The realization space is
  [1   1   0   -x1^2 - x1 + 1   0   1   1        0    -x1^2 - x1 + 1         1      x1 - 1]
  [0   1   1     -2*x1^2 + x1   0   0   1   x1 - 1      -2*x1^2 + x1        x1   x1^2 - x1]
  [0   0   0                0   1   1   1      -x1   x1^3 - 2*x1 + 1   -x1 + 1       -x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^15 - 24*x1^14 + 37*x1^13 + 15*x1^12 - 100*x1^11 + 117*x1^10 - 65*x1^9 + 18*x1^8 - 2*x1^7)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^4 - 3*x1^3 - x1^2 + 3*x1 - 1, x1^3 - x1^2 - 2*x1 + 1, x1^2 - 3*x1 + 1, x1^2 + x1 - 1, x1 + 1, x1^3 - 2*x1^2 - x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^3 - x1^2 + 2*x1 - 1]