The realization space is
  [1   1   0   2*x1 - 2   0   1   1        0   4*x1^2 - 6*x1 + 2   2*x1 - 1    1]
  [0   1   1         -1   0   0   1       x1           -2*x1 + 1     x1 - 1   x1]
  [0   0   0          0   1   1   1   x1 - 1       2*x1^2 - 2*x1         x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-48*x1^9 + 240*x1^8 - 516*x1^7 + 632*x1^6 - 494*x1^5 + 260*x1^4 - 92*x1^3 + 20*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, 2, x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1^2 - 1, 6*x1^2 - 8*x1 + 3, 2*x1^2 - 4*x1 + 1, 2*x1^2 + 2*x1 - 1, 6*x1^2 - 4*x1 + 1]