The realization space is
  [1   1   0   0   1   1        0    1    2*x1 - 1      2*x1 - 1]
  [1   0   1   0   1   0   x1 - 1   x1   x1^2 - x1   2*x1^2 - x1]
  [0   0   0   1   1   1       x1   x1        x1^2          x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^9 + 16*x1^8 - 21*x1^7 + 3*x1^6 + 18*x1^5 - 18*x1^4 + 7*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, 2*x1 - 1]