The realization space is
  [1   0   1          1   0   1    0    1          x1    1               1]
  [0   1   1   x1^2 + 1   0   0    1    1   x1^3 + x1   x1              x1]
  [0   0   0          0   1   1   -1   x1    x1^2 + 1    1   x1^2 - x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, x1^2 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^5 - x1^4 + x1^2 - x1 + 1, x1^4 - x1^3 - 1, x1 + 1, x1^3 + x1^2 + 1]