J:= [(x[2]-x[1])*(x[2]-x[3]), (x[4]-x[1])*(-x[5]+x[4]), (x[4]-x[2])*(x[4]-x[6]), (-x[3]+x[5])*(x[5]-x[6]), x[1]^3-1, x[2]^3-1, x[3]^3-1, x[4]^3-1, x[5]^3-1, x[6]^3-1];

J1:=map(LeadingMonomial, l, grlex(x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12]));

l2:={x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[11],x[12]};

factor(HilbertSeries(J, l2, t));

factor(HilbertSeries(J1, l2, t));