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