The realization space is
  [1   1   0   x1 - 1   0   1   x1^2 + x1 - 1   1               0    1          x1 - 1]
  [1   0   1      -x1   0   1   x1^2 + x1 - 1   0   x1^2 + x1 - 1   x1   x1^2 + x1 - 1]
  [0   0   0        0   1   1     2*x1^2 - x1   1       x1^2 - x1   x1       x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^8 + 5*x1^7 - 4*x1^6 - 3*x1^5 + 16*x1^4 - 25*x1^3 + 19*x1^2 - 7*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, x1^2 + x1 - 1, x1^2 - 3*x1 + 1, x1^2 + 2*x1 - 1, 3*x1 - 2, 2*x1^2 - 1]