The realization space is
  [1   1   0      1   0   1   1            0      1   -x1^2 + x1 - 1              1]
  [1   0   1   x1^2   0   1   0   -x1^2 + x1   x1^2            -x1^2   -x1^3 + x1^2]
  [0   0   0      0   1   1   1            1     x1            -x1^2             x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^13 - 4*x1^12 + 6*x1^11 - 2*x1^10 - 7*x1^9 + 13*x1^8 - 11*x1^7 + 5*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1^4 - x1^3 + 2*x1 - 1, x1^2 - x1 + 1, x1 - 1, x1^2 - 2*x1 + 2, x1 + 1, x1^3 - x1^2 + 1, x1^2 + x1 - 1, x1^2 + x1 + 1, x1^2 + 1, x1^2 - x1 - 1]