The realization space is
  [1   1   0   0   1   1                  0               x1*x2 - x2      x1 - 1   x1*x2 - x2    1]
  [0   1   1   0   0   1             x2 - 1               x1*x2 - x1   x1^2 - x1   x1*x2 - x1   x1]
  [0   0   0   1   1   1   x1*x2 - 2*x2 + 1   x1^2*x2 - 2*x1*x2 + x1      x2 - 1    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[x1*x2 - 2*x2 + 1, x1, x1 - x2, x1^2*x2 - 2*x1*x2 + x1 - x2^2 + x2, x1 - 1, x1^3*x2 - 3*x1^2*x2 + x1^2 + 3*x1*x2 - x1 - x2^2, x1^2*x2 - x1*x2^2 - 2*x1*x2 + x1 + x2^2, x1^2*x2 - 3*x1*x2 + x1 - x2^2 + 3*x2 - 1, x2, x1^2*x2 - 2*x1*x2 + x1 - x2^2 + 2*x2 - 1, x1^2*x2 - 3*x1*x2 + x1 - x2^2 + 4*x2 - 2, x2 - 1, x1 + x2 - 1, x1^2*x2 - x1*x2^2 - 2*x1*x2 + x1 + x2^3, x1^2*x2 - x1*x2 + x1 - x2^2, x1*x2 - x2^2 - x2 + 1, x1 - x2^2, x1^3*x2 - 3*x1^2*x2 + x1^2 + 2*x1*x2 - x1 - x2^2 + 2*x2 - 1, x1^4*x2 - 4*x1^3*x2 + x1^3 + 5*x1^2*x2 - 2*x1^2 - x1*x2 - x2^2 + x2, x1^4*x2 - 5*x1^3*x2 + x1^3 + 8*x1^2*x2 - 3*x1^2 - 3*x1*x2 + x1 - x2^2 + x2, x1^3*x2 - 3*x1^2*x2 + x1^2 + 3*x1*x2 - 2*x1 - x2^2 + x2, x1^3*x2 - 4*x1^2*x2 + x1^2 + 6*x1*x2 - 3*x1 - x2^2 - x2 + 1, x1^2 - x1 - x2 + 1, x1^2 - 2*x1 + x2, x1*x2 - 3*x2 + 2, x1^2*x2 - 3*x1*x2 + x1 + x2]