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