The realization space is
  [1       x1   1   0   1   0    x1 - 1        1    x1 - 1          x1    0]
  [1   x1 + 1   0   1   1   0    x1 - 1        0   -x1 - 1      x1 + 1    1]
  [0        0   0   0   1   1   -x1 - 1   x1 + 1   -x1 - 1   x1^2 + x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^9 - 12*x1^8 - 28*x1^7 - 30*x1^6 - 10*x1^5 + 8*x1^4 + 8*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1 - 1, x1^2 + 1, 2*x1 + 1, 2, 2*x1^2 - 1, 2*x1 - 1]