Left Termination of the query pattern f_in_3(a, a, g) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

f(0, 1, X) :- f(X, X, X).

Queries:

f(a,a,g).

(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