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   x1 + 1]
  [0   0   0        0   1   1   4*x1 + 3   -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 - 1, 48*x1^7 + 8*x1^6 - 56*x1^5 - 8*x1^4 + 8*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 3, x1 + 1, 2*x1 + 1, 2, 4*x1 + 3, 2*x1 - 1, 3*x1^2 + x1 - 1, 3*x1 + 2, 4*x1^2 + x1 - 1]