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