The realization space is
  [1   0   1    1   0   1    1    0           x1            x1            x1]
  [0   1   1   x1   0   0    0    1           x1   -x1*x2 + x2   -x1*x2 + x2]
  [0   0   0    0   1   1   x2   -1   x1*x2 - x2            x1    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 + x1^2 - 2*x1*x2^2 + x2^2)
avoiding the zero loci of the polynomials
RingElem[x1*x2 - x1 - x2, x2, x1 - 1, x1*x2 + x1 - x2, x1^2 + x1*x2 - x2, x1, x1*x2 - x2 + 1, x2 - 1, x1^2*x2 - x1^2 - 2*x1*x2 + x2, x1^2*x2 - x1^2 + x1*x2^2 - x2^2, 2, x1 + x2, 2*x1*x2 - x1 - x2, x1*x2^2 + x1*x2 - x1 - x2^2, x1 - x2]