The realization space is
  [1   0   1   1   0   1    0    1        x1   x1        x1]
  [0   1   1   2   0   0    1    1      2*x1    1         1]
  [0   0   0   0   1   1   -1   x1   -x1 + 1   x1   -x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1 - 2, 4*x1^5 - 8*x1^4 + 3*x1^3 + 2*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, 3*x1 - 1, x1 - 1, x1^2 + x1 - 1, 3*x1^2 - 1, x1, 2, 5*x1^2 - 4*x1 + 1, 3*x1^2 - 3*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, 4*x1 - 1, x1 + 1, 2*x1^2 - 1]