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