The realization space is
  [1   1   0   0         1         1   0    1        1         1     1]
  [0   1   1   1   -x1 - 1       -x1   0    0        1   -x1 - 1   -x1]
  [0   0   0   1   -x1 - 1   -x1 - 1   1   x1   x1 + 1    x1 + 1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^5 + 14*x1^4 + 16*x1^3 + 8*x1^2 + 2*x1)
avoiding the zero loci of the polynomials
RingElem[2, x1 + 1, 2*x1 + 1, x1, x1 + 2, 2*x1 + 3, 2*x1^2 + 4*x1 + 1, x1^2 + x1 - 1, x1 - 1, x1^2 + 3*x1 + 1]