  Systems of wave equations may fail to be globally well posed, even for small
initial data. Attempts to classify systems into well and ill-posed categories
work by identifying structural properties of the equations that can work as
indicators of well-posedness. The most famous of these are the null and weak
null conditions. As noted by Keir, related formulations may fail to properly
capture the effect of undifferentiated terms in systems of wave equations. We
show that this is because null conditions are good for categorising behaviour
close to null infinity, but not at timelike infinity. In this paper, we propose
an alternative condition for semilinear equations that work for
undifferentiated non-linearities as well. We illustrate the strength of this
new condition by proving global well and ill-posedness statements for some
systems of equation that are not critical according to the our classification.
Furthermore, we given two examples of systems satisfying the weak null
condition with global ill-posedness due to undifferentiated terms, thereby
disproving the weak null conjecture as stated in [DP18].
