The realization space is
  [1   1   x1^2 - 1   0   0   1      1    x1^2 - 1    0   x1 - 1      1]
  [1   0       x1^2   1   0   1      0        x1^2    1       x1     x1]
  [0   0          0   0   1   1   x1^2   x1^2 + x1   x1       x1   x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 + 2*x1^11 - 3*x1^10 - 6*x1^9 + 3*x1^7 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, x1, x1 - 1, x1^2 - x1 - 1, x1 - 2, x1^3 + x1^2 - 2*x1 - 1, x1^2 + x1 - 1, 2*x1 + 1]