Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex1_2_AEL03_L)

The rewrite relation of the following TRS is considered.

2ndspos(s(N),cons(X))	→	rcons(posrecip(Y),2ndsneg(N,Z))	(1)
2ndsneg(s(N),cons(X))	→	rcons(negrecip(Y),2ndspos(N,Z))	(2)
from(X)	→	cons(X)	(3)
2ndspos(0,Z)	→	rnil	(4)
2ndsneg(0,Z)	→	rnil	(5)
pi(X)	→	2ndspos(X,from(0))	(6)
plus(0,Y)	→	Y	(7)
plus(s(X),Y)	→	s(plus(X,Y))	(8)
times(0,Y)	→	0	(9)
times(s(X),Y)	→	plus(Y,times(X,Y))	(10)
square(X)	→	times(X,X)	(11)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	2ndspos(s(N),cons(X))
	→	rcons(posrecip(2ndspos(s(N),cons(X))),2ndsneg(N,Z))
	=	t₁

where t₁ = C[t₀σ] and σ = {Y/2ndspos(s(N),cons(X))} and C = rcons(posrecip(☐),2ndsneg(N,Z))