The realization space is
  [1   1         1   0   1   0                 1         1                       x2    1    0]
  [0   1   -x1 + 1   1   0   0                 0   -x1 + 1          x1*x2 + x1 - x2    1    1]
  [0   0         0   0   1   1   x1*x2 + x1 - x2        x1   x1*x2^2 + x1*x2 - x2^2   x1   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[x1 - x2, x1, x2 - 1, x2, x1 - x2 - 1, x1 - 1, x1*x2 + x1 - x2, x2 + 1, x1*x2 - x2 - 1, x1*x2 + x1 - 2*x2, x1*x2^2 - x1*x2 - x1 - x2^2 + 2*x2, x1*x2 + x1 - x2^2 - 2*x2, x1*x2 - x2 + 1, x1 - 2, x1*x2^2 + 2*x1*x2 + x1 - x2^2 - 2*x2, 2*x1*x2 + x1 - 2*x2]