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