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