  This paper considers numerical semigroups $S$ that have a non-principal
relative ideal $I$ such that $\mu_S(I)\mu_S(S-I)=\mu_S(I+(S-I)) $. We show the
existence of an infinite family of such which $I+(S-I)=S\backslash\{0\}$. We
also show examples of such pairs that are not members of this family. We
discuss the computational process used to find these examples and present some
open questions pertaining to them.
