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), r(X)).
p(X) :- =(X, 2).
q(X) :- ','(=(X, 1), !).
q(X) :- =(X, 3).
r(X) :- ','(=(X, 1), !).
r(X) :- =(X, 4).
=(X, X).

Queries:

p(a).

(1) BuiltinConflictTransformerProof (SOUND transformation)

Renamed defined predicates conflicting with built-in predicates [PROLOG].

(2) Obligation:

Clauses:

p(X) :- ','(q(X), r(X)).
p(X) :- user_defined_=(X, 2).
q(X) :- ','(user_defined_=(X, 1), !).
q(X) :- user_defined_=(X, 3).
r(X) :- ','(user_defined_=(X, 1), !).
r(X) :- user_defined_=(X, 4).
user_defined_=(X, X).

Queries:

p(a).

(3) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

(4) Obligation:

Triples:


Clauses:


Afs:

(5) TPisEmptyProof (EQUIVALENT transformation)

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

(6) YES