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