The realization space is
  [1   1           1   0   0   1     1         1           1         1    1]
  [0   1   -x1^2 + 1   1   0   0     0         1   -x1^2 + 1        x1   x1]
  [0   0           0   0   1   1   -x1   -x1 + 1         -x1   -x1 + 1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - x1 + 1, 2*x1^10 + x1^9 - 6*x1^8 - x1^7 + 5*x1^6 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + x1 - 1, x1 + 1, x1^2 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, x1^2 - x1 - 1, x1^3 + 2*x1^2 - x1 - 1, 2*x1^2 - 1, x1^3 - x1^2 + 1]