The realization space is
  [1   1         1   0   1   0   x1^2 - x1 - 1         1   -x1^3 + x1^2 + x1    1                 0]
  [0   1   -x1 + 1   1   0   0               0   -x1 + 1          -x1^2 + x1    1   x1^2 - 2*x1 + 1]
  [0   0         0   0   1   1       x1^2 - x1        x1        -x1^3 + x1^2   x1      -x1^2 + 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^15 - 7*x1^14 + 19*x1^13 - 24*x1^12 + 12*x1^11 + x1^10 - 2*x1^9)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 - 1, 2*x1^2 - 4*x1 + 1, x1 - 2, x1^3 - 2*x1^2 + x1 - 1, x1^3 - x1^2 - 1, x1 - 1, 2*x1 - 3, x1^3 - 2*x1^2 - x1 + 3, x1^2 - 2*x1 - 1]