Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-270)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(b(x1)) → c(a(x1)) (2)
c(c(x1)) → b(b(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(b(c(b(c(c(b(b(c(b(c(c(b(c(x1)))))))))))))))
→ c(b(b(c(b(b(b(c(b(a(b(b(c(b(c(c(b(c(x1))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(a(b(c(b(c(c(b(c(x1))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(c(a(c(b(c(c(b(c(x1))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(c(c(b(c(c(b(c(x1)))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(a(b(c(x1))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(c(a(c(x1))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(c(c(x1)))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(a(b(b(b(c(b(c(c(x1))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(a(b(b(c(b(c(c(x1))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(a(b(c(b(c(c(x1))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(c(a(c(b(c(c(x1))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(c(c(b(c(c(x1)))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(c(c(b(b(b(c(b(a(x1))))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(c(c(b(b(b(c(b(x1)))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(b(b(c(b(a(b(b(b(c(b(x1))))))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(b(b(c(b(c(a(b(b(c(b(x1))))))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(b(b(c(b(c(c(a(b(c(b(x1))))))))))))))))))))))))))
→ c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(c(b(b(c(b(c(c(b(c(b(x1)))))))))))))))))))))))))
= t18
where t18 = C[t0σ] and σ = {x1/b(x1)} and C = c(b(b(c(b(b(b(c(b(☐)))))))))