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