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