Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/bacaaaaaa-aaaaaaabacbac.srs)

The rewrite relation of the following TRS is considered.

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