The realization space is
  [1   1   0   0   1   1             0              1                1       -x1 + 1                1]
  [1   0   1   0   1   0       -x1 + 1             x1        x1^2 - x1           -x1               x1]
  [0   0   0   1   1   1   x1^2 - 2*x1   -x1^2 + 2*x1   -x1^3 + 2*x1^2   x1^2 - 2*x1   -x1^3 + 2*x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 8*x1^9 + 24*x1^8 - 30*x1^7 + 4*x1^6 + 25*x1^5 - 20*x1^4 + 4*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1^2 - x1 - 1, x1, x1 - 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^4 - 4*x1^3 + 4*x1^2 + x1 - 1, x1^3 - 2*x1^2 - x1 + 1, x1^2 - 2*x1 - 1, x1^2 - 3*x1 + 1]