The realization space is
  [1   0   1   x1 - 1   0   1    0    x1 - 2   x1^2 - 3*x1 + 2         x1 - 1         x1 - 1]
  [0   1   1       x1   0   0    1    x1 - 2       x1^2 - 2*x1   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0        0   1   1   -1   -x1 + 1           -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 (2*x1^8 - 20*x1^7 + 85*x1^6 - 200*x1^5 + 284*x1^4 - 248*x1^3 + 129*x1^2 - 36*x1 + 4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, x1^2 - x1 - 1, x1^2 - 3*x1 + 1, 2*x1 - 3, x1^3 - 2*x1^2 + 2*x1 - 2, x1^3 - 5*x1^2 + 6*x1 - 1, x1^2 - 2]