The realization space is
  [1   1   x1^2 - x1 - 1   0   0   1   x1 + 1        x1^2 - x1 - 1        0      1      x1 + 1]
  [1   0            x1^2   1   0   1        0                 x1^2   x1 + 1   x1^2   x1^2 + x1]
  [0   0               0   0   1   1     x1^2   x1^4 - x1^3 - x1^2       x1   x1^2        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^11 + 9*x1^10 + 14*x1^9 + 5*x1^8 - 10*x1^7 - 13*x1^6 - 6*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1 - 1, x1 - 2, x1^3 - 3*x1 - 1, x1^2 - 2*x1 - 1, x1^2 - x1 - 1, x1^3 - x1^2 - x1 - 1, x1^4 - x1^3 - 2*x1^2 + 1]