The realization space is
  [1   1   0   0       x1   x1   0    1        1          x1     x1]
  [1   0   1   1   x1 - 1   -1   0    1        0      x1 - 1     -1]
  [0   0   0   1       -1   -1   1   x1   x1 - 1   x1^2 - x1   x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^9 - x1^8 + x1^7 + x1^5 + x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1 + 1, x1 - 1, 2, x1^2 - x1 + 1, x1^2 + 1, x1, x1^2 + x1 + 1, x1^3 - x1^2 - 1, x1^3 - x1 + 1]