The realization space is
  [1   0   1   0   1    0     1   -x1 - 1     -x1 - 1   x1^3 + 2*x1^2 + x1            1]
  [0   1   1   0   0    1     1       -x1         -x1     x1^3 + x1^2 + x1           x1]
  [0   0   0   1   1   -1   -x1      x1^2   x1^2 + x1         -x1^4 - x1^3   -x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1^2 + x1 + 1, x1^3 + x1^2 - 1, x1^4 + x1^3 + x1^2 + x1 + 1, x1^2 + 1, x1 - 1, x1^2 - x1 + 1, x1^3 - x1 - 1]