Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-231)

The rewrite relation of the following TRS is considered.

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