The realization space is
  [1   0   1   -x1^2 + 2*x1 + 1   0   1    0   x1^2 - 2*x1   -x1^2 + 2*x1 + 1     1     1]
  [0   1   1         -x1^2 + x1   0   0    1   x1^2 - 2*x1         -x1^2 + x1   -x1   -x1]
  [0   0   0                  0   1   1   -1             1             x1 - 1     1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 6*x1^7 - 11*x1^6 + 4*x1^5 + x1^4 + 10*x1^3 - 5*x1^2 - 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1 + 1, x1 - 2, x1^3 - 2*x1^2 - 1, x1 - 3, 2, x1^2 - 2*x1 - 1, x1^2 - x1 - 1]