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