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