AUX2 AUX1 VERB3

[sylvainkahane]

In Wolof, there is one AUX which topicalizes its dependent: lemma=na. So when we have the order AUX na … VERB, na must be the head.
In other cases with two AUXs, the more distant AUX is the head.

[kimgerdes]

German auxiliaries have the following standard orders:

Er ist gekommen.
He has come
pron aux verb

in subordinate sentences it's inverted:

weil er gekommen ist.
because he come has
sconj pron verb aux

for the transfer grammars, we have to look at the double aux cases (pattern { VERB -[aux]-> AUX1 ; VERB -[aux]-> AUX2 ; })

always, the further away aux is the higher one.
if both aux are neighbors as in

er will gewusst haben, dass
he wants known have, that
pron aux1 verb aux2 sconj
'he wants to have known that'

the first aux is the higher aux.

We can look at some simple examples where the first aux is in V2 such as Er soll herausgefunden haben and many of the so-called Oberfeldumstellung: http://match.grew.fr/?corpus=UD_German-HDT@2.6&custom=5edfe0a1ab07d

The only exception is the Zwischenstellung:

dass er kommen hat können
that he come has can
that he verb aux1 aux2
that he was able to come

but I couldn't find a single example in the German treebanks as it's a dialectical variant.

Also, there is no case of 3 aux on the same verb: http://match.grew.fr/?corpus=UD_German-HDT@2.6&custom=5edfe592c2463

Can this rule of "furthest aux higher, left before right if equal distance" be integrated in the transfer grammar?