The steps taken by NCProcess1 are:

- I. Preparation for the main call to NCMakeGB
- (1) Run the GBA on the equations in
*start*which do not involve any unknown variables together with the user selects for at most*n*+1 iterations. Let*A*denote this partial GB. - (2) Shrink
*A*using the RemoveRedundantProtected operation. Call this shrunken set*B*.

- (1) Run the GBA on the equations in
- II. The main call to NCMakeGB
- (3) Run NCMakeGB with the input
*B*together with*start*for at most*n*iterations. In this NCMakeGB run, S-polynomials between two elements of the partial GB of*A*are not computed. Let*C*denote this partial GB.

- (3) Run NCMakeGB with the input
- III. Shrinking the partial GB
- (4) Shrink
*C*using the RemoveRedundantProtected operation. Call this shrunken set*D*. - (5) 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 . - (6) Let
*F*be the union of*E*and the user selects. Let*G*be a reduced form of*F*(see the beginning of §). - (7) Shrink
*G*by SmallBasisByCategory using iteration parameters*n*+1 and*n*+2 (see §). Call this shrunken set*H*.

- (4) Shrink
*IV*. Attempt Decompose- (8) Construct the collected forms
(as described in
§)
of the polynomials in
*H*.

- (8) Construct the collected forms
(as described in
§)
of the polynomials in
*V*. Displaying the results- (9) For elements of
*H*, if the polynomial's only collected form is trivial (see discussion following Definition §), then display the rule corresponding to the polynomial, otherwise display the collected form of the polynomial. This is the step in which the ``spreadsheets'' of the results of this paper are constructed.

- (9) For elements of
*VI*. Return a three tuple to the user for future use- (10) Return the triple to the
user where
*A*is from item 1 above, is the set of polynomials in*H*which are digested and is the set of polynomials in*H*which are undigested.

- (10) Return the triple to the
user where

Wed Jul 3 10:27:42 PDT 1996