The realization space is
  [1   1   x1^2 - x1 - 1   0   0   1           1    x1^3 - 2*x1^2 + 1        0   x1 - 1           1]
  [1   0       x1^2 - x1   1   0   1           0   x1^3 - 2*x1^2 + x1        1       x1          x1]
  [0   0               0   0   1   1   x1^2 - x1     x1^3 - x1^2 - x1   x1 - 1       x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^18 - 10*x1^17 + 41*x1^16 - 86*x1^15 + 89*x1^14 - 21*x1^13 - 41*x1^12 + 31*x1^11 - 4*x1^9)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, x1^2 - x1 - 1, 2*x1 - 3, x1^3 - 2*x1^2 + x1 - 1, x1^4 - 2*x1^3 - 2*x1^2 + 5*x1 - 1, x1 + 1, x1^2 - 2]