The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1         0   x1^3 - 3*x1^2 + 3*x1 - 1         1      x1 - 1]
  [0   1   1       2*x1^2 - x1   0   0   1        x1       2*x1^3 - 3*x1^2 + x1   -x1 + 1       -x1^2]
  [0   0   0                 0   1   1   1   -x1 + 1             -2*x1^3 + x1^2        x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^11 - 11*x1^10 + 21*x1^9 - 6*x1^8 - 41*x1^7 + 78*x1^6 - 69*x1^5 + 34*x1^4 - 9*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 + x1 - 1, x1^4 + 3*x1^3 - 6*x1^2 + 4*x1 - 1, x1^4 + 2*x1^2 - 3*x1 + 1, 3*x1^3 - 4*x1^2 + 3*x1 - 1]