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) 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