The realization space is
  [1   0   1           1   0   1    0    1           1    1      1]
  [0   1   1   x1^2 + x1   0   0    1    1   x1^2 + x1   x1     x1]
  [0   0   0           0   1   1   -1   x1      x1 + 1    1   x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 3*x1^8 + x1^7 + 2*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1 + 1, x1^2 - x1 - 1, x1^4 + x1^3 - 2*x1^2 + 1, x1^3 + x1^2 - 2*x1 - 1, x1^2 + x1 - 1, x1^2 - 2, x1 + 2, x1^3 - x1 + 1]