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