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