Certification Problem

Input (TPDB SRS_Standard/Mixed_SRS/1)

The rewrite relation of the following TRS is considered.

b(c(x1)) → a(b(b(x1))) (1)
b(a(x1)) → a(c(b(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(a(c(a(a(c(a(b(b(b(b(b(b(x1)))))))))))))
→ a(c(b(c(a(a(c(a(b(b(b(b(b(b(x1))))))))))))))
→ a(c(a(b(b(a(a(c(a(b(b(b(b(b(b(x1)))))))))))))))
→ a(c(a(b(a(c(b(a(c(a(b(b(b(b(b(b(x1))))))))))))))))
→ a(c(a(b(a(c(a(c(b(c(a(b(b(b(b(b(b(x1)))))))))))))))))
→ a(c(a(b(a(c(a(c(a(b(b(a(b(b(b(b(b(b(x1))))))))))))))))))
→ a(c(a(b(a(c(a(c(a(b(a(c(b(b(b(b(b(b(b(x1)))))))))))))))))))
→ a(c(a(b(a(c(a(c(a(a(c(b(c(b(b(b(b(b(b(b(x1))))))))))))))))))))
→ a(c(a(b(a(c(a(c(a(a(c(a(b(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))
→ a(c(a(a(c(b(c(a(c(a(a(c(a(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))
→ a(c(a(a(c(a(b(b(a(c(a(a(c(a(b(b(b(b(b(b(b(b(b(x1)))))))))))))))))))))))
= t10
where t10 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = a(c(a(a(c(a(b(☐)))))))