The leading ideal of a complete intersection of height two

Let be a Noetherian local ring and let I=(f,g) be an ideal in S generated by a regular sequence f,g of length two. Assume that the associated graded ring of S with respect to is a UFD. We examine generators of the leading form ideal I* of I in and prove that I* is a perfect ideal of , if I* is 3-generated. Thus, in this case, letting R=S/I and , if is Cohen–Macaulay, then is Cohen–Macaulay. As an application, we prove that if is a one-dimensional Gorenstein local ring of embedding dimension 3, then is Cohen–Macaulay if the reduction number of is at most 4.