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This work addressed how self-replicating molecules can evolve to become more complex. Subjecting a system in which two self-replicating molecules compete for a common food source to a regime in which they are both degraded leads to survival of the most complex of the two replicators, even though this replicator is less efficient at replicating. These results show that chemical fueling of a replication process can drive the complexification of the replicator. The more complex replicator is also more proficient at catalyzing a model reaction, showing that complexification can also enhance (catalytic) function.