The realization space is
  [1   0   1    1   1   0   -x1 + 1   1               1   0            1]
  [0   1   1   x1   0   0         0   1   x1^2 - x1 + 1   1           x1]
  [0   0   0    0   1   1     -x1^2   1      -x1^2 + x1   1   -x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^11 + 8*x1^10 - 13*x1^9 + 10*x1^8 - x1^7 - 5*x1^6 + 4*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1 - 1, x1^2 + 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, 2, 2*x1 - 1, x1^2 + x1 - 1]