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