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