Mobile computations example

In an attempt to use a new Web diagramming tool (Gliffy), I just put into a simple time-line an example of what I want to make possible with my project:

Basically it is a client that starts by asking the server for a specific code execution. the server, however, opts to stop the execution midway, and transfers its work in progress to the client. Now a couple of noteworthy behaviors can be verified on the client:

1. The client finishes the remainder of the computation, not contacting the server anymore in the process;
2. The client now knows how to make that kind of computations, so it will never bug the server again for that.

I'll welcome any comment on this idea, specially constructive criticism :)