The realization space is
  [0   1   1   0   0   1                       x2               x2                                    -x1*x2 + x2^2 + x2                                                    x2                                                    x2]
  [1   1   0   1   0   0   x1^2 - x1*x2 - x1 + x2   x1^2 - x1 + x2   -x1^3 + x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2^2 + x2   -x1^3 + x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2^2 + x2   -x1^3 + x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2^2 + x2]
  [1   1   0   0   1   1                        0            x1*x2                                                  x2^2                                                 x1*x2                                                  x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1^3 - x1^2*x2 - 2*x1^2 + 2*x1*x2 + x1 - x2^2, x1^2 - x1 + x2, x1 - x2 - 1, x1^3 - x1^2*x2 - x1^2 + x1*x2 - x2^2, x1 - 1, x1, x1^2 - 2*x1 + x2, x1 - 2, x2, x1^3 - 2*x1^2*x2 - x1^2 + x1*x2^2 + 2*x1*x2 - 2*x2^2, x1^3 - x1^2*x2 - 2*x1^2 + 2*x1*x2 + x1 - 2*x2, x2 - 1, x1^3 - x1^2*x2 - 2*x1^2 + 3*x1*x2 + x1 - x2^2 - 2*x2, x1^2 - 2*x1 + x2 + 1, x1^2 - x1*x2 - x1 + 2*x2]