The realization space is
  [1   0   1   x1 - 1   0   1    0         x1 - 1   x1^2 - 3*x1 + 2         x1 - 1         x1 - 1]
  [0   1   1       x1   0   0    1         x1 - 1       x1^2 - 2*x1   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0        0   1   1   -1   -x1^2 + 2*x1           -x1 + 1         x1 - 1      x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 10*x1^9 + 43*x1^8 - 107*x1^7 + 176*x1^6 - 205*x1^5 + 170*x1^4 - 94*x1^3 + 30*x1^2 - 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, x1^2 - x1 - 1, x1^4 - 4*x1^3 + 4*x1^2 - x1 + 1, x1^3 - 5*x1^2 + 6*x1 - 1, 2*x1 - 3, x1^2 - 3*x1 + 1, x1^3 - 4*x1^2 + 3*x1 + 1, x1^3 - 2*x1^2 + x1 - 1]