The realization space is
  [1   0   1     1   0   1    0    1     1    1]
  [0   1   1   -x1   0   0    1    1   -x1   x2]
  [0   0   0     0   1   1   -1   x1    x1    1]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 - x1 - 1, x1^3*x2 + x1^2*x2^2 + x1^2*x2 - 2*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x2 + 1, x1, x1 - 1, x1*x2 + 1, x1 + x2, x2, x1 + 1, x1*x2 - 1, x2 - 1, x1^2 + x1*x2 - x1 - 1, x1 - x2, x1 + x2 + 1, 2*x1 + 1]