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