The realization space is
  [1    1   1   0                x1                       x1   1   0                x1    1                                    0]
  [1   x1   0   1   x1*x2 + x1 - x2   x1^2*x2 + x1^2 - x1*x2   1   0   x1*x2 + x1 - x2    0   x1^2*x2 + x1^2 - 2*x1*x2 - x1 + x2]
  [1   x1   0   0                x1                     x1^2   0   1             x1*x2   x2                         x1^2 - 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*x2^2 + x1 + x2^2 - x2, x1^2*x2 - 2*x1*x2 - x1 + x2, x1 - x2, x2, x1, x1*x2 - 2*x2 + 1, x1*x2 + x1 - x2, x1^2*x2^2 + x1^2*x2 + x1^2 - 2*x1*x2^2 - 2*x1*x2 + x2^2, x1*x2^2 - x1*x2 - x1 + x2, x2 - 1, x1 + x2^2 - x2, x1 - 1, x1^2*x2 - x1 - x2^2 + x2, x1^2*x2 - x1*x2 - x1 + x2, x1*x2^2 + x1 - x2^2, x1*x2^2 + x1*x2 + x1 - x2^2 - x2, 2*x1 - x2, x2 + 1]