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*x1^6 - 28*x1^5 + 31*x1^4 - 20*x1^3 + 7*x1^2 - x1)
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]