The realization space is
  [1   1   0   0        1    1   0   x1 - 2   x1 - 2            x1 - 2        x1 - 2]
  [0   1   1   1   x1 - 1   x1   0        0   x1 - 2   x1^2 - 3*x1 + 2   x1^2 - 2*x1]
  [0   1   1   0        0    1   1       x1       x1         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 - 12*x1^5 + 28*x1^4 - 34*x1^3 + 24*x1^2 - 8*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 2*x1 + 2, 2, x1^2 - 3*x1 + 3, x1^2 - x1 + 1, x1 - 2, x1^2 - x1 + 2, x1^2 - 2, x1^3 - 2*x1^2 + 2*x1 - 2, x1^2 - 3*x1 + 4]