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