The realization space is
  [1   0   1     1   0   1   x1 + 1    0         1     1      x1 + 1]
  [0   1   1   -x1   0   0        0    1         1   -x1         -x1]
  [0   0   0     0   1   1    -x1^2   -1   -x1 - 1    x1   x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 + 4*x1^9 + 5*x1^8 + 6*x1^7 + 4*x1^6 + x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 + 1, x1 + 1, x1^2 - x1 - 1, 2, 3*x1^2 + 3*x1 + 1, 2*x1^2 + 2*x1 + 1, x1^2 + x1 + 1, x1 + 2]