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