Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/OvConsOS_nosorts_FR)

The rewrite relation of the following TRS is considered.

zeros	→	cons(0,n__zeros)	(1)
and(tt,X)	→	activate(X)	(2)
length(nil)	→	0	(3)
length(cons(N,L))	→	s(length(activate(L)))	(4)
take(0,IL)	→	nil	(5)
take(s(M),cons(N,IL))	→	cons(N,n__take(M,activate(IL)))	(6)
zeros	→	n__zeros	(7)
take(X1,X2)	→	n__take(X1,X2)	(8)
activate(n__zeros)	→	zeros	(9)
activate(n__take(X1,X2))	→	take(activate(X1),activate(X2))	(10)
activate(X)	→	X	(11)

The evaluation strategy is outermost

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by AProVE @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	length(activate(n__zeros))
	→	length(zeros)
	→	length(cons(0,n__zeros))
	→	s(length(activate(n__zeros)))
	=	t₃

where t₃ = C[t₀] and C = s(☐)