Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-18)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
a(x1) → x1 (1)
b(a(a(a(x1)))) → a(a(a(a(b(b(b(x1))))))) (3)

1.1 Loop

The following loop proves nontermination.

t0 = b(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))
→ a(a(a(a(b(b(b(a(a(a(a(a(a(a(a(a(x1))))))))))))))))
→ a(a(a(a(b(b(a(a(a(a(b(b(b(a(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(b(b(a(b(b(a(a(a(a(b(b(b(a(a(a(x1)))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(b(b(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(a(x1))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(b(b(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(x1)))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(a(a(a(a(b(b(b(x1)))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(a(a(a(a(b(b(b(a(b(b(b(x1))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(x1)))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(a(a(a(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(a(a(a(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(a(a(a(a(b(b(b(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(b(a(a(a(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(b(b(b(a(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(b(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(b(a(a(a(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(b(a(a(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t27
where t27 = C[t0σ] and σ = {x1/b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(a(b(b(b(a(a(a(b(b(b(a(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))} and C = a(a(a(a(☐))))