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