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