Adaptable user interfaces (UI) have shown a great variety of advantages in human computer interaction compared to classic UI designs. We show how adaptable UIs can be built by introducing coloured Petri nets to connect the UI’s physical representation with the system to be controlled. UI development benefits from formal modelling approaches regarding the derived close integration of creation, execution, and reconfiguration of formal UI models. Thus, adaptation does not only change the physical representation, but also the connecting Petri net. For the latter transformation, we enhance the DPO rewriting formalism by using an order on the set of labels and softening the label-preserving property of morphisms, i.e., an element can also be mapped to another element if the label is larger. We use lattices to ensure correctness and state application conditions of rewriting steps. Finally we define an order compatible with our framework for the use in our implementation.