The realization space is
  [1   1   0   x1 - 1   0   1   1                 0      x1 - 1         -3*x1 + 2    1]
  [0   1   1    -x1^2   0   0   1   x1^2 - 2*x1 + 1       -x1^2   x1^2 - 2*x1 + 1   x1]
  [0   0   0        0   1   1   1    -x1^2 - x1 + 1   x1^2 - x1    -x1^2 - x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-6*x1^9 + 43*x1^8 - 134*x1^7 + 237*x1^6 - 260*x1^5 + 181*x1^4 - 78*x1^3 + 19*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1^2 + x1 - 1, x1 - 1, 2*x1^2 - 1, 3*x1 - 2, 2*x1^3 - 2*x1^2 + 2*x1 - 1, 5*x1^3 - 4*x1^2 - x1 + 1, 5*x1^3 - 7*x1^2 + 4*x1 - 1, x1^3 + 3*x1^2 - 4*x1 + 1, x1^4 + 2*x1^3 - 4*x1^2 + 3*x1 - 1]