  We present a bounded equivalence verification technique for higher-order
programs with local state. This technique combines fully abstract symbolic
environmental bisimulations similar to symbolic game semantics, novel up-to
techniques, and lightweight state invariant annotations. This yields an
equivalence verification technique with no false positives or negatives. The
technique is bounded-complete, in that all inequivalences are automatically
detected given large enough bounds. Moreover, several hard equivalences are
proved automatically or after being annotated with state invariants. We realise
the technique in a tool prototype called Hobbit and benchmark it with an
extensive set of new and existing examples. Hobbit can prove many classical
equivalences including all Meyer and Sieber examples.
