The realization space is
  [1   0   1        1   0   1                x1    0    1         1        x1 + 2]
  [0   1   1   x1 + 1   0   0                 0    1    1    x1 + 1     -x1^2 + 1]
  [0   0   0        0   1   1   x1^2 + 2*x1 + 1   -1   x1   -x1 - 1   x1^2 + 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 - 5*x1^7 - 11*x1^6 - 13*x1^5 - 4*x1^4 + 9*x1^3 + 14*x1^2 + 9*x1 + 2)
avoiding the zero loci of the polynomials
RingElem[2*x1 + 1, x1 + 1, x1^2 + x1 + 1, x1, x1 - 1, x1^3 + 2*x1^2 + 4*x1 + 2, x1^4 + 2*x1^3 + 2*x1^2 + 3*x1 + 1, x1^3 + 3*x1^2 + 4*x1 + 1, x1 + 2]