Singular

>LIB "teachstd.lib";
> printlevel=1;
>    ring r=0,(x,y,z),dp;
>    poly f = x2y2z2+x5+yx3+z6-3y3;
>    ideal G = x2y+x2,y3+xyz,xyz2+z6;
>    NFMora(f,G);"";

// Input for NFMora is (f,T):
// f:
x2y2z2+z6+x5+x3y-3y3
// T:
T[1]=x2y+x2
T[2]=y3+xyz
T[3]=z6+xyz2
// Reduce f with T, eventually enlarging T for local ordering

//                Reduction-step in NFMora: 0
// h = (f after 0 reductions) reduction with g from T:
// g = element of minimal ecart in T s.t. LM(g)|LM(h):
// h:
x2y2z2+z6+x5+x3y-3y3
// g:
x2y+x2
// T-set enlarged for next reduction? (yes/no = 1/0):   0

//                Reduction-step in NFMora: 1
// h = (f after 1 reductions) reduction with g from T:
// g = element of minimal ecart in T s.t. LM(g)|LM(h):
// h:
z6+x5-x2yz2+x3y-3y3
// g:
z6+xyz2
// T-set enlarged for next reduction? (yes/no = 1/0):   0

// normal form is:
x5-x2yz2+x3y-xyz2-3y3