The realization space is
  [1   1   0   -2*x1 + 1   0   1   1          0   -2*x1^2 + 3*x1 - 1   x1 - 1      -2*x1 + 1]
  [1   0   1         -x1   0   1   0         x1           -x1^2 + x1      -x1          -x1^2]
  [0   0   0           0   1   1   1   2*x1 - 1          2*x1^2 - x1      -x1   -2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-12*x1^8 + 52*x1^7 - 91*x1^6 + 82*x1^5 - 40*x1^4 + 10*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 2, x1 - 1, 2*x1 - 1, x1^2 + x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1 - 1, 2]