The realization space is
  [1    1   1   0      x1*x2         x2   1   0           x1^2*x2 - x1*x2    1                                              0]
  [1   x1   0   1   -x1 + x2   -x1 + x2   1   0   -x1^2 + x1*x2 + x1 - x2    0                         x1^2 - x1*x2 - x1 + x2]
  [1   x1   0   0      x1*x2      x1*x2   0   1   -x1^2*x2 - x1^2 + x1*x2   x2   x1^2*x2^2 + x1^2*x2 + x1^2 - x1*x2^2 - x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^2*x2^2 + 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x1 + x2^2 - x2, x1*x2 + x1 - x2, x1^2*x2 + x1 - x2, x2, x1, x1*x2^2 + x1*x2 + x1 - x2^2 - x2, 2*x1*x2 + x1 - 2*x2, x1^2*x2^2 + x1^2*x2 - x1*x2^2 + x1 - x2, x1^2*x2^3 + 2*x1^2*x2^2 + 3*x1^2*x2 + x1^2 - 2*x1*x2^3 - 4*x1*x2^2 - 3*x1*x2 + x2^3 + 2*x2^2, x1 - 1, x1^3*x2^2 + 2*x1^3*x2 + x1^3 - 2*x1^2*x2^2 - 3*x1^2*x2 + 2*x1*x2^2 + x1*x2 - x2^2, x1*x2^2 + 2*x1*x2 + x1 - x2^2 - 2*x2, x1^3*x2^3 + x1^3*x2^2 - x1^2*x2^3 + x1^2*x2^2 + 3*x1^2*x2 + x1^2 - x1*x2^3 - 4*x1*x2^2 - 3*x1*x2 + x2^3 + 2*x2^2, x1 - x2, x2 - 1, x1^2*x2^2 - x1^2*x2 - x1^2 + 2*x1*x2 - x2^2, x1^3*x2^2 + 3*x1^3*x2 + x1^3 - 3*x1^2*x2^2 - 4*x1^2*x2 + 3*x1*x2^2 + x1*x2 - x2^2]