Both numeric planning and Hierarchical Task Network (HTN) planning are highly expressive planning formalisms – at the cost of being undecidable in general. For both formalisms, decidable fragments are known. Studying these restricted fragments has lead to valuable insights, which ultimately gave rise to the development of new efficient planning algorithms.

We identify new decidable fragments of both numeric and HTN planning. For HTN planning, we introduce the fragments of one-hole-digging, initial, and final problems. The former restrict every task network to have at most one compound task, while the latter two restrict compound tasks to be order-minimal or order-maximal, respectively. For numeric planning, we introduce Positive Numeric Planning (PNP) where the value of numeric variables can only be non-negative. We determine the complexity of these fragments: they are Ackermann-complete – which is significantly more difficult than any prior known decidable fragment, but still barely decidable.