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