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