The realization space is
  [1   1   0   0        1    1   0       x1       x1                x1                x1]
  [1   0   1   1   x1 + 1   x1   0       x1        0         x1^2 + x1              x1^2]
  [1   0   1   0        1    0   1   x1 + 1   x1 + 1   x1^2 + 2*x1 + 1   x1^2 + 2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^6 + 5*x1^5 + 7*x1^4 + 5*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^2 + x1 + 1, x1 + 1, x1 + 2, x1, x1^2 + 2*x1 + 2, x1 - 1, 2, x1^3 + x1^2 + x1 - 1, x1^3 + 2*x1^2 + 3*x1 + 1, 2*x1 + 1, x1^3 + x1^2 - 1, x1^2 + 1]