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(X).
p(X) :- ','(no(q(X)), p(X)).
q(X).
no(X) :- ','(X, ','(!, failure(a))).
no(X1).
failure(b).

Queries:

p(a).

(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