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