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