The realization space is
  [1   1   0   0   1   1                       0                                   x1*x2                     x1         x1 - x2^2 + 2*x2 - 1    1]
  [0   1   1   0   0   1                   x1*x2                        -x1*x2^2 + x1*x2            -x1*x2 + x1             -x1*x2^2 + x1*x2   x1]
  [0   0   0   1   1   1   -x1 + x2^2 - 2*x2 + 1   x1*x2 - x1 - x2^3 + 3*x2^2 - 3*x2 + 1   x1 - x2^2 + 2*x2 - 1   x1*x2 - x2^3 + 2*x2^2 - x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1, x1 + x2 - 1, x2, x2 - 1, x1 - x2^2 + 2*x2 - 1, x1*x2^2 - x1*x2 + x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1 + 2*x2 - 1, x1^2*x2 - x1^2 + 3*x1*x2^2 - 4*x1*x2 + 2*x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1^2 - 2*x1*x2^2 + 3*x1*x2 - 2*x1 - x2^3 + 3*x2^2 - 3*x2 + 1, x1^2 + x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, x1 - x2, x1 - 1, x1*x2 - x2^2 + 2*x2 - 1, 2*x1*x2^2 - 2*x1*x2 + x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1^2*x2^3 - x1^2*x2 + x1^2 - x1*x2^4 + 4*x1*x2^3 - 7*x1*x2^2 + 6*x1*x2 - 2*x1 - x2^5 + 5*x2^4 - 10*x2^3 + 10*x2^2 - 5*x2 + 1, x1*x2^2 - x1*x2 + x1 - x2^2 + 2*x2 - 1, x1*x2 + x1 - x2^2 + 2*x2 - 1, x1 + x2^3 - 3*x2^2 + 3*x2 - 1]