The realization space is
  [1   1   0   x1 - 1   0   1   1                 0      x1 - 1         -3*x1 + 2    1]
  [0   1   1    -x1^2   0   0   1   x1^2 - 2*x1 + 1       -x1^2   x1^2 - 2*x1 + 1   x1]
  [0   0   0        0   1   1   1    -x1^2 - x1 + 1   x1^2 - x1    -x1^2 - x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^13 + 25*x1^12 - 68*x1^11 + 86*x1^10 - 63*x1^9 + 29*x1^8 - 8*x1^7 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1^2 + x1 - 1, x1 - 1, 2*x1^2 - 1, 3*x1 - 2, 2*x1^3 - 2*x1^2 + 2*x1 - 1, 5*x1^3 - 4*x1^2 - x1 + 1, 5*x1^3 - 7*x1^2 + 4*x1 - 1, x1^3 + 3*x1^2 - 4*x1 + 1, x1^4 + 2*x1^3 - 4*x1^2 + 3*x1 - 1]