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