Before presenting the actual binarization, we determine the parsing complexity of the binarized grammar.
because the binarization preserves the fan-out of the original grammar, and because in a grammar with fan-out k, for concatenation functions conc : k 1 k 2 we have k 1 + k 2 − 1 ≤ k and for wrapping functions wrap : k 1 k 2 j we have k 1 + k 2 − 2 ≤ k, we can rewrite the general parsing complexities as c(conc : the maximal parsing complexity in the binarized grammar is 2k + 2; this is achieved by wrapping operations.