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