The realization space is
  [1   1   0   0   1   1          0          2           2             2*x1 - 1                   1]
  [0   1   1   0   0   1          1          1           1                  -x1                  x1]
  [0   0   0   1   1   1   4*x1 - 2   4*x1 - 2   -4*x1 + 2   -4*x1^2 + 4*x1 - 1   4*x1^2 - 4*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-64*x1^4 + 96*x1^3 - 48*x1^2 + 8*x1)
avoiding the zero loci of the polynomials
RingElem[2, x1, 2*x1 - 1, x1 - 1, 4*x1 - 1, 4*x1 - 3, 8*x1 - 3, 8*x1^2 - 9*x1 + 2, 3*x1 - 1]