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