The realization space is
  [1   0   1   x1 - 1   0   1           2    0    1   x1     1]
  [0   1   1   x1 + 1   0   0           0    1    1    1   -x1]
  [0   0   0        0   1   1   x1^2 + x1   -1   x1   x1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^4 + 12*x1^3 - 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, x1, x1 - 1, 2, x1^2 + 1, x1^2 + 2*x1 - 1, x1 + 2, x1^2 - 2, x1^2 - 3, x1 - 2]