to be based
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to be based on
To rest on something as a foundation, to rely on something, or to proceed from something. It is always used with the preposition 'auf' and the dative.
Die Anklage basiert auf den Aussagen mehrerer Zeugen.
The accusation is based on the statements of several witnesses.
The verb 'basieren' (to be based) is almost always used with the preposition 'auf' and the dative. The structure is: something (nominative) is based on something (dative).
Der Film basiert auf einem Roman.
The film is based on a novel.
'Basieren' (to be based) is related to the noun 'die Basis' (the basis). If something is based on something, that thing is the conceptual foundation or starting point.
Seine Theorie basiert auf einer einfachen Annahme.
His theory is based on a simple assumption.
Common foundations on which something can be based are abstract concepts such as facts, data, an assumption, a theory, or a true story.
Die Studie basiert auf Daten von über 10.000 Teilnehmern.
The study is based on data from over 10,000 participants.
to build up
'aufbauen auf' and 'basieren auf' both have to do with a foundation or basis. 'basieren auf' means that something is based on a foundation or relies on it. 'aufbauen auf' is more active: you use an existing foundation and develop something further from it. Learners may confuse the words because both can be used with 'auf' and the dative. If you are only naming the basis, 'basieren auf' fits. If you want to show that something is developed further from it, 'aufbauen auf' is a better fit.
Die Entscheidung basiert auf den Ergebnissen der Umfrage.
The decision is based on the results of the survey.
Der zweite Kurs baut auf den Übungen aus dem ersten Kurs auf.
The second course builds on the exercises from the first course.