ring rr = (2,X),(A,Z,Z_1,a2,a1,a0,z2,z1,z0,t),lp;
minpoly = X^3+X+1;

proc or_gate(poly a, poly b) /* function of 2-input OR gate */
{
  return (a+b+a*b);
}

ideal J = 
A + a0 + a1*X + a2*X^2,
Z + z0 + z1*X + z2*X^2,
/* Word definition */

z0 + or_gate(a0, or_gate(a1, a2)),
z1 + or_gate(a1*(1+a2), a0*(1+a1)*a2),
z2 + or_gate(a1, (1+a0)*a2),
/* circuit description */

Z_1 - ((X^2+X+1)*A^7+(X^2+1)*A^6+(X)*A^5+(X+1)*A^4+(X^2+X+1)*A^3+(X^2+1)*A),
/* spec polynomial */

t*(Z-Z_1) -1,
/* miter */

A^8 - A,
Z^8 - Z,
Z_1^8 - Z_1,
t^8 - t,
a0^2 - a0,
a1^2 - a1,
a2^2 - a2,
z0^2 - z0,
z1^2 - z1,
z2^2 - z2;
/* vanishing polynomials */

slimgb(J);