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