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