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