Left Termination of the query pattern num_in_1(g) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

num(0).
num(X) :- ','(no(zero(0)), ','(p(X, Y), num(Y))).
p(0, 0).
p(s(X), X).
zero(0).
no(X) :- ','(X, ','(!, failure(a))).
no(X1).
failure(b).

Queries:

num(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