Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex1_GM03_Z)

The rewrite relation of the following TRS is considered.

p(0)	→	0	(1)
p(s(X))	→	X	(2)
leq(0,Y)	→	true	(3)
leq(s(X),0)	→	false	(4)
leq(s(X),s(Y))	→	leq(X,Y)	(5)
if(true,X,Y)	→	activate(X)	(6)
if(false,X,Y)	→	activate(Y)	(7)
diff(X,Y)	→	if(leq(X,Y),n__0,n__s(diff(p(X),Y)))	(8)
0	→	n__0	(9)
s(X)	→	n__s(X)	(10)
activate(n__0)	→	0	(11)
activate(n__s(X))	→	s(X)	(12)
activate(X)	→	X	(13)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	diff(X,Y)
	→	if(leq(X,Y),n__0,n__s(diff(p(X),Y)))
	=	t₁

where t₁ = C[t₀σ] and σ = {Y/Y, X/p(X)} and C = if(leq(X,Y),n__0,n__s(☐))