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