The realization space is
  [1   1   0   0          x1          x1   0        1    1                 x1          x1]
  [1   0   1   1     -x1 - 2   -2*x1 - 2   0        1    0            -x1 - 2   -2*x1 - 2]
  [0   0   0   1   -2*x1 - 2   -2*x1 - 2   1   x1 + 1   x1   -x1^2 - 3*x1 - 2        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^2 + 6*x1 + 4)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, 5*x1^2 + 8*x1 + 4, 3*x1^2 + 4*x1 + 2, x1 + 2, 2*x1^2 + 3*x1 + 2, 2, x1^2 + 2*x1 + 2, x1, 3*x1 + 2, x1^3 + 6*x1^2 + 8*x1 + 4, 3*x1 + 4]