Let 
and 
be two rules of a term
rewriting system, and suppose these rules have no variables in common. If they
do, rename the variables. If 
is a subterm of 
(or the term 
itself) such that it is not a variable, and the pair 
is unifiable
with the most general unifier 
, then 
and the result of replacing 
in 
by 
are called a critical pair.
The fact that all critical pairs of a term rewriting system are joinable, i.e., can be reduced to the same expression, implies that the system is locally confluent.
For instance, if 
and 
,
then 
and 
would form a critical pair because they can both be derived from 
.
Note that it is possible for a critical pair to be produced by one rule, used in two different ways. For instance, in the string rewrite "AA" -> "B", the critical pair ("BA", "AB") results from applying the one rule to "AAA" in two different ways.
