The realization space is
  [1   1   0   2   0   1   1          0      2        2*x1 - 1        4*x1 - 2]
  [0   1   1   1   0   0   1          1      1        3*x1 - 1        3*x1 - 1]
  [0   0   0   0   1   1   1   4*x1 - 2   4*x1   4*x1^2 - 2*x1   4*x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (128*x1^5 - 384*x1^4 + 400*x1^3 - 192*x1^2 + 44*x1 - 4)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, x1 - 1, 4*x1 - 1, 2*x1 - 1, 2, 4*x1^2 - 3*x1 + 1, 4*x1^2 - 6*x1 + 1, 4*x1^2 + 2*x1 - 1, 4*x1 - 3]