Overpass turbo: runtime error: Query timed out in "query" - What to do?

I like to download all places(nodes) which are tagged in osm with highway"="services and which contains "Raststätte" in the name value, which have a maximal distance to a motorway of 100 meter.

When I run my query on a smaller area it work fine but with this I get a error message like this:

An error occured during the execution of the overpass query! This is what overpass API returned:

runtime error: Query timed out in "query" at line 17 after 199 seconds.

Below is my querry:

[bbox:45.0,4.7,50.2,9.3];

(

  node["name"~"Raststätte"];   (way["name"~"Raststätte"];>;);   (relation["name"~"Raststätte"];>;);
     node["highway"="services"];   (way["highway"="services"];>;);   (relation["highway"="services"];>;); )->.rasten;

way(around.rasten:100)["highway"="motorway"]
->.motorway;

( node.rasten(around.motorway:100);   way.rasten(around.motorway:100);   rel.rasten(around.motorway:100);  )->.matchingRasten;

(.matchingRasten;); out body; (._;>;); out skel qt;

What possibility I have to solve this problem?