The realization space is
  [1   1   0        1   0   1   1          0            2*x1 - 3                  2*x1 - 3        2*x1 - 3]
  [0   1   1   x1 - 1   0   0   1   2*x1 - 3   2*x1^2 - 5*x1 + 3   -2*x1^3 + 7*x1^2 - 6*x1   2*x1^2 - 3*x1]
  [0   0   0        0   1   1   1     x1 - 2       x1^2 - x1 - 1   -x1^3 + 3*x1^2 - x1 - 2   x1^2 - x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (16*x1^8 - 192*x1^7 + 936*x1^6 - 2376*x1^5 + 3241*x1^4 - 1950*x1^3 - 351*x1^2 + 1080*x1 - 405)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1 - 1, x1, x1 - 2, 3*x1^2 - 6*x1 + 2, x1^3 - 2*x1^2 + 2*x1 - 2, 2*x1 - 3, 3*x1^3 - 10*x1^2 + 9*x1 - 1, 3*x1 - 5]