The realization space is
  [1   1   x1 + 1   0   1   0     2*x1 + 1   x1 + 1   2*x1^2 + 3*x1 + 1   x1 + 1    0]
  [0   1        1   1   0   0            0        1       x1^2 + x1 + 1   x1 + 1    1]
  [0   0        0   0   1   1   -x1^2 + x1       x1          -x1^3 + x1       x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^14 + 7*x1^13 + 15*x1^12 + 10*x1^11 - 5*x1^10 - 15*x1^9 - 11*x1^8 - 2*x1^7)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + x1 + 1, x1 + 1, x1 + 2, x1^2 - 2*x1 - 2, 2*x1 + 1, x1^3 - 3*x1 - 1]