Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/bbcaaaaaa-aaaaaabbcbbca.srs)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

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