Left Termination of the query pattern fold_in_3(g, g, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

fold(X, [], X).
fold(X, Y, Z) :- ','(no(empty(Y)), ','(head(Y, H), ','(tail(Y, T), ','(myop(X, H, V), fold(V, T, Z))))).
myop(a, b, c).
head([], X1).
head(.(H, X2), H).
tail([], []).
tail(.(X3, T), T).
empty([]).
no(X) :- ','(X, ','(!, failure(a))).
no(X4).
failure(b).

Queries:

fold(g,g,a).

(1) CutEliminatorProof (SOUND transformation)

Eliminated all cuts by simply ignoring them[PROLOG].

(2) Obligation:

Clauses:

fold(X, [], X).
fold(X, Y, Z) :- ','(no(empty(Y)), ','(head(Y, H), ','(tail(Y, T), ','(myop(X, H, V), fold(V, T, Z))))).
myop(a, b, c).
head([], X1).
head(.(H, X2), H).
tail([], []).
tail(.(X3, T), T).
empty([]).
no(X) :- ','(X, failure(a)).
no(X4).
failure(b).

Queries:

fold(g,g,a).