The realization space is
  [1   1   x1   0    1       x1 - x2   x1   0    1    1              0]
  [1   0   x2   1   x1   -x1*x2 + x2   x1   0   x1    0      x1^2 - x2]
  [1   0   x2   0    1             0   x2   1   x2   x2   x1*x2 - x2^2]
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[x1^2*x2 - x1^2 + x1*x2 - 2*x2^2 + x2, x2, x1^3 - x1^2 - x2^2 + x2, x1 - x2, 2*x1^2*x2 - x1^2 - x1*x2^2 - x2^2 + x2, x1, x1^3 - 2*x1*x2 + x2, x1^2 - x1*x2^2 - x1*x2 + 2*x2^2 - x2, x1 - 1, x2 - 1, x1^2*x2 - x1^2 - x1*x2 + x2, x1^2*x2 - x1^2 - x1*x2^2 + x2, x1^2 - x1*x2 + x2^2 - x2, x1*x2 - 2*x2 + 1, x1^2*x2 + x1^2 - 3*x1*x2 + x2, x1^2 - x1 - x2 + 1, x1^2 - x2, x1*x2 + x1 - 2*x2]