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 ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(b(b(a(b(b(a(x739))))))))
	→	b(a(b(b(b(a(b(b(a(x739)))))))))
	→	b(a(a(a(a(b(b(a(x739))))))))
	→	b(a(a(b(a(b(b(b(a(x739)))))))))
	→	b(a(a(b(a(a(a(a(x739))))))))
	→	b(a(a(b(b(a(b(a(a(x739)))))))))
	→	b(a(a(b(b(a(b(b(a(b(x739))))))))))
	=	t₆

where t₆ = C[t₀σ] and σ = {x739/b(x739)} and C = b(☐)