A new decidable problem, with applications

A number of decision problems that are unsolvable in general are solvable when restricted to systems with sufficiently simple "loop structure". Examples of such problems are the equivalence problems for flowchart schemata with nonintersecting loops and for the LOOP(l) programs of Meyer and Ritchie. We here present a theorem that gives a unifying view of the solvability of both of these problems, and also of a variety of other old and new solvable decision problems in automata theory, schematology, and logic.