Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-558)

The rewrite relation of the following TRS is considered.

a(b(x1)) → x1 (1)
a(c(x1)) → c(b(c(b(x1)))) (2)
b(c(x1)) → a(a(x1)) (3)

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(a(c(c(a(a(c(b(b(x1)))))))))))
→ c(c(c(a(c(c(a(c(b(c(b(b(b(x1)))))))))))))
→ c(c(c(a(c(c(c(b(c(b(b(c(b(b(b(x1)))))))))))))))
→ c(c(c(a(c(c(c(a(a(b(b(c(b(b(b(x1)))))))))))))))
→ c(c(c(a(c(c(c(a(b(c(b(b(b(x1)))))))))))))
→ c(c(c(a(c(c(c(c(b(b(b(x1)))))))))))
→ c(c(c(c(b(c(b(c(c(c(b(b(b(x1)))))))))))))
→ c(c(c(c(b(c(a(a(c(c(b(b(b(x1)))))))))))))
→ c(c(c(c(a(a(a(a(c(c(b(b(b(x1)))))))))))))
→ c(c(c(c(a(a(a(c(b(c(b(c(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(a(c(a(a(b(c(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(a(c(a(c(b(b(b(x1)))))))))))))
→ c(c(c(c(a(a(c(b(c(b(a(c(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(c(a(a(b(a(c(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(c(a(a(c(b(b(b(x1)))))))))))))
→ c(c(c(c(a(a(c(a(c(b(c(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(c(c(b(c(b(b(c(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(a(c(c(a(a(b(b(c(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(a(c(c(a(b(c(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(a(c(c(c(b(b(b(b(x1)))))))))))))
→ c(c(c(c(a(c(b(c(b(c(c(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(c(b(c(a(a(c(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(c(a(a(a(a(c(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(c(a(a(a(c(b(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(a(a(c(b(c(b(b(c(b(b(b(b(b(x1)))))))))))))))))))
→ c(c(c(c(a(c(a(a(c(a(a(b(b(c(b(b(b(b(b(x1)))))))))))))))))))
→ c(c(c(c(a(c(a(a(c(a(b(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(a(a(c(c(b(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(c(a(c(b(c(b(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(a(c(a(a(b(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(a(c(a(c(b(b(b(b(b(x1)))))))))))))))
→ c(c(c(c(a(c(c(b(c(b(a(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(c(a(a(b(a(c(b(b(b(b(b(x1)))))))))))))))))
→ c(c(c(c(a(c(c(a(a(c(b(b(b(b(b(x1)))))))))))))))
= t33
where t33 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = c(☐)