Split infinitives—did Old English have them?

I've read a few articles as well as questions on this site about splitting infinitives. In the Wikipedia article, it claims:

In Old English, infinitives were single words ending in -n or -an (compare modern Dutch and German -n, -en). Gerunds were formed using "to" followed by a verbal noun in the dative case, which ended in -anne or -enne (e.g. tō cumenne = "coming, to come").

I read a bit on the use of infinitives in Old English; apparently, Old English has a to-infinitive that became Modern English infinitive. For example, the following sentence from (I think) Alfred's English translation of "Consolation of Philosophy":

he wilnað good to habbanne ond mid goode to bionne.

"He wills good to have and mid good to be"

Since the infinitives, "to habbanne" and "to bionne" are also two words, did the English speakers back then ever think of putting an adverb between them? For example, would Alfred or Bede have written something along the line of this:

he wilnað good to ā habbanne ond mid goode to sælige bionne.

"He wills good to forever have and mid good to happily be"

It seems English texts from that time don't contain this kind of sentences, but would it have been considered correct?

What about other Germanic languages?

Solution 1:

A search of the York-Toronto-Helsinki Corpus of Old English Prose for the infinitive marker to followed by anything other than a non-finite verb form yields no relevant examples. This is consistent with the other modern West Germanic languages, where zu (in German) and te (in Dutch) can't be separated from the following non-finite verb. The same is true of the early West Germanic languages (Old High German, Old Saxon).

It's safe to say that Old English didn't have split infinitives. Though absence of evidence is not the same as evidence of absence, there are so many examples of to + infinitive constructions in these early languages that it seems incredibly unlikely that splitting the two was a grammatical possibility.