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 ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(a(b(a(a(x2917))))))
	→	b(b(b(b(a(a(x2917))))))
	→	a(b(a(b(b(a(a(x2917)))))))
	→	a(b(a(a(b(a(a(a(x2917))))))))
	→	a(b(a(a(b(b(b(b(x2917))))))))
	→	a(b(a(a(a(b(a(b(b(x2917)))))))))
	→	a(b(a(a(a(b(a(a(b(a(x2917))))))))))
	=	t₆

where t₆ = C[t₀σ] and σ = {x2917/b(a(x2917))} and C = a(b(☐))