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