  In this article, by using the technique of gluing semigroups, we give
infinitely many families of 1-dimensional local rings with non-decreasing
Hilbert functions. More significantly, these are local rings whose associated
graded rings are not necessarily Cohen-Macaulay. In this sense, we give an
effective technique to construct large families of 1-dimensional Gorenstein
local rings associated to monomial curves, which support Rossi's conjecture
saying that every Gorenstein local ring has non-decreasing Hilbert function.
