Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z042)

The rewrite relation of the following TRS is considered.

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

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(a(b(c(b(c(b(a(b(a(b(a(b(a(x1)))))))))))))))))
→ a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(c(b(a(b(a(x1)))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(c(b(c(b(a(b(c(b(c(b(a(b(a(x1)))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(c(b(c(b(a(b(c(b(a(b(a(b(a(b(c(b(c(x1)))))))))))))))))))))))))))))
→ a(b(a(b(a(b(a(b(a(b(a(b(c(b(c(b(a(b(a(b(a(b(a(b(c(b(c(b(a(b(c(b(c(x1)))))))))))))))))))))))))))))))))
= t4
where t4 = C[t0σ] and σ = {x1/b(c(b(c(b(a(b(c(b(c(x1))))))))))} and C = a(b(a(b(a(b(☐))))))