The realization space is
  [1   1   0   x1^2 - 2*x1   0   1   1             0               x1^2 - 2*x1    1        x1 - 2]
  [1   0   1           -x1   0   1   0        x1 - 1                       -x1   x1        x1 - 1]
  [0   0   0             0   1   1   1   x1^2 - 2*x1   -x1^4 + 4*x1^3 - 4*x1^2   x1   x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 9*x1^7 - 34*x1^6 + 71*x1^5 - 89*x1^4 + 66*x1^3 - 26*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - 3*x1 + 1, x1 - 1, x1 - 2, x1 - 3, x1^3 - 3*x1^2 + 2*x1 - 1, 2*x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 1, x1^2 - x1 - 1]