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