Certification Problem

Input (TPDB SRS_Standard/Zantema_06/loop2)

The rewrite relation of the following TRS is considered.

b(b(b(x1)))	→	a(a(x1))	(1)
a(a(x1))	→	b(a(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	=	a(a(b(b(a(b(b(x1)))))))
	→	b(a(b(b(b(a(b(b(x1))))))))
	→	b(a(a(a(a(b(b(x1)))))))
	→	b(b(a(b(a(a(b(b(x1))))))))
	→	b(b(a(b(b(a(b(b(b(x1)))))))))
	→	b(b(a(b(b(a(a(a(x1))))))))
	→	b(b(a(b(b(b(a(b(a(x1)))))))))
	→	b(b(a(a(a(a(b(a(x1))))))))
	→	b(b(a(a(b(a(b(b(a(x1)))))))))
	→	b(b(b(a(b(b(a(b(b(a(x1))))))))))
	→	a(a(a(b(b(a(b(b(a(x1)))))))))
	=	t₁₀

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