The realization space is
  [1   0   1    1   0   1        0    1         1         1]
  [0   1   1   -1   0   0        1    1   -x1 + 1   -x1 + 1]
  [0   0   0    0   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 (x1^2 - 2*x1 + 2, 2*x1^3 - 6*x1^2 + 8*x1 - 4)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - x1 + 1, 2, x1^2 - 3*x1 + 3]