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