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