Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#4.15)

The rewrite relation of the following TRS is considered.

f(0,1,g(x,y),z)	→	f(g(x,y),g(x,y),g(x,y),h(x))	(1)
g(0,1)	→	0	(2)
g(0,1)	→	1	(3)
h(g(x,y))	→	h(x)	(4)

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(0,1),g(0,1),g(0,1),h(0))
	→	f(g(0,1),1,g(0,1),h(0))
	→	f(0,1,g(0,1),h(0))
	→	f(g(0,1),g(0,1),g(0,1),h(0))
	=	t₃

where t₃ = t₀