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