  The termination method of weakly monotonic algebras, which has been defined
for higher-order rewriting in the HRS formalism, offers a lot of power, but has
seen little use in recent years. We adapt and extend this method to the
alternative formalism of algebraic functional systems, where the simply-typed
lambda-calculus is combined with algebraic reduction. Using this theory, we
define higher-order polynomial interpretations, and show how the implementation
challenges of this technique can be tackled. A full implementation is provided
in the termination tool WANDA.
