The realization space is
  [1   1   0            x1 - 2   0   1   1                 0            x1 - 2      x1^2 - 3*x1 + 2      x1^2 - 3*x1 + 1]
  [0   1   1   x1^2 - 3*x1 + 1   0   0   1   x1^2 - 3*x1 + 1   x1^2 - 3*x1 + 1   x1^3 - 3*x1^2 + x1   x1^3 - 3*x1^2 + x1]
  [0   0   0                 0   1   1   1           -x1 + 1                -1              -x1 + 1                  -x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^9 + 14*x1^8 - 82*x1^7 + 262*x1^6 - 500*x1^5 + 587*x1^4 - 420*x1^3 + 174*x1^2 - 37*x1 + 3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1^3 - 4*x1^2 + 3*x1 - 1, x1 - 1, x1^2 - 3*x1 + 1, x1 - 3, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 4*x1^2 + 4*x1 - 2, x1^2 - 4*x1 + 2]