Q = ZZ/2[x1,x2,x3,Le,Ge] / ideal(x1^2-x1,x2^2-x2,x3^2-x3,Le^2-Le,Ge^2-Ge)

RingElement | RingElement :=(x,y)->x+y+x*y;
RingElement & RingElement :=(x,y)->x*y;

Ge = 0_Q
Le = 1_Q

f1 = (1+Ge) & (x3 | Le);
f2 = x1;
f3 = (1+Ge) & ((Le & x2) | (x3 & (1+x2)));

(f1, f2, f3);
I = ideal(f1+x1, f2+x2, f3+x3);
G = gens gb I