Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-521)

The rewrite relation of the following TRS is considered.

a(a(b(x1))) → a(b(c(a(a(x1))))) (1)
a(c(x1)) → b(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(b(c(a(b(a(a(b(a(a(a(a(x1))))))))))))))
→ a(a(a(b(c(a(b(a(b(c(a(a(a(a(a(a(x1))))))))))))))))
→ a(a(b(c(a(a(c(a(b(a(b(c(a(a(a(a(a(a(x1))))))))))))))))))
→ a(a(b(c(a(b(a(a(b(a(b(c(a(a(a(a(a(a(x1))))))))))))))))))
→ a(a(b(c(a(b(a(b(c(a(a(a(b(c(a(a(a(a(a(a(x1))))))))))))))))))))
→ a(a(b(c(a(b(a(b(c(a(a(b(c(a(a(c(a(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(b(c(a(b(a(b(c(a(a(b(c(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))
→ a(a(b(c(a(b(a(b(c(a(b(c(a(a(c(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))
→ a(a(b(c(a(b(a(b(c(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))
→ a(b(c(a(a(c(a(b(a(b(c(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(b(c(a(b(a(a(b(a(b(c(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(a(a(b(c(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(a(b(c(a(a(c(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(a(b(c(a(b(a(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(b(c(a(a(c(a(b(a(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(b(c(a(b(a(a(b(a(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))
→ a(b(c(a(b(a(b(c(a(b(c(a(b(a(b(c(a(a(a(a(b(c(a(b(a(a(b(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))))
= t16
where t16 = C[t0σ] and σ = {x1/a(a(a(x1)))} and C = a(b(c(a(b(a(b(c(a(b(c(a(b(a(b(c(a(☐)))))))))))))))))