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