Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-525)

The rewrite relation of the following TRS is considered.

a(a(b(x1))) → b(b(c(a(a(x1))))) (1)
a(c(x1)) → 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(a(a(a(b(b(c(b(b(c(a(a(a(a(a(x1)))))))))))))))
→ a(a(b(b(c(a(a(b(c(b(b(c(a(a(a(a(a(x1)))))))))))))))))
→ a(a(b(b(c(b(b(c(a(a(c(b(b(c(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(b(b(c(b(b(c(a(a(a(b(b(c(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(b(b(c(b(b(c(a(b(b(c(a(a(b(c(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(b(b(c(b(b(c(a(b(b(c(b(b(c(a(a(c(a(a(a(a(a(x1)))))))))))))))))))))))
→ a(a(b(b(c(b(b(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))
→ b(b(c(a(a(b(c(b(b(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))
→ b(b(c(b(b(c(a(a(c(b(b(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ b(b(c(b(b(c(a(a(a(b(b(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ b(b(c(b(b(c(a(b(b(c(a(a(b(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))
→ b(b(c(b(b(c(a(b(b(c(b(b(c(a(a(c(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ b(b(c(b(b(c(a(b(b(c(b(b(c(a(a(a(a(b(b(c(b(b(c(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
= t12
where t12 = C[t0σ] and σ = {x1/a(a(a(x1)))} and C = b(b(c(b(b(c(a(b(b(c(b(b(c(☐)))))))))))))