  Several counterexample models to the Nelson-Seiberg theorem have been
discovered in previous literature, with generic superpotentials respecting the
R-symmetry and non-generic R-charge assignments for chiral fields. This work
present a sufficient condition for such counterexample models: The number of
R-charge 2 fields, which is greater than the number of R-charge 0 fields, must
be less than or equal to the number of R-charge 0 fields plus the number of
independent field pairs with opposite R-charges and satisfying some extra
requirements. We give a correct count of such field pairs when there are
multiple field pairs with degenerated R-charges. These models give
supersymmetric vacua with spontaneous R-symmetry breaking, thus are
counterexamples to both the Nelson-Seiberg theorem and its extensions.
