The realization space is
  [1   1   0        x1^2 - x1   0   1   1        0        x1^2 - x1    1              x1]
  [1   0   1   -x1^2 + x1 - 1   0   1   0   x1 - 1   -x1^2 + x1 - 1   x1   x1^2 - x1 + 1]
  [0   0   0                0   1   1   1       x1            -x1^2   x1            x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 4*x1^9 + 6*x1^8 - 3*x1^7 - 3*x1^6 + 6*x1^5 - 4*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, 2*x1 - 1, x1 - 2, 3*x1^2 - 2*x1 + 1]