The realization space is
  [1   1   0   x1^2 + x1 - 1   0   1   1        0      x1^2 + x1 - 1    1          x1 - 1]
  [1   0   1     x1^3 - x1^2   0   1   0   x1 - 1        x1^3 - x1^2   x1       x1^2 - x1]
  [0   0   0               0   1   1   1       x1   x1^3 + x1^2 - x1   x1   x1^2 + x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^14 - 5*x1^13 + 15*x1^11 - 21*x1^10 + 3*x1^9 + 18*x1^8 - 18*x1^7 + 7*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1 - 1, x1, x1^3 + x1^2 + x1 - 1, x1^5 - x1^4 - 2*x1^3 - x1^2 + 3*x1 - 1, x1^3 - 2*x1^2 - x1 + 1, x1^2 + x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1 + 1, x1^4 - x1^3 - x1^2 - x1 + 1]