(a(b(a(b(a(x1))))))))))))
= t24
where t24 = t0σ and σ = {x1/a(x1)}