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