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