The command RegularizeInitial(f, rc, R) returns a list of pairs  where each  is a regular chain of R and each  is a polynomial of R.

The set of all the regular chains  form a decomposition of in_rc in the sense of Kalkbrener.

Each polynomial  is either constant or its initial is regular modulo .

Each polynomial  is equal to f modulo the saturated ideal of .

The function is based on Regularize.

This command is part of the RegularChains package, so it can be used in the form RegularizeInitial(..) only after executing the command with(RegularChains).  However, it can always be accessed through the long form of the command by using RegularChains[RegularizeInitial](..).