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