The realization space is
  [1   1   0   0   1   1                         0                    x1 - 1                         x1*x2 - x1 + x2^2 - 3*x2 + 2               x1 + x2 - 2    1]
  [1   0   1   0   1   0   x1^2 + x1*x2 - 3*x1 + 1       x1^2 + x1*x2 - 2*x1   x1^2*x2 - x1^2 + x1*x2^2 - 4*x1*x2 + 3*x1 + x2 - 1       x1^2 + x1*x2 - 2*x1   x1]
  [0   0   0   1   1   1   x1*x2 + x2^2 - 3*x2 + 1   x1*x2 + x2^2 - 3*x2 + 1           x1*x2^2 - x1*x2 + x2^3 - 4*x2^2 + 4*x2 - 1   x1*x2 + x2^2 - 3*x2 + 1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x2 - 1, x1, x1 - x2, x1 + x2 - 2, x1 + x2 - 1, x1*x2 + x2^2 - 3*x2 + 1, x2, x1 + x2 - 3, x1^2 - 2*x1 - x2^2 + 3*x2 - 1, x1^3 + 2*x1^2*x2 - 5*x1^2 - 4*x1*x2 + 7*x1 - x2^3 + 4*x2^2 - 3*x2 - 1, x1^3 + 3*x1^2*x2 - 5*x1^2 + 2*x1*x2^2 - 9*x1*x2 + 8*x1 - x2^2 + 4*x2 - 3, x1^2 + 2*x1*x2 - 3*x1 + x2^2 - 4*x2 + 3, x1^2*x2 + x1*x2^2 - 3*x1*x2 + 1, x1^2 + x1*x2 - 3*x1 + 1]