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