The realization space is
  [1   0   1         1   0   1    1    0                  1         1         1]
  [0   1   1   -x1 + 3   0   0    0    1                  1   -x1 + 2   -x1 + 2]
  [0   0   0         0   1   1   x1   -1   -x1^2 + 2*x1 - 1         1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - 4*x1^2 + 5*x1 - 3, x1^6 - 6*x1^5 + 17*x1^4 - 28*x1^3 + 27*x1^2 - 14*x1 + 3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 - 2, x1^3 - 4*x1^2 + 4*x1 - 2, x1^2 - x1 + 1, x1^2 - 2*x1 + 2, 2, x1, x1^2 - 3*x1 + 1, x1 - 3, x1^2 - 3*x1 + 3, x1^3 - 3*x1^2 + 4*x1 - 3, 2*x1 - 3, x1^2 - x1 - 1, x1^3 - 5*x1^2 + 8*x1 - 5]