The realization space is
  [0   1   1   x1 - 2   0   0                 0   1    1        x1 - 2        x1^2 - 3*x1 + 2]
  [1   0   1       -1   1   0   x1^2 - 3*x1 + 2   1   x1   x1^2 - 2*x1   x1^3 - 3*x1^2 + 2*x1]
  [1   0   1       -1   0   1                -1   0    1            -1                    -x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^8 - 10*x1^7 + 44*x1^6 - 112*x1^5 + 182*x1^4 - 196*x1^3 + 139*x1^2 - 60*x1 + 12)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - 2*x1 + 2, x1^3 - 4*x1^2 + 6*x1 - 2, x1^2 - 3*x1 + 3, x1 - 2]