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