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