The realization space is
  [1   1   0              x1   0   1   1        0              x1   2*x1 - 1    1]
  [0   1   1   x1^2 - x1 + 1   0   0   1       x1   x1^2 - x1 + 1         x1   x1]
  [0   0   0               0   1   1   1   x1 - 1            x1^2     x1 - 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^8 - 16*x1^7 + 31*x1^6 - 40*x1^5 + 36*x1^4 - 21*x1^3 + 7*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1^3 - 2*x1^2 + 2*x1 - 1, 2, x1^3 - x1^2 + 2*x1 - 1, x1^2 - x1 + 1, 3*x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1]