Certification Problem

Input (TPDB SRS_Standard/Zantema_06/loop1)

The rewrite relation of the following TRS is considered.

a(b(b(x1)))	→	b(b(a(a(x1))))	(1)
a(a(x1))	→	b(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(b(b(b(b(b(b(x1043)))))))
	→	b(b(a(a(b(b(b(b(x1043))))))))
	→	b(b(a(b(b(a(a(b(b(x1043)))))))))
	→	b(b(a(b(b(a(b(b(a(a(x1043))))))))))
	→	b(b(a(b(b(b(b(a(a(a(a(x1043)))))))))))
	→	b(b(a(b(b(b(b(b(a(a(x1043))))))))))
	→	b(b(a(b(b(b(b(b(b(x1043)))))))))
	=	t₆

where t₆ = C[t₀σ] and σ = {x1043/x1043} and C = b(b(☐))