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