Automata allow many constraints on sequences of variables to be specified in a high-level way for constraint programming solvers. An automaton with accumulators induces a decomposition of the specified constraint into a conjunction of constraints with existing inference algorithms, called propagators. Towards improving propagation, we design a fully automated tool that selects, in an off-line process, constraints that are implied by such a decomposition. We show that a suitable problem-specific choice among the tool-selected implied constraints can considerably improve solving time and propagation, both on a decomposition in isolation and on entire constraint problems containing the decomposition.