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