The arity restriction implies that the category of every node u on the spine properly between f and r takes the form Xˇu, jˇuj > 0, and that the category at the root takes the form Xˇ, jˇj 0.
the category X is never exposed in c, except perhaps at r. As we will see in Section 5.4, this property, together with a careful selection of "split nodes", will allow us to decompose derivations into smaller, shareable parts.