Certification Problem

Input (TPDB SRS_Standard/Bouchare_06/09)

The rewrite relation of the following TRS is considered.

b(a(a(x1))) a(x1) (1)
a(a(a(x1))) b(b(b(x1))) (2)
b(b(x1)) a(b(a(x1))) (3)

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(a(a(x1)))))
a(b(b(b(b(x1)))))
a(b(b(a(b(a(x1))))))
a(a(b(a(a(b(a(x1)))))))
a(a(a(b(a(x1)))))
b(b(b(b(a(x1)))))
b(b(a(b(a(a(x1))))))
b(b(a(a(x1))))
a(b(a(a(a(x1)))))
= t8
where t8 = t0σ and σ = {x1/x1}