Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/bababababaa-aababababababa.srs)

The rewrite relation of the following TRS is considered.

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

1.1 Loop

The following loop proves nontermination.

t0 = a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(a(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(a(b(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(a(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t32
where t32 = C[t0σ] and σ = {x1/a(a(a(b(a(a(a(b(a(b(a(a(a(b(a(a(a(b(a(b(a(b(a(a(a(b(a(a(a(b(a(b(a(a(a(b(a(a(a(b(a(b(a(b(a(b(a(a(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))} and C = a(b(a(b(a(b(a(b(a(b(a(b(☐))))))))))))