The realization space is
  [1   0   1   0   1    0   x1 - 1   x1^2 - 2*x1   x1^3 - 3*x1^2 + 2*x1             x1 - 2                    x1 - 2]
  [0   1   1   0   0    1   x1 - 1       -x1 + 1       -x1^2 + 2*x1 - 1   -x1^2 + 2*x1 - 1   -x1^3 + 2*x1^2 + x1 - 3]
  [0   0   0   1   1   -1        1            -1            x1^2 - 2*x1        x1^2 - 2*x1               x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^9 - 7*x1^8 + 17*x1^7 - 12*x1^6 - 14*x1^5 + 22*x1^4 + x1^3 - 11*x1^2 + x1 + 2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1, x1 - 1, x1^3 - 3*x1^2 + 2*x1 + 1, 2*x1 - 3, x1 - 2, x1^2 - 3*x1 + 3, x1^3 - 3*x1^2 + x1 + 3, x1^3 - 2*x1^2 - x1 + 3]