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