Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-519)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = b(c(a(c(b(b(x1))))))
→ b(c(a(a(a(a(a(c(b(x1)))))))))
→ b(c(b(c(a(a(c(b(x1))))))))
→ b(a(a(a(a(c(c(a(a(c(b(x1)))))))))))
→ b(b(c(a(c(c(a(a(c(b(x1))))))))))
→ b(b(c(a(c(c(a(a(a(a(a(a(c(x1)))))))))))))
→ b(b(c(a(c(c(a(a(a(b(c(c(x1))))))))))))
→ b(b(c(a(c(c(b(c(b(c(c(x1)))))))))))
→ b(b(c(a(c(c(b(a(a(a(a(c(c(c(x1))))))))))))))
→ b(b(c(a(c(c(b(b(c(a(c(c(c(x1)))))))))))))
→ b(b(c(a(c(a(a(a(a(c(b(c(a(c(c(c(x1))))))))))))))))
→ b(b(c(a(c(b(c(a(c(b(c(a(c(c(c(x1)))))))))))))))
→ b(b(c(a(c(b(c(a(a(a(a(a(c(c(a(c(c(c(x1))))))))))))))))))
→ b(b(c(a(c(b(c(b(c(a(a(c(c(a(c(c(c(x1)))))))))))))))))
→ b(b(c(a(c(b(a(a(a(a(c(c(a(a(c(c(a(c(c(c(x1))))))))))))))))))))
→ b(b(c(a(c(b(b(c(a(c(c(a(a(c(c(a(c(c(c(x1)))))))))))))))))))
= t15
where t15 = C[t0σ] and σ = {x1/c(a(c(c(a(a(c(c(a(c(c(c(x1))))))))))))} and C = b(☐)