Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-475)

The rewrite relation of the following TRS is considered.

a(a(x1)) → a(b(x1)) (1)
b(b(c(x1))) → c(c(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 = b(b(b(b(c(c(a(c(c(a(b(b(b(b(b(x1)))))))))))))))
→ b(b(c(c(a(a(a(c(a(c(c(a(b(b(b(b(b(x1)))))))))))))))))
→ b(b(c(c(a(a(b(c(a(c(c(a(b(b(b(b(b(x1)))))))))))))))))
→ b(b(c(c(a(b(b(c(a(c(c(a(b(b(b(b(b(x1)))))))))))))))))
→ b(b(c(c(a(c(c(a(a(a(a(c(c(a(b(b(b(b(b(x1)))))))))))))))))))
→ b(b(c(c(a(c(c(a(a(a(b(c(c(a(b(b(b(b(b(x1)))))))))))))))))))
→ b(b(c(c(a(c(c(a(a(b(b(c(c(a(b(b(b(b(b(x1)))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(b(b(c(c(a(b(b(b(b(b(x1)))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(a(a(c(a(b(b(b(b(b(x1)))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(a(b(c(a(b(b(b(b(b(x1)))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(b(b(c(a(b(b(b(b(b(x1)))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(c(c(a(a(a(a(b(b(b(b(b(x1)))))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(c(c(a(a(a(b(b(b(b(b(b(x1)))))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(c(c(a(a(b(b(b(b(b(b(b(x1)))))))))))))))))))))))
→ b(b(c(c(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))
→ c(c(a(a(a(c(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(a(b(c(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(b(b(c(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(c(c(a(a(a(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(a(b(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(b(b(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(b(b(c(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(a(a(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(a(b(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(b(b(c(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(c(c(a(a(a(a(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(c(c(a(a(a(b(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(c(c(a(a(b(b(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(b(c(c(a(c(c(a(b(b(b(b(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))))))))))
= t28
where t28 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = c(c(a(c(c(a(b(c(c(a(c(c(a(☐)))))))))))))