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