The steps taken by NCProcess2 are:

- I. Shrinking the input equations
- (1) Shrink
*start*using the RemoveRedundantProtected operation. Call this shrunken set*D*. - (2) Let be the set of polynomials in
*D*which do not involve any unknowns. Let . Let be a set of the normal forms of the elements of with respect to . Let . - (3) Let
*F*be the union of*E*and the user selects. Let*G*be a reduced form of*F*. (see the beginning of §). - (4) Shrink
*G*by SmallBasis. Set*H*equal to the result of the shrinking.

- (1) Shrink
*II*. The ``Attempt Decompose'' ``Displaying the results'' and ``Return a three tuple to the user for future use'' as in §.

**Appendices**

Wed Jul 3 10:27:42 PDT 1996