Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-518)

The rewrite relation of the following TRS is considered.

a(a(a(x1))) → b(b(c(c(x1)))) (1)
c(b(x1)) → a(a(c(x1))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = c(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))
→ c(b(b(c(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))
→ a(a(c(b(c(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))
→ a(a(a(a(c(c(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))
→ a(a(a(a(c(c(c(b(b(c(c(a(a(a(a(a(a(x1)))))))))))))))))
→ a(a(a(a(c(c(a(a(c(b(c(c(a(a(a(a(a(a(x1))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(c(c(c(a(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(a(a(c(c(b(b(c(c(a(c(c(c(a(a(a(a(a(a(x1))))))))))))))))))))
→ a(a(a(a(c(a(a(c(b(c(c(a(c(c(c(a(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(c(b(b(c(c(a(a(a(x1)))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(a(a(c(b(c(c(a(a(a(x1))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(a(a(a(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(b(b(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(a(a(c(b(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(c(b(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(a(a(c(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(a(a(a(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(c(b(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(a(a(c(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1)))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(x1))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(b(b(c(c(x1)))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(a(a(c(b(c(c(x1))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(a(a(a(a(c(c(c(x1)))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(b(b(c(c(a(c(c(c(x1))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(a(a(c(b(c(c(a(c(c(c(x1)))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(a(a(a(a(c(c(c(a(c(c(c(x1))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(b(b(c(c(a(c(c(c(a(c(c(c(x1)))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(x1))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(x1)))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(b(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(x1))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(a(a(c(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(a(a(a(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(b(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(a(a(c(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(b(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(a(a(c(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(a(a(a(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(b(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(a(a(c(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(b(b(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(a(a(c(b(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(a(a(a(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(b(b(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(a(a(c(b(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(b(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(a(a(c(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(a(a(a(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(c(b(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(a(a(c(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(c(b(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(a(a(c(b(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(a(a(a(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(c(b(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(a(a(c(b(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(a(a(a(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(c(b(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(a(a(c(b(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(a(a(a(a(a(a(a(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t81
where t81 = C[t0σ] and σ = {x1/c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(c(c(c(a(c(c(c(a(c(c(c(a(a(a(c(c(c(a(c(c(c(a(c(c(c(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))} and C = a(a(a(a(☐))))