The realization space is
  [0   1   1   0   0   1                   1            1      1                   1    1]
  [1   1   0   1   0   0   x1*x2 + x1 - x2^2   x1*x2 + x1     x1   x1*x2 + x1 - x2^2   x1]
  [1   1   0   0   1   1                   0         x2^2   x2^2                  x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1*x2^2 + x1*x2 - x1 - x2^3, x1^3*x2^4 - x1^3*x2^2 + x1^2*x2^4 - x1^2*x2^2 - x1*x2^6 + x1*x2^4)
avoiding the zero loci of the polynomials
RingElem[x2, x1 - x2, x2 - 1, x1 - 1, x1, x1 - x2 + 1, x1*x2 - x2^2 + x2 - 1, x1*x2 + x1 - x2^2, x1*x2 + 2*x1 - x2^2 - x2 - 1, x1*x2 + 2*x1 - x2^2 - x2, x1*x2 + x1 - x2^2 - x2 - 1, x1*x2^2 - x1 - x2^3, x2 + 1, x1*x2 + x1 - x2^2 - 1, x1*x2 + x1 - x2^2 - x2 + 1, x1*x2^2 + x1*x2 - x1 - x2^3 + x2, x1 - x2^2 + 1, x1 - x2^2, x1*x2 + x1 - 1]