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