  This paper is a continuation of the paper "Numerical Semigroups: Ap\'ery Sets
and Hilbert Series". We consider the general numerical AA-semigroup, i.e.,
semigroups consisting of all non-negative integer linear combinations of
relatively prime positive integers of the form $a,a+d,a+2d,\dots,a+kd,c$. We
first prove that, in contrast to arbitrary numerical semigroups, there exists
an upper bound for the type of AA-semigroups that only depends on the number of
generators of the semigroup. We then present two characterizations of
pseudo-symmetric AA-semigroups. The first one leads to a polynomial time
algorithm to decide whether an AA-semigroup is pseudo-symmetric. The second one
gives a method to construct pseudo-symmetric AA-semigroups and provides
explicit families of pseudo-symmetric semigroups with arbitrarily large number
of generators.
