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