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