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