For example, one way to binarize the permutation {2, 1, 3, 4} is to introduce a proper split into {2, 1; 3, 4}, then recursively another proper split of {2, 1} into {2; 1} and {3, 4} into {3; 4}.
the permutation {2, 4, 1, 3} is non-binarizable.