The realization space is
  [1   1   0                x1   0   1   1        0                x1        1        1]
  [1   0   1   x1^2 - 2*x1 + 1   0   1   0   x1 - 2   x1^2 - 2*x1 + 1   x1 - 1   x1 - 1]
  [0   0   0                 0   1   1   1   x1 - 1         x1^2 - x1   x1 - 1       x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^9 - 18*x1^8 + 69*x1^7 - 150*x1^6 + 205*x1^5 - 181*x1^4 + 100*x1^3 - 31*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, 2, x1^2 - x1 + 1, x1^2 - 3*x1 + 1, x1, 2*x1 - 3, x1^2 - 2*x1 + 2, x1^2 - x1 - 1, 2*x1^2 - 4*x1 + 1, x1^3 - 2*x1^2 + x1 - 1]