Let me make the example more concrete. Say O1 gets as input a data stream T1
which it splits into two using some function and produces DataStreams of
type T2 and T3, each of which are partitioned by the same key function TK.
Now after O2 processes a stream, it could sometimes send the stream to O3
(T4) using the same key function again. Now I want to know whether: 

1. Data from streams T3 with key K and T4 with key K end up affecting the
state variables for the same key K or different. I would think that would be
the case but wanted a confirmation
2. An explicit join is needed or not, i.e. whether this will achieve what I
want:

result2 = T1.filter(fn2).keyBy(TK).map(richfn2).keyBy(TK).map(whatever O3
does)
result3 = T1.filter(fn3).keyBy(TK).map(whatever O3 does)




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