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