The analysis put forward in  combines Hinrichs and Nakazawa's analysis of the German verb cluster with an approach to word order that allows for orderings that do not respect constituent structure. Kathol not only focuses on German, but also extends the analysis to Dutch. Kathol's proposals are interesting for our purposes as he does not appeal to phrase structure to account for word order. Instead, word order constraints are formulated. These constraints can be adopted in our framework as well.
While Kathol accepts the left-branching analysis of the verb cluster argued for by Hinrichs and Nakazawa, he also observes that this analysis does not account for all the German data, and furthermore cannot easily be extended to Dutch. First, Kathol observes that the left-branching analysis of the verb cluster fails to account for examples such as (17), discussed by , where the auxiliary appears in so-called Zwischenstellung:
If the phrase entscheiden müssen has constituent status, as is the case in a left-branching analysis, this word order is clearly problematic.
Second, Kathol notes that a branching account of the Dutch verb cluster cannot account for examples of participle inversion. That is, an account which assumes that Dutch verb clusters are right-branching (i.e. they differ from the German verb cluster only in that argument-inheritance verbs normally precede the verbs they govern), cannot account for verb sequences such as gelezen moet hebben (read[psp] must[fin] have[inf]), where the governing modal moet interrupts the participle-auxiliary sequence gelezen hebben. The position of separable verb prefixes in Dutch is equally problematic for a branching analysis of the verb cluser.8
The conclusion drawn by Kathol from these examples is not that the branching analysis is wrong, but rather that the analysis must be extended to incorporate some notion of discontinuity. In particular, Kathol, following a proposal of  and an account of German word order based on the notion of topological field described in , assumes that the derivation of verb clusters by means of a binary rule schema leads to an ( word) order domain that is flat, i.e. in which all verbs that are present in the verb cluster are sisters. Order among sisters is constrained by linear precedence (LP) statements. An example of a word order domain is given in (18).
Note that in the derivation of this domain, the elements finden and können are combined first, with wird taking this constituent as verbal complement, after which the NP's are added. The labels cf, mf, and vc refer to the topological fields complementizer field, Mittelfeld, and verb cluster. LP-constraints ensure that cf elements must precede mf elements, and that mf elements must precede vc elements. Word order within the vc field is determined by a feature GVOR (governor). The value of this feature and associated LP constraints determine whether a governed verb must precede or follow its governor, and whether a governed verb is necessarily adjacent to its governor. These constraints are dealt with in detail in the next section.
Note that there is a similarity between the word order domain constructed here and the `flat' VP's produced by the HEAD-COMPLEMENT schema in (4). In both cases, the elements which can be ordered relative to each order by means of word order constraints are roughly the same (ignoring the treatment of complementizers and possibly the subject). This suggests that the word order constraints proposed by Kathol may carry over to an approach which derives `flat' word order domains directly.