Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z128)

The rewrite relation of the following TRS is considered.

a(a(a(x1))) b(a(b(x1))) (1)
b(a(b(x1))) a(b(a(x1))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(a(a(b(a(a(x699))))))
b(a(b(b(a(a(x699))))))
a(b(a(b(a(a(x699))))))
a(a(b(a(a(a(x699))))))
a(a(b(b(a(b(x699))))))
a(a(b(a(b(a(x699))))))
a(a(a(b(a(a(x699))))))
= t6
where t6 = t0σ and σ = {x699/x699}