The realization space is
  [0   1   1   0   0   1   -x1   -x1^3 + x1^2 + x1   -x1^3 + x1^2 + x1     -x1   x1^4 - 2*x1^2 - x1]
  [1   1   0   1   0   0    -1              x1 + 1                   1      -1              -x1 - 1]
  [1   1   0   0   1   1     0                x1^2                x1^2   -x1^2                -x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^16 - 2*x1^15 + 2*x1^13 - x1^12)
avoiding the zero loci of the polynomials
RingElem[x1^3 - x1 - 1, x1^2 + x1 - 1, x1, x1 - 1, x1^3 + x1^2 - 2*x1 - 1, x1^2 - 2, x1 + 1, x1^2 - x1 - 1, x1^2 + x1 + 1, x1^3 - x1^2 + 1]