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In the dependently typed functional programming language Agda one can easily mix induction and coinduction. The implementation of the termination/productivity checker is based on a simple extension of a termination checker for a language with inductive types. However, this simplicity comes at a price: only types of the form X .Y .F X Y can be handled directly, not types of the form Y .X .F X Y . We explain the implementation of the termination checker and the ensuing problem.

Termination Checking in the Presence of Nested Inductive and Coinductive Types