Certification Problem

Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-2)

The rewrite relation of the following TRS is considered.

a(a(a(a(x1)))) → a(c(a(c(c(x1))))) (1)
c(c(c(x1))) → a(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(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(x1))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(a(c(a(c(c(a(x1)))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(c(c(c(a(c(c(a(x1))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(a(a(a(a(c(c(a(x1))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(a(c(a(c(c(c(c(a(x1)))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(a(c(a(a(a(a(c(a(x1)))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(a(c(a(c(a(c(c(c(a(x1))))))))))))))))))))))))
→ a(a(a(a(c(a(a(a(c(a(a(c(a(c(a(a(c(a(c(a(a(a(a(a(x1))))))))))))))))))))))))
→ a(c(a(c(c(c(a(a(a(c(a(a(c(a(c(a(a(c(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))
→ a(c(a(a(a(a(a(a(a(c(a(a(c(a(c(a(a(c(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(c(c(c(a(a(c(a(c(a(a(c(a(c(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(a(a(a(c(a(c(a(a(c(a(c(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(c(c(c(a(c(a(a(c(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(a(a(a(c(a(a(c(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(c(c(c(a(a(c(a(c(a(a(a(a(a(x1))))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(c(a(c(a(a(a(a(a(x1))))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(c(a(c(c(c(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(c(a(a(a(a(a(c(a(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(c(a(a(c(a(c(c(c(a(a(a(a(a(x1))))))))))))))))))))))))))))))
→ a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))
→ a(c(a(c(a(c(c(c(a(a(a(c(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(c(a(c(a(a(a(a(a(a(a(c(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(c(a(c(a(a(a(a(c(a(c(c(c(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))
→ a(c(a(c(a(a(a(a(c(a(a(a(a(a(a(c(a(a(a(c(a(a(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))
= t23
where t23 = C[t0σ] and σ = {x1/a(x1)} and C = a(c(a(c(a(a(a(a(c(a(a(☐)))))))))))