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