The realization space is
  [1   1   0   1   0   0     x2 - 1                    x1*x2 - x1          x2 - 1       x2 - 1        x1*x2 - x1]
  [1   0   1   1   0   1   -x1 + x2            -x1^2*x2 + x1*x2^2   -x1*x2 + x2^2     -x1 + x2     -x1*x2 + x2^2]
  [0   0   0   1   1   1     x2 - 1   -x1^2*x2 + 2*x1*x2^2 - x2^2       x2^2 - x2   x1*x2 - x1   x1*x2^2 - x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^3*x2 - x1^2*x2^2 - 2*x1^2*x2 - x1*x2^3 + 5*x1*x2^2 - 2*x1*x2 + x1 - x2^2)
avoiding the zero loci of the polynomials
RingElem[x2 - 1, x1 - x2, x2, x1 - 1, x1*x2^2 + x1*x2 - x1 - x2^2, x1 - x2^2, x1^2*x2 - 3*x1*x2 + x1 + x2^2, 2*x1*x2 - x1 - x2^2, x1*x2 - 1, x1^2*x2^2 - 3*x1*x2 + x1 + x2, 2*x1*x2 - x1 - x2, x1, x1*x2 - x2^2 + x2 - 1, x1^2*x2 - 2*x1*x2^2 + x1*x2 - x1 + x2^2, x1^2 - 2*x1*x2 + x2, x1 + x2 - 2]