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