WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(activate(X)) activate(n__h(X)) -> h(activate(X)) f(X) -> g(n__h(n__f(X))) f(X) -> n__f(X) h(X) -> n__h(X) - Signature: {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(f) = {1}, uargs(h) = {1} Following symbols are considered usable: {activate,f,h} TcT has computed the following interpretation: p(activate) = [3] x1 + [8] p(f) = [1] x1 + [2] p(g) = [0] p(h) = [1] x1 + [2] p(n__f) = [1] x1 + [1] p(n__h) = [1] x1 + [1] Following rules are strictly oriented: activate(X) = [3] X + [8] > [1] X + [0] = X activate(n__f(X)) = [3] X + [11] > [3] X + [10] = f(activate(X)) activate(n__h(X)) = [3] X + [11] > [3] X + [10] = h(activate(X)) f(X) = [1] X + [2] > [0] = g(n__h(n__f(X))) f(X) = [1] X + [2] > [1] X + [1] = n__f(X) h(X) = [1] X + [2] > [1] X + [1] = n__h(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))