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