Certification Problem

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

The rewrite relation of the following TRS is considered.

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

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

1.1 Loop

The following loop proves nontermination.

t0 = b(a(a(a(a(a(a(a(a(a(x1))))))))))
→ a(a(a(b(b(b(b(a(a(a(a(a(a(a(x1))))))))))))))
→ a(a(a(b(b(b(a(a(a(b(b(b(b(a(a(a(a(a(x1))))))))))))))))))
→ a(a(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(x1))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(a(a(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(a(b(b(b(b(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(b(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(b(a(a(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(b(a(a(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(b(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(b(a(a(a(a(a(a(a(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t64
where t64 = C[t0σ] and σ = {x1/b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(b(b(b(b(a(a(b(b(b(b(a(b(b(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))} and C = a(a(a(☐)))