Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/ExIntrod_Zan97)

The rewrite relation of the following TRS is considered.

fact(X)	→	if(zero(X),s(0),prod(X,fact(p(X))))	(1)
add(0,X)	→	X	(2)
add(s(X),Y)	→	s(add(X,Y))	(3)
prod(0,X)	→	0	(4)
prod(s(X),Y)	→	add(Y,prod(X,Y))	(5)
if(true,X,Y)	→	X	(6)
if(false,X,Y)	→	Y	(7)
zero(0)	→	true	(8)
zero(s(X))	→	false	(9)
p(s(X))	→	X	(10)

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	=	fact(X)
	→	if(zero(X),s(0),prod(X,fact(p(X))))
	=	t₁

where t₁ = C[t₀σ] and σ = {X/p(X)} and C = if(zero(X),s(0),prod(X,☐))