The realization space is
  [1   1   0                  1   0   1   1        0                  1              1              1]
  [0   1   1   -x1^2 + 3*x1 - 2   0   0   1   x1 - 1   -x1^2 + 3*x1 - 2   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0                  0   1   1   1       -1             x1 - 1         x1 - 1             x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, x1^2 - 2*x1 + 2, x1^2 - 3*x1 + 1, x1^2 - x1 + 1, x1^2 - 3*x1 + 3, x1^2 - x1 - 1, x1^3 - 4*x1^2 + 7*x1 - 5]