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