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