The realization space is
  [1   1   0   0                          x2                          x2   0    1                          x1                                 x1*x2    1]
  [0   1   1   1   -x1^2 + 2*x1*x2 + x1 - x2        -x1^2 + 2*x1*x2 + x1   0    0                          x1      -x1^3 + 2*x1^2*x2 + x1^2 - x1*x2   x1]
  [0   0   0   1   -x1^2 + 2*x1*x2 + x1 - x2   -x1^2 + 2*x1*x2 + x1 - x2   1   x2   -x1^2 + 2*x1*x2 + x1 - x2   -x1^2*x2 + 2*x1*x2^2 + x1*x2 - x2^2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1 - 1, x1^2 - 2*x1*x2 - x1 + x2, x1 - x2 - 1, x1 - 2*x2, x1, x2, x1 - 2*x2 - 1, x1^3 - 2*x1^2*x2 - x1 + x2, x1^3 - 3*x1^2*x2 - x1^2 + x1*x2^2 + 2*x1*x2 - x2^2, x1^3 - 4*x1^2*x2 - 2*x1^2 + 4*x1*x2^2 + 6*x1*x2 + x1 - 3*x2^2 - 2*x2, x1^3 - 3*x1^2*x2 - x1^2 + 2*x1*x2^2 + 3*x1*x2 - x2^2, x1^2 - x1*x2 + x2, x1^3 - 2*x1^2*x2 - x1^2 + 2*x1*x2 - x2, x1^2 - 2*x1*x2 + x2, x2 + 1, x1^2*x2 + x1^2 - 2*x1*x2^2 - 3*x1*x2 - x1 + 2*x2^2 + x2]