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