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