The realization space is
  [1   0   1   0   1    0           1          1           1      1      3]
  [0   1   1   0   0    1           1   2*x1 - 1    2*x1 - 1     -1      1]
  [0   0   0   1   1   -1   -3*x1 + 2         x1   -3*x1 + 2   3*x1   3*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^2 - 3*x1 + 1, -6*x1^3 - 2*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[2, 3, x1, 3*x1 - 2, 3*x1^2 - 6*x1 + 2, 3*x1^2 - 1, 2*x1 - 1, 3*x1 - 1, x1 - 1, 3*x1 + 1]