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