Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/test75)

The rewrite relation of the following TRS is considered.

f(0,1,X)	→	f(g(X,X),X,X)	(1)
g(X,Y)	→	X	(2)
g(X,Y)	→	Y	(3)

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	=	f(g(g(0,1),g(0,1)),g(0,1),g(0,1))
	→	f(g(g(0,1),g(0,1)),1,g(0,1))
	→	f(g(0,1),1,g(0,1))
	→	f(0,1,g(0,1))
	→	f(g(g(0,1),g(0,1)),g(0,1),g(0,1))
	=	t₄

where t₄ = t₀