The realization space is
  [1   1   0                 x1   0   1   1        0                 x1         1]
  [0   1   1   -x1^2 + 2*x1 - 1   0   0   1   x1 - 1   -x1^2 + 2*x1 - 1   -x1 + 1]
  [0   0   0                  0   1   1   1      -x1               x1^2        x1]
in the multivariate polynomial ring in 1 variable over ZZ
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1]