Left Termination of the query pattern p_in_1(a) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

p(X) :- ','(q(f(Y)), p(Y)).
q(g(Y)).

Queries:

p(a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

(2) Obligation:

Clauses:

(3) PPisEmptyProof (EQUIVALENT transformation)

The Prolog program is empty. Hence, it trivially terminates.

(4) YES