Left Termination of the query pattern f_in_1(a) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

f(X) :- ','(p(X), q(X)).
p(a) :- !.
p(X) :- p(Y).
q(b).

Queries:

f(a).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

(2) Obligation:

Triples:


Clauses:

pc11(a).

Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

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

(4) YES