Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-492)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(b(a(b(c(c(a(c(c(b(b(b(b(x1)))))))))))))
→ a(b(c(c(a(a(a(a(c(a(c(c(b(b(b(b(x1))))))))))))))))
→ a(b(c(c(a(a(b(c(a(c(c(b(b(b(b(x1)))))))))))))))
→ a(b(c(c(a(c(c(a(a(a(a(a(c(c(b(b(b(b(x1))))))))))))))))))
→ a(b(c(c(a(c(c(a(a(a(b(c(c(b(b(b(b(x1)))))))))))))))))
→ a(b(c(c(a(c(c(b(a(b(c(c(b(b(b(b(x1))))))))))))))))
→ a(b(c(c(a(c(c(b(c(c(a(a(a(a(c(b(b(b(b(x1)))))))))))))))))))
→ a(b(c(c(a(c(c(b(c(c(a(a(b(c(b(b(b(b(x1))))))))))))))))))
→ a(b(c(c(a(c(c(b(c(c(a(c(c(a(a(a(a(b(b(b(b(x1)))))))))))))))))))))
→ a(b(c(c(a(c(c(b(c(c(a(c(c(a(a(b(b(b(b(b(x1))))))))))))))))))))
→ a(b(c(c(a(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1)))))))))))))))))))
→ c(c(a(a(a(a(c(a(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))))
→ c(c(a(a(b(c(a(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1)))))))))))))))))))))
→ c(c(a(c(c(a(a(a(a(a(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ c(c(a(c(c(a(a(a(b(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1)))))))))))))))))))))))
→ c(c(a(c(c(b(a(b(c(c(b(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))))
→ c(c(a(c(c(b(c(c(a(a(a(a(c(b(c(c(a(c(c(b(b(b(b(b(b(x1)))))))))))))))))))))))))
→ c(c(a(c(c(b(c(c(a(a(b(c(b(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ c(c(a(c(c(b(c(c(a(c(c(a(a(a(a(b(c(c(a(c(c(b(b(b(b(b(b(x1)))))))))))))))))))))))))))
→ c(c(a(c(c(b(c(c(a(c(c(a(b(a(b(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))))))))
= t19
where t19 = C[t0σ] and σ = {x1/b(b(x1))} and C = c(c(a(c(c(b(c(c(a(c(c(☐)))))))))))