The realization space is
  [1   1   0                        x1*x2   0   1   1    0                        x1*x2        x1      x1]
  [0   1   1   -x1*x2^2 + x1*x2 - x1 + x2   0   0   1    1   -x1*x2^2 + x1*x2 - x1 + x2        x2      x2]
  [0   0   0                            0   1   1   1   x1                      x1*x2^2   x1 - x2   x1*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*x2 + x1^2 + x1*x2^2 - 2*x1*x2 + x2^2)
avoiding the zero loci of the polynomials
RingElem[x1*x2 - x1 + x2, x2, x1 - x2, x1*x2^2 - x1*x2 + x1 + x2^2 - x2, x2 - 1, x1, x1*x2^2 - x1*x2 + x1 - x2, x1 - 1, x1*x2^3 - x1*x2^2 + 2*x1*x2 - x1 - 2*x2^2 + x2, x1*x2^3 - 2*x1*x2^2 + 2*x1*x2 - x1 - 2*x2^2 + x2, x1*x2^2 + x1 - x2, x1^2*x2 - x1^2 + x1*x2 + x1 - x2, x1^2*x2^2 - x1^2*x2 + x1^2 + 2*x1*x2^2 - 2*x1*x2 + x2^2, x1 + 1, x1^2 - x1*x2 - x2, x1 - 2*x2, x1^2 - x1*x2^2 - x1*x2 - x1 + x2, x1*x2^2 + x1 + x2^2 - x2, x1*x2^2 - x1*x2 + x1 + x2^2 - 2*x2, x1*x2^2 + x1 + x2^2 - 2*x2, 2*x1*x2^2 - x1*x2 + x1 - x2, x1*x2^2 + x1 - 2*x2, x1*x2^2 - x1*x2 + x1 - 2*x2]