  In this note we give a simple unifying proof of the undecidability of several
diagrammatic properties of term rewriting systems that include: local
confluence, strong confluence, diamond property, subcommutative property, and
the existence of successor. The idea is to code configurations of Turing
Machines into terms, and then define a suitable relation on those terms such
that the termination of the Turing Machine becomes equivalent to the
satisfiability of the diagrammatic property.
