Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z046)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = c(a(a(b(a(a(a(x110)))))))
→ a(a(b(a(c(c(a(a(b(a(a(x110)))))))))))
→ a(a(b(a(c(a(a(b(a(c(c(a(a(b(a(x110)))))))))))))))
→ a(a(b(a(c(a(a(b(a(c(a(a(b(a(c(c(a(a(b(x110)))))))))))))))))))
→ a(a(b(a(c(a(a(b(a(a(a(b(a(c(c(a(a(b(c(c(a(a(b(x110)))))))))))))))))))))))
= t4
where t4 = C[t0σ] and σ = {x110/b(a(c(c(a(a(b(c(c(a(a(b(x110))))))))))))} and C = a(a(b(a(☐))))