The realization space is
  [1   1   0           4*x1^2 - 4*x1 + 1   0   1   1                   0           4*x1^2 - 4*x1 + 1           2*x1 - 1           2*x1 - 1]
  [0   1   1   -x1^3 + 4*x1^2 - 4*x1 + 1   0   0   1    -x1^2 + 3*x1 - 1   -x1^3 + 4*x1^2 - 4*x1 + 1   -x1^2 + 3*x1 - 1   -x1^2 + 3*x1 - 1]
  [0   0   0                           0   1   1   1   2*x1^2 - 3*x1 + 1        2*x1^3 - 3*x1^2 + x1          x1^2 - x1        2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-16*x1^9 + 120*x1^8 - 356*x1^7 + 550*x1^6 - 490*x1^5 + 261*x1^4 - 82*x1^3 + 14*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - 3*x1 + 1, 2*x1 - 1, 3*x1 - 1, x1^2 + 2*x1 - 1, x1^4 + x1^3 - 7*x1^2 + 5*x1 - 1, 2*x1^2 - 4*x1 + 1, 5*x1^3 - 11*x1^2 + 6*x1 - 1, 3*x1^2 - 6*x1 + 2]