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 (-x1^9 + 14*x1^8 - 86*x1^7 + 303*x1^6 - 670*x1^5 + 952*x1^4 - 848*x1^3 + 432*x1^2 - 96*x1)
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]