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