Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.17)

The rewrite relation of the following TRS is considered.

f(g(x),s(0),y)	→	f(g(s(0)),y,g(x))	(1)
g(s(x))	→	s(g(x))	(2)
g(0)	→	0	(3)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	f(g(s(0)),s(0),s(0))
	→	f(g(s(0)),s(0),g(s(0)))
	→	f(g(s(0)),s(0),s(g(0)))
	→	f(g(s(0)),s(0),s(0))
	=	t₃

where t₃ = t₀