<s>
In	O
database	B-General_Concept
design	I-General_Concept
,	O
a	O
lossless	B-Algorithm
join	I-Algorithm
decomposition	I-Algorithm
is	O
a	O
decomposition	O
of	O
a	O
relation	O
into	O
relations	O
such	O
that	O
a	O
natural	O
join	O
of	O
the	O
two	O
smaller	O
relations	O
yields	O
back	O
the	O
original	O
relation	O
.	O
</s>
<s>
Let	O
be	O
a	O
set	O
of	O
functional	B-Application
dependencies	I-Application
on	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
the	O
decomposition	O
is	O
a	O
lossless-join	B-Algorithm
decomposition	I-Algorithm
of	O
if	O
at	O
least	O
one	O
of	O
the	O
following	O
functional	B-Application
dependencies	I-Application
are	O
in	O
+	O
(	O
where	O
+	O
stands	O
for	O
the	O
closure	O
for	O
every	O
attribute	O
or	O
attribute	O
sets	O
in	O
)	O
:	O
</s>
<s>
Let	O
be	O
the	O
set	O
of	O
functional	B-Application
dependencies	I-Application
.	O
</s>
<s>
is	O
a	O
superkey	O
in	O
,	O
meaning	O
we	O
have	O
a	O
functional	B-Application
dependency	I-Application
.	O
</s>
