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