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