Left Termination of the query pattern w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

goal :- ','(lte(X, s(s(s(s(0))))), even(X)).
lte(0, Y) :- !.
lte(X, s(Y)) :- ','(p(X, P), lte(P, Y)).
even(0).
even(s(s(X))) :- even(X).
p(0, 0).
p(s(X), X).

Queries:

goal().

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

There are no more dependency triples. Hence, the dependency triple problem trivially terminates.

(4) YES