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