Abstract canonical systems and inference (ACSI) were introduced by Dershowitz and Kirchner to formalize the intuitive notions of good proof and good inference appearing typically in first-order logic or in Knuth-Bendix like completion procedures. Since this abstract framework is intended to be generic, it is of fundamental interest to show its adequacy to represent the main systems of interest. This has been done by Dershowitz for ground completion (where all equational axioms are ground) and was an open question for the general completion process. By showing that the standard completion (Knuth-Bendix) is an instance of the ACSI framework we close the question. For this purpose, two proof representations, proof terms and proofs by replacement, are compared to built a proof ordering that provides an instantiation adapted to the abstract canonical system framework.