The realization space is
  [1   1   0        1   0   1   1         0             x1 - 2             x1^2 - 4*x1 + 4             x1 - 2]
  [0   1   1   x1 - 1   0   0   1    x1 - 2    x1^2 - 3*x1 + 2    x1^3 - 4*x1^2 + 5*x1 - 2        x1^2 - 2*x1]
  [0   0   0        0   1   1   1   -x1 + 1   -x1^2 + 3*x1 - 3   -x1^3 + 4*x1^2 - 6*x1 + 3   -x1^2 + 3*x1 - 3]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 13*x1^7 - 73*x1^6 + 231*x1^5 - 448*x1^4 + 538*x1^3 - 379*x1^2 + 132*x1 - 12)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 3, x1 - 1, x1 - 2, x1^3 - 4*x1^2 + 5*x1 - 1, 2*x1 - 3, x1, 2*x1^2 - 6*x1 + 5, x1^3 - 3*x1^2 + 2*x1 + 1]