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