Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The success of such planners on many of the current benchmarks suggests that in those task’s state spaces relaxed goal distances yield a heuristic function of high quality. Recent work has revealed empirical evidence confirming this intuition, stating several hypotheses about the local search topology of the current benchmarks, concerning the non-existence of dead ends and of local minima, as well as a limited maximal distance to exits on benches. Investigating a large range of planning domains, we prove that the above hypotheses do in fact hold true for the majority of the current benchmarks. This explains the recent success of heuristic planners. Specifically, it follows that FF’s search algorithm, using an idealized heuristic function, is polynomial in (at least) eight commonly used benchmark domains. Our proof methods shed light on what the structural reasons are behind the topological phenomena, giving hints on how these phenomena might be automatically recognizable.