The realization space is
  [1   1   x1 - 1   0   0   1    1          x1 - 1   0      1      1]
  [1   0       x1   1   0   1    0              x1   2   2*x1   2*x1]
  [0   0        0   0   1   1   x1   2*x1^2 - 2*x1   1   2*x1     x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^5 - 8*x1^4 + 3*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, 2, 2*x1 - 3, 4*x1 - 5, 4*x1^2 - 6*x1 + 1, x1 - 1, 2*x1 + 1, 4*x1^2 - 4*x1 - 1]