ring r=0,(x,y),dp;
poly g=(1-x)*(x2-y3);
poly h=y2-x2;
ideal i=g,h;
poly f=x2-x2y; NF(f,std(i));

==>

-y3+y2

It follows that f is not contained in the ideal <g,h> of Q[x,y]. This changes if we consider the localization at <x,y> : ring r1=0,(x,y),ds;
poly g=(1-x)*(x2-y3);
poly h=y2-x2;
ideal i=g,h;
poly f=x2-x2y; NF(f,std(i));

==>

0