Tight bounds for HTN planning with task insertion

Hierarchical Task Network (HTN) planning with Task Insertion (TIHTN planning) is a formalism that hybridizes classical planning with HTN planning by allowing the insertion of operators from outside the method hierarchy. This additional capability has some practical benefits, such as allowing more flexibility for design choices of HTN models: the task hierarchy may be specified only partially, since "missing required tasks" may be inserted during planning rather than prior planning by means of the (predefined) HTN methods. While task insertion in a hierarchical planning setting has already been applied in practice, its theoretical properties have not been studied in detail, yet - only EXPSPACE membership is known so far. We lower that bound proving NEXPTIME-completeness and further prove tight complexity bounds along two axes: whether variables are allowed in method and action schemas, and whether methods must be totally ordered. We also introduce a new planning technique called acyclic progression, which we use to define provably efficient TIHTN planning algorithms.