Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-22)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(x1) → b(x1) (2)
b(b(c(x1))) → a(c(c(c(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(b(b(b(c(c(x1))))))))
→ c(c(c(b(a(c(c(c(a(b(c(x1)))))))))))
→ c(c(c(b(a(c(c(c(b(b(c(x1)))))))))))
→ c(c(c(b(b(c(c(c(b(b(c(x1)))))))))))
→ c(c(c(a(c(c(c(a(b(c(c(b(b(c(x1))))))))))))))
→ c(c(c(c(c(c(a(b(c(c(b(b(c(x1)))))))))))))
→ c(c(c(c(c(c(b(b(c(c(b(b(c(x1)))))))))))))
→ c(c(c(c(c(c(a(c(c(c(a(b(c(b(b(c(x1))))))))))))))))
→ c(c(c(c(c(c(c(c(c(a(b(c(b(b(c(x1)))))))))))))))
→ c(c(c(c(c(c(c(c(c(b(b(c(b(b(c(x1)))))))))))))))
→ c(c(c(c(c(c(c(c(c(a(c(c(c(a(b(b(b(c(x1))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(a(b(b(b(c(x1)))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(b(b(b(b(c(x1)))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(b(b(a(c(c(c(a(b(x1))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(b(b(a(c(c(c(b(x1)))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(b(b(b(c(c(c(b(x1)))))))))))))))))))
= t15
where t15 = C[t0σ] and σ = {x1/c(b(x1))} and C = c(c(c(c(c(c(c(c(c(☐)))))))))