The realization space is
  [1   0   1   0   1   0         x2 - 2            x1 - x2 + 1                  x2 - 2                  x2 - 2    1]
  [1   1   0   1   0   0   -x1 + x2 - 1          -x1*x2 + 2*x1            -x1 + x2 - 1            x1*x2 - 2*x1   x1]
  [1   1   0   0   1   1              0   x1 - x2^2 + 2*x2 - 1   -x1 + x2^2 - 2*x2 + 1   -x1 + x2^2 - 2*x2 + 1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x2 - 1, x1 - x2^2 + 2*x2 - 2, x1 - x2^2 + x2, x1 - x2^2 + 2*x2 - 1, x1*x2 - x1 - x2^2 + x2 + 1, x1 - x2 + 1, x2, x1 - x2, x1 - x2^2 + 3*x2 - 3, x2 - 2, x1^2 - 2*x1*x2 + 2*x1 + x2^3 - 4*x2^2 + 6*x2 - 3, x1*x2 - x1 - x2^2 + 3*x2 - 3, x1 - 2*x2 + 3]