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