Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-511)

The rewrite relation of the following TRS is considered.

a(a(a(x1))) → a(b(x1)) (1)
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(c(c(a(b(x1)))))))
→ b(b(c(c(a(a(a(c(a(b(x1))))))))))
→ b(b(c(c(a(b(c(a(b(x1)))))))))
→ b(b(c(c(a(c(c(a(a(a(a(b(x1))))))))))))
→ b(b(c(c(a(c(c(a(a(b(b(x1)))))))))))
→ b(c(c(a(a(a(c(a(c(c(a(a(b(b(x1))))))))))))))
→ b(c(c(a(b(c(a(c(c(a(a(b(b(x1)))))))))))))
→ b(c(c(a(c(c(a(a(a(a(c(c(a(a(b(b(x1))))))))))))))))
→ b(c(c(a(c(c(a(a(b(c(c(a(a(b(b(x1)))))))))))))))
→ b(c(c(a(c(c(a(a(c(c(a(a(a(c(a(a(b(b(x1))))))))))))))))))
→ b(c(c(a(c(c(a(a(c(c(a(b(c(a(a(b(b(x1)))))))))))))))))
→ b(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(a(a(b(b(x1))))))))))))))))))))
→ b(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(b(b(b(x1)))))))))))))))))))
→ b(c(c(a(c(c(a(a(c(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))
→ c(c(a(a(a(c(a(c(c(a(a(c(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))
→ c(c(a(b(c(a(c(c(a(a(c(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))
→ c(c(a(c(c(a(a(a(a(c(c(a(a(c(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))
→ c(c(a(c(c(a(a(b(c(c(a(a(c(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(a(a(c(a(a(c(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(b(c(a(a(c(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(a(a(c(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(b(c(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(b(b(c(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(b(c(c(a(a(a(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(b(c(c(a(b(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(a(a(c(a(b(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(b(c(a(b(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(a(a(b(c(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(b(b(c(a(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(b(c(c(a(a(a(a(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(b(c(c(a(a(b(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(a(a(c(a(a(b(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(b(c(a(a(b(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(a(a(b(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(b(b(c(c(a(b(b(b(b(x1)))))))))))))))))))))))))))))))))))))
→ c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(c(c(a(b(b(b(c(c(a(b(b(b(b(x1))))))))))))))))))))))))))))))))))))
= t35
where t35 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = c(c(a(c(c(a(a(c(c(a(c(c(a(c(c(a(c(c(a(a(c(c(a(c(c(a(☐))))))))))))))))))))))))))