In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term rewrite system. Our analysis does not restrict the input rewrite system in any way so that rewrite systems may serve as abstractions of first-order, eagerly evaluated functional programs over user-defined inductive data-types. This facilitates integration in a general framework for resource analysis of programs. In particular, we have implemented the method and integrated it into our analysis tool TcT. Furthermore, we have coupled the established analysis with a complexity reflecting transformation from pure OCaml programs. This extends the provided analysis to a fully automated resource analysis of higher-order functional programs.