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