The realization space is
  [1   0   1         1   0   1   x1^2 - 4*x1 + 4    0   x1 - 2         1         1]
  [0   1   1   -x1 + 3   0   0                 0    1   x1 - 2   -x1 + 2   -x1 + 2]
  [0   0   0         0   1   1           -x1 + 3   -1       -1         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 - 1, x1 - 2, x1^2 - 3*x1 + 1, 2, 2*x1 - 5, x1 - 3, x1^3 - 4*x1^2 + 5*x1 - 3, x1^3 - 3*x1^2 + 3, x1, 2*x1^2 - 8*x1 + 7]