  Generalization techniques have many applications, including template
construction, argument generalization, and indexing. Modern interactive provers
can exploit advancement in generalization methods over expressive type theories
to further develop proof generalization techniques and other transformations.
So far, investigations concerned with anti-unification (AU) over
$\lambda$-terms and similar type theories have focused on developing algorithms
for well-studied variants. These variants forbid the nesting of generalization
variables, restrict the structure of their arguments, and are \textit{unitary}.
Extending these methods to more expressive variants is important to
applications. We consider the case of nested generalization variables and show
that the AU problem is \textit{nullary} (using \textit{capture-avoiding}
substitutions), even when the arguments to free variables are severely
restricted.
