However, in the first pre-processing step we might have introduced some non-linear (copying) rules in N (see rule ( ) in Example 5), and it is known that "nondeterminism [in M ] followed by copying [in N ]" is a feature that prevents composition to work (Engelfriet, 1975;Baker, 1979).
our copying is very local and the copies are only used to project to different subtrees.