Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/cime4)

The rewrite relation of the following TRS is considered.

g(X)	→	u(h(X),h(X),X)	(1)
u(d,c(Y),X)	→	k(Y)	(2)
h(d)	→	c(a)	(3)
h(d)	→	c(b)	(4)
f(k(a),k(b),X)	→	f(X,X,X)	(5)

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(u(d,h(d),X'),u(d,h(d),X'),u(d,h(d),X'))
	→	f(u(d,h(d),X'),u(d,c(b),X'),u(d,h(d),X'))
	→	f(u(d,h(d),X'),k(b),u(d,h(d),X'))
	→	f(u(d,c(a),X'),k(b),u(d,h(d),X'))
	→	f(k(a),k(b),u(d,h(d),X'))
	→	f(u(d,h(d),X'),u(d,h(d),X'),u(d,h(d),X'))
	=	t₅

where t₅ = t₀