This specification describes a system and process for treating waste, for example municipal solid waste (MSW) or post-recycling municipal solid waste. The system includes a press and a pulper. The press is adapted to provide a wet fraction of the waste suitable for anaerobic digestion and rejects. The pulper is adapted to receive the rejects and produce pulp. The pulper may be, for example, a drum pulper. In the process, waste is separated into a press into an organic fraction and rejects. The organic fraction is treated by way of anaerobic digestion. The rejects are separated, optionally in a drum pulper, to produce a fraction containing pulp. The pulp can be re-used to make paper or other products. In some case, 70% or more or 80% or more of MSW can be diverted from landfill.