Documentation

Mathematica Teacher's Edition

Built-in Functions

Programming

Rule Application

ReplaceRepeated

expr //. rules repeatedly performs replacements until expr no longer changes.

expr //. rules effectively applies /. repeatedly, until the results it gets no longer change.
It performs one complete pass over the expression using /., then carries out the next pass.
You should be very careful to avoid infinite loops when you use the //. operator. The command x //. x -> x + 1 will, for example, lead to an infinite loop.
ReplaceRepeated will try to apply the rules you give a maximum of 65536 times.
See The Mathematica Book on the web: Section 2.4.1.
See also: ReplaceAll, Rule, Set, FixedPoint.

Further Examples