The realization space is
  [1   1   0               x1   0   1   1         0               x1         1    1]
  [0   1   1   -x1^2 + x1 + 1   0   0   1        x1   -x1^2 + x1 + 1        x1   x1]
  [0   0   0                0   1   1   1   -x1 - 1             x1^2   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2, 2*x1^9 + x1^8 - 15*x1^7 + 9*x1^6 + 19*x1^5 - 16*x1^4 - 7*x1^3 + 7*x1^2 + x1 - 1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, 2*x1 + 1, x1 + 1, 2*x1^2 - 1, 3*x1^3 + x1^2 - 2*x1 - 1, x1^2 - x1 - 1, x1^3 - 3*x1^2 + 1, 2*x1^2 - 2*x1 - 1, x1^2 + 3*x1 + 1, x1 + 2, x1^2 - 2*x1 - 1, x1^3 + 2*x1^2 - x1 - 1, x1^3 + x1^2 - 2*x1 - 1]