The realization space is
  [1    1   1   0   0   1    1      1    0                   1                1]
  [1   x1   0   1   0   1   x1      0   x1   -x1^3 + x1^2 + x1   -x1^2 + x1 + 1]
  [0    0   0   0   1   1   x1   x1^2   -1                x1^2               x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^11 - 3*x1^10 + x1^9 + 3*x1^8 - 3*x1^6 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 - 1, x1 + 1, x1^3 - x1 - 1, x1^3 - x1^2 - 1, x1^2 - 2, x1^2 + x1 - 1, x1^2 + x1 + 1, x1^2 - x1 + 1]