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