Left Termination of the query pattern p_in_1(a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

p(X) :- ','(no(letter(X)), q(X)).
q(x) :- p(X1).
letter(x).
no(X) :- ','(X, ','(!, failure(a))).
no(X2).
failure(b).

Queries:

p(a).

(1) CutEliminatorProof (SOUND transformation)

Eliminated all cuts by simply ignoring them[PROLOG].

(2) Obligation:

Clauses:

p(X) :- ','(no(letter(X)), q(X)).
q(x) :- p(X1).
letter(x).
no(X) :- ','(X, failure(a)).
no(X2).
failure(b).

Queries:

p(a).