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