One aspect is a method for producing a first intermediate product. A feedstock is provided that comprises a first polyester. The feedstock is contacted with a first amount of a first organic compound in a volume section V.sub.1 to obtain a first initial mixture. The first amount is in the form of a liquid. The first polyester is contacted with a further organic compound in a volume section V.sub.3 to obtain a further initial mixture. A weight average molar mass of the first polyester is reduced in the volume section V.sub.3 to obtain a first intermediate mixture. The first intermediate mixture comprises a first intermediate product and the further organic compound. The first polyester is transported in a first direction that is at least partially opposite the direction of gravity when the first polyester has an intrinsic viscosity that is larger than or equal to Y.sub.IV,1, where Y.sub.IV,1 is 0.10 dL/g, and in further direction that is at least partially along the direction of gravity when the first polyester has an intrinsic viscosity that is less than or equal to Y.sub.IV,2, where Y.sub.IV,2 is 0.09 dL/g.

A method and system for separating materials using a combination of screen beds and gravity separators is included. Materials are collected from the waste stream and pass through a screen. The collected larger materials are then directed to a first gravity separator with a specific gravity. Plastics are recovered and residual metals are recovered.