The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1         0          x1^3 - 2*x1^2 + x1         1      x1 - 1]
  [0   1   1       2*x1^2 - x1   0   0   1        x1               2*x1^3 - x1^2   -x1 + 1       -x1^2]
  [0   0   0                 0   1   1   1   -x1 + 1   -x1^3 + 3*x1^2 - 3*x1 + 1        x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^10 + 3*x1^9 + 3*x1^8 - 8*x1^7 + 5*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, x1^2 + x1 - 1, x1^4 + 3*x1^3 - 6*x1^2 + 4*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - 4*x1 + 2, 3*x1 - 2, 3*x1^3 - 4*x1^2 + 3*x1 - 1]