The realization space is
  [1   1   0                 1   0   1   1        0                     x1 - 1                 x1 - 1                 1]
  [1   0   1   x1^2 - 3*x1 + 2   0   1   0   x1 - 1   x1^3 - 4*x1^2 + 5*x1 - 2   x1^3 - 3*x1^2 + 2*x1   x1^2 - 2*x1 + 1]
  [0   0   0                 0   1   1   1        1                x1^2 - 2*x1            x1^2 - 2*x1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^9 + 23*x1^8 - 110*x1^7 + 283*x1^6 - 423*x1^5 + 370*x1^4 - 181*x1^3 + 44*x1^2 - 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - 3*x1 + 1, x1 - 2, x1^3 - 3*x1^2 + 2*x1 - 1, x1 - 1, x1^3 - 2*x1^2 - x1 + 1, x1^2 - 2*x1 - 1]