The realization space is
  [1   1   0   0        1    1   0   x1 + 1   x1^2 - 1    x1^2 - 1]
  [1   0   1   1   x1 + 1   x1   0   x1 + 1          0   x1^3 - x1]
  [1   0   1   0        1    0   1        1         x1          x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^13 + x1^12 + 5*x1^11 - 3*x1^10 - 9*x1^9 + 2*x1^8 + 6*x1^7 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 - 1, x1 - 1, x1 - 2, x1^2 - 2, x1 + 1]