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