Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-520)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(a(a(a(a(b(c(b(a(a(a(x1)))))))))))
→ a(a(a(a(b(c(a(c(b(a(a(a(x1))))))))))))
→ a(a(a(a(b(c(b(a(a(b(a(a(a(x1)))))))))))))
→ a(a(a(a(b(c(b(a(b(c(a(a(a(a(x1))))))))))))))
→ a(a(a(b(c(a(c(b(a(b(c(a(a(a(a(x1)))))))))))))))
→ a(a(a(b(c(b(a(a(b(a(b(c(a(a(a(a(x1))))))))))))))))
→ a(a(a(b(c(b(a(b(c(a(a(b(c(a(a(a(a(x1)))))))))))))))))
→ a(a(a(b(c(b(a(b(c(a(b(c(a(c(a(a(a(a(x1))))))))))))))))))
→ a(a(a(b(c(b(a(b(c(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(b(c(a(c(b(a(b(c(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))
→ a(a(b(c(b(a(a(b(a(b(c(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(b(c(b(a(b(c(a(a(b(c(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(b(c(b(a(b(c(a(b(c(a(c(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))
→ a(a(b(c(b(a(b(c(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))
→ a(b(c(a(c(b(a(b(c(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))
→ a(b(c(b(a(a(b(a(b(c(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(a(b(c(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(a(c(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(a(a(b(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(a(b(c(a(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(a(c(a(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(a(a(c(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(a(b(a(a(b(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(b(c(a(a(a(b(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(b(c(a(a(b(c(a(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(b(c(a(b(c(a(c(a(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))))))
→ a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(b(c(a(b(c(b(a(a(a(a(a(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))))))))
= t26
where t26 = C[t0σ] and σ = {x1/a(a(a(x1)))} and C = a(b(c(b(a(b(c(a(b(c(b(a(b(c(b(a(b(c(a(b(c(b(a(☐)))))))))))))))))))))))