Join has cross-product in SPARQL query - sparql

Question

I am trying to come up with a trivial minimal functional example of a federated query not using any web interface or something, but a local query engine (in my case AG free tier).
Now this at least doesn't throw any errors and returns stuff, but I'm getting a warning that the query contains a cross-product. Now I guess the problem is that there is nothing that actually relates the results from the two endpoints.
join has cross-product. Unique LHS variables: ?actor_1_1, ?birthDate, ?spouseURI_1_2, ?spouseName; Unique RHS variables ?actor_2_1, ?gender
But how do I relate them then? In a generic manner, since I guess this information needs to be passed to the query-resolver, and eventually I'll query other databases.
PREFIX dbpo: <http://dbpedia.org/ontology/>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX wdt: <http://www.wikidata.org/prop/direct/>
SELECT ?birthDate ?spouseName ?gender {
{ SERVICE <https://dbpedia.org/sparql>
{ SELECT ?birthDate ?spouseName WHERE {
?actor rdfs:label "Arnold Schwarzenegger"#en ;
dbpo:birthDate ?birthDate ;
dbpo:spouse ?spouseURI .
?spouseURI rdfs:label ?spouseName .
FILTER ( lang(?spouseName) = "en" )
}
}
}
{ SERVICE <https://query.wikidata.org/sparql>
{ SELECT ?gender WHERE {
?actor wdt:P1559 "Arnold Alois Schwarzenegger"#de .
?actor wdt:P21 ?gender .
}
}
}
}
I'd appreciate any help here, I haven't had as hard a time getting into a subject since forever.