Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/abaaaaaa-aaaaaaaababab.srs)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(b(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(a(a(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(a(b(a(b(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(a(a(a(a(a(x1)))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(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(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(a(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(a(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(b(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(a(a(a(a(a(a(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(b(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(a(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
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a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(a(b(a(b(a(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
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a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(b(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(b(a(a(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
a(a(a(a(a(a(a(a(b(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(a(a(a(a(a(a(a(a(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t729
where t729 = C[t0σ] and σ = {x1/a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(b(a(b(a(b(a(a(a(b(a(b(a(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))} and C = a(a(a(a(a(a(a()))))))