The realization space is
  [1   1   0   x1 + 1   0   1      1   1        0      x1 + 1]
  [0   1   1       x1   0   0      0   1        1          x1]
  [0   0   0        0   1   1   x1^2   1   x1 + 1   x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^9 + 4*x1^8 + 5*x1^7 + x1^6 - 3*x1^5 - 4*x1^4 - 3*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, x1, x1 - 1, x1^2 + x1 - 1, x1^2 + x1 + 1, x1 + 2]