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