  In this paper, we analyze the complexity of functional programs written in
the interaction-net computation model, an asynchronous, parallel and confluent
model that generalizes linear-logic proof nets. Employing user-defined sized
and scheduled types, we certify concrete time, space and space-time complexity
bounds for both sequential and parallel reductions of interaction-net programs
by suitably assigning complexity potentials to typed nodes. The relevance of
this approach is illustrated on archetypal programming examples. The provided
analysis is precise, compositional and is, in theory, not restricted to
particular complexity classes.
