The realization space is
  [1   1               1   0   0   1           1    1               1    1    1]
  [1   0   x1^2 - x1 + 1   1   0   1           1    0   x1^2 - x1 + 1   x1   x1]
  [0   0               0   0   1   1   x1^2 - x1   x1       x1^2 - x1   x1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - 2*x1^2 + x1 - 1, -x1^9 + 6*x1^8 - 16*x1^7 + 24*x1^6 - 20*x1^5 + 7*x1^4 + x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - x1 - 1, 2*x1^3 - 4*x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - x1^2 - 1, x1^2 - 3*x1 + 1, x1 + 1]