The realization space is
  [1   1   0   0   1   1        0                  x1^2 - x1      x1 - 1              x1      x1^3 - 2*x1^2 + 2*x1 - 1]
  [1   0   1   0   1   0       x1                       x1^3        x1^2            x1^2                          x1^4]
  [0   0   0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^2 - x1   x1^2 - x1 + 1   x1^4 - 2*x1^3 + 2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^13 + 8*x1^12 - 26*x1^11 + 46*x1^10 - 49*x1^9 + 32*x1^8 - 12*x1^7 + 2*x1^6)
avoiding the zero loci of the polynomials
RingElem[x1^3 + x1^2 - 2*x1 + 1, x1, x1 - 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1 + 1, x1^2 - x1 + 1, 2*x1^4 - 3*x1^3 + 4*x1^2 - 3*x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1, 2*x1 - 1]