The realization space is
  [1   1   0   0   1   1        0           1      x1 + 1          x1         x1]
  [1   0   1   0   1   0   x1 + 1        x1^2   x1^2 + x1   x1^2 + x1       x1^2]
  [0   0   0   1   1   1       x1   x1^2 - x1        x1^2    x1^2 - 1   x1^2 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^7 - 4*x1^6 - 2*x1^5 + 5*x1^4 + 2*x1^3 - 2*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 + 1, x1^2 - x1 - 1, x1, 2*x1 + 1, x1^2 - 2*x1 - 1, 2*x1^2 - 1]