1. Download the polynomial system of {6,21,4} and the check polynomial.
6-21-4_poly_13.gz
6-21-4_chkpoly.gz

2. Expand these files.
gzip -d 6-21-4_poly_13.gz
gzip -d 6-21-4_chkpoly.gz

3. Start Asir

4. Execute the following commands on Asir:
load("gr")$ /* load of the Groebner package */
load("weight")$ /* load of automatic weight package */
P=bload("./6-21-4_poly_13")$ /* load of the polynomial system of {6,21,4} */
weight(P,vars(P),0); /* Weights computation of this polynomial system */
dp_set_weight(newvect(7,[18,12,6,5,4,3,2]))$ /* Setting the weights */
cputime(1)$ /* Display setting of cpu time */
G=nd_gr_trace(P,[g,f,e,d,c,b,a],0,-1,2)$ /* Groebner basis computation */
C=bload("./6-21-4_chkpoly")$ /* load of the check polynomial C */
N=p_nf(C,G,[g,f,e,d,c,b,a],2); /* Computation of normal form of C w.r.t G */

5. We get 0 by the above command. This shows that C in G=Id(P).