The realization space is
  [1   1         1   0   1   0   x1^2 - x1 - 1         1   x1^2 - x1 - 1    1    0]
  [0   1   -x1 + 1   1   0   0               0   -x1 + 1          x1 - 1    1    1]
  [0   0         0   0   1   1       x1^2 - x1        x1       x1^2 - x1   x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^10 + 6*x1^9 - 12*x1^8 + 6*x1^7 + 8*x1^6 - 8*x1^5 - x1^4 + 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 - 1, x1 + 1, x1^3 - x1^2 - 2*x1 + 1, x1^2 - 2, x1 - 2, x1^2 - 2*x1 - 1]