The realization space is
  [1   0   1   1   x1 - 2    1   0   x1^2 - 3*x1 + 3                 0   x1^3 - 5*x1^2 + 9*x1 - 6        x1^2 - 3*x1 + 3]
  [0   1   1   1       -1   x1   0                 0   x1^2 - 3*x1 + 3           -x1^2 + 3*x1 - 3   x1^3 - 3*x1^2 + 3*x1]
  [0   0   0   1       -1    1   1                 1   x1^2 - 3*x1 + 2           -x1^2 + 3*x1 - 2                -x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 7*x1^7 - 23*x1^6 + 45*x1^5 - 57*x1^4 + 47*x1^3 - 24*x1^2 + 6*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - 2*x1 + 2, x1, x1 - 2, x1^2 - 3*x1 + 3, x1^4 - 5*x1^3 + 9*x1^2 - 7*x1 + 1, x1^3 - 3*x1^2 + 4*x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 3, x1^2 - x1 + 1, x1^3 - 5*x1^2 + 8*x1 - 5]