We present a polynomial time algorithm for deciding confluence of
ground term rewrite systems. We generalize the decision procedure
to get a polynomial time algorithm for deciding confluence of
left-linear right-ground term rewrite systems.
These two problems have been open for a long time and only recently
the first result was independently announced in \cite{ComonGodoyNieuwenhuis01:FOCS}.
Our decision procedure is based on the concepts of
abstract congruence closure \cite{BachmairTiwari00:CADE} and
abstract rewrite closure \cite{Tiwari01:FSTTCS}.
