The realization space is
  [1   1   0   -x2^2 + x2 - 1   0   1   1    0      -x2^2 + x2 - 1    1            1]
  [1   0   1              -x2   0   1   0    1                 -x2   x2           x2]
  [0   0   0                0   1   1   1   x1   -x2^3 + x2^2 - x2   x2   -x2^2 + x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x2 - 1, x2, x1*x2 - x1 + x2^2 - x2 + 1, x1 + x2, x1 + x2 - 1, x1, x1*x2 + x2^2 - x2 + 1, x2^2 - x2 + 1, x1*x2 - x1 - x2, x1 - 1, x1*x2^2 - x1*x2 - x2^2 + x2 - 1, x1*x2 - x2 + 1, 2*x2 - 1, x1*x2^2 - 2*x1*x2 + x1 + x2^3 - x2^2 + x2, x1 - x2^2 + x2 - 1, x1*x2 - x2^3 + 2*x2^2 - 2*x2 + 1, x2^3 - 2*x2^2 + 3*x2 - 1, x1 + 1, x1*x2^2 - 2*x1*x2 + x1 - x2^2 + x2 - 1]