The realization space is
  [1   1   0   -x1^2 - x1 + 1   0   1   1        0        -x1^3 + 2*x1 - 1         1      x1 - 1]
  [0   1   1     -2*x1^2 + x1   0   0   1   x1 - 1   -2*x1^3 + 3*x1^2 - x1        x1   x1^2 - x1]
  [0   0   0                0   1   1   1      -x1      x1^4 + x1^3 - x1^2   -x1 + 1       -x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^11 + 6*x1^8 - x1^7 - 15*x1^6 + 17*x1^5 - 7*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^2 + x1 - 1, x1^4 - x1^3 + 4*x1^2 - 4*x1 + 1, x1^4 + 2*x1^2 - 3*x1 + 1, x1^4 + x1^3 + x1^2 - 3*x1 + 1, x1^3 + x1 - 1, x1^3 + x1^2 + x1 - 1, x1^3 + 3*x1^2 - 4*x1 + 1, x1^3 - x1^2 + 2*x1 - 1]