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