The realization space is
  [1   1   0   0        1    1   0   x1        x1          x1              x1^2]
  [1   0   1   1   x1 + 1   x1   0   x1         0   x1^2 + x1              x1^3]
  [0   0   0   1       x1   x1   1   -1   -x1 - 1     -x1 - 1   x1^3 - x1^2 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^11 + 2*x1^9 - 3*x1^8 + x1^7 - 3*x1^6 + x1^5 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^3 - 2, x1 - 1, x1^2 + x1 + 1, x1 + 1, x1^3 + x1 - 1, x1^3 + x1^2 + x1 - 1, x1^2 + 1, x1^2 - x1 + 1, x1, x1^3 - x1^2 - 1, x1^3 + x1^2 - 1]