Resource Control Graphs are an abstract representation of programs. Each state of the program is abstracted by its size, and each instruction is abstracted by the effects it has on the state size whenever it is executed. The abstractions of instruction effects are then used as weights on the arcs of a program’s Control Flow Graph. Termination is proved by finding decreases in a well-founded order on state-size, in line with other termination analyses, resulting in proofs similar in spirit to those produced by Size Change Termination analysis. However, the size of states may also be used to measure the amount of space consumed by the program at each point of execution. This leads to an alternative characterisation of the Non Size Increasing programs, i.e. of programs that can compute without allocating new memory. This new tool is able to encompass several existing analyses and similarities with other studies suggest that even more analyses might be expressable in this framework, thus giving hopes for a generic tool for studying programs.

f(0, y) = g(y) f(x + 1, y) = h(x, y, f(j1(x), y),..., f(jk(x), y) where g, h, j1,..., jk are primitive recursive and ji(x) ≤ x for i ∈ {1,..., k} , are themselves primitive recursive. A similar remark holds for recursion with parameter substituhal-00642731,