Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-566)

The rewrite relation of the following TRS is considered.

a(b(x1)) → x1 (1)
a(c(x1)) → c(c(c(b(x1)))) (2)
b(c(x1)) → a(b(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(a(a(c(c(c(c(b(b(x1))))))))))))
→ c(c(c(a(a(c(c(c(b(c(c(c(b(b(x1))))))))))))))
→ c(c(c(a(a(c(c(c(a(b(c(c(b(b(x1))))))))))))))
→ c(c(c(a(a(c(c(c(a(a(b(c(b(b(x1))))))))))))))
→ c(c(c(a(a(c(c(c(a(c(b(b(x1))))))))))))
→ c(c(c(a(c(c(c(b(c(c(a(c(b(b(x1))))))))))))))
→ c(c(c(a(c(c(c(a(b(c(a(c(b(b(x1))))))))))))))
→ c(c(c(a(c(c(c(a(a(b(a(c(b(b(x1))))))))))))))
→ c(c(c(a(c(c(c(a(a(b(c(c(c(b(b(b(x1))))))))))))))))
→ c(c(c(a(c(c(c(a(a(a(b(c(c(b(b(b(x1))))))))))))))))
→ c(c(c(a(c(c(c(a(a(a(a(b(c(b(b(b(x1))))))))))))))))
→ c(c(c(a(c(c(c(a(a(a(c(b(b(b(x1))))))))))))))
→ c(c(c(a(c(c(c(a(a(c(c(c(b(b(b(b(x1))))))))))))))))
→ c(c(c(a(c(c(c(a(c(c(c(b(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(a(c(c(c(a(c(c(c(a(b(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(a(c(c(c(a(c(c(c(c(b(b(b(b(x1))))))))))))))))
→ c(c(c(a(c(c(c(c(c(c(b(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(a(c(c(c(c(c(c(a(b(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(a(c(c(c(c(c(c(c(c(b(b(b(b(x1))))))))))))))))
→ c(c(c(c(c(c(b(c(c(c(c(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(b(c(c(c(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(b(c(c(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(b(c(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(a(b(c(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(a(a(b(c(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(a(a(a(b(c(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(a(a(c(b(b(b(b(x1))))))))))))))))
→ c(c(c(c(c(c(a(a(a(a(c(c(c(b(b(b(b(b(x1))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(c(c(c(b(c(c(b(b(b(b(b(x1))))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(c(c(c(a(b(c(b(b(b(b(b(x1))))))))))))))))))))
→ c(c(c(c(c(c(a(a(a(c(c(c(c(b(b(b(b(b(x1))))))))))))))))))
= t30
where t30 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = c(c(c(☐)))