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