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