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