Hi Mira:

I am still thinking about adjusters and visitors ...

I still tend to distinguish between visitors and adjusters. 
It is good to call them both APPCs but there is still
a difference:

Visitors:
one strategy in interface
Attached with traversal ("during") to a class (ConnectivityAndCycleCheck below)

Adjusters:
several strategies in interface
Attached without traversal ("during") to a class (Pricing below)

The insight is that in order to add one method to a class we 
express all the baggage which comes along as an APPC.

Quote::+{Float negPrice() = Pricing with {Renaming}};

Network::+{connectivityAndCycleCheck() = 
  ConnectivityAndCycleCheck during s1 with {Renaming}}

Is "during" just a way to influence the traversal from the outside?

So what is the difference between an APPC which is intended to be used
with "during" and one without "during"?

with "during":
also might need obligations although graph example does not show them.
no role names needed?
one traversal per APPC. Traversals of composed APPC
need to be subtraversals of each other.

without "during":
have role names available defined through strategies.
many traversals

So my point is: we cannot take any adjuster X
and use it with during:

X during s1 with {Renaming}

X must have a distinguished strategy (maybe the first) to match with s1.

-- Karl