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