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