Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-514)

The rewrite relation of the following TRS is considered.

a(a(a(x1))) → a(b(c(c(c(x1))))) (1)
c(b(x1)) → b(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 = c(c(c(b(a(a(b(b(a(a(a(c(c(c(x1))))))))))))))
→ c(c(b(a(a(a(b(b(a(a(a(c(c(c(x1))))))))))))))
→ c(c(b(a(b(c(c(c(b(b(a(a(a(c(c(c(x1))))))))))))))))
→ c(c(b(a(b(c(c(b(a(b(a(a(a(c(c(c(x1))))))))))))))))
→ c(c(b(a(b(c(b(a(a(b(a(a(a(c(c(c(x1))))))))))))))))
→ c(c(b(a(b(b(a(a(a(b(a(a(a(c(c(c(x1))))))))))))))))
→ c(c(b(a(b(b(a(b(c(c(c(b(a(a(a(c(c(c(x1))))))))))))))))))
→ c(c(b(a(b(b(a(b(c(c(b(a(a(a(a(c(c(c(x1))))))))))))))))))
→ c(c(b(a(b(b(a(b(c(b(a(a(a(a(a(c(c(c(x1))))))))))))))))))
→ c(c(b(a(b(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))
→ c(b(a(a(b(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))
→ b(a(a(a(b(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))
→ b(a(b(c(c(c(b(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))
→ b(a(b(c(c(b(a(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))
→ b(a(b(c(b(a(a(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))
→ b(a(b(b(a(a(a(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))
→ b(a(b(b(a(b(c(c(c(b(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))
→ b(a(b(b(a(b(c(c(b(a(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))
→ b(a(b(b(a(b(c(b(a(a(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(a(a(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(c(c(c(b(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(c(c(b(a(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(c(b(a(a(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(a(a(a(a(c(c(c(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(a(a(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(b(c(c(c(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(b(c(c(b(a(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(b(c(b(a(a(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(a(a(b(a(a(b(b(a(a(a(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(a(b(b(a(b(c(c(c(b(a(a(b(b(a(a(a(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
= t29
where t29 = C[t0σ] and σ = {x1/c(c(c(x1)))} and C = b(a(b(b(a(b(b(a(a(b(b(a(b(☐)))))))))))))