The realization space is
  [1   0   1     1   0   1        1    0    0    1]
  [0   1   1   -x1   0   0        0    1    1    1]
  [0   0   0     0   1   1   x1 + 1   -1   x1   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 + 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, 2*x1 + 1, x1 - 1]