WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} + 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(d) = {1} Following symbols are considered usable: {activate,c,d,f,h} TcT has computed the following interpretation: p(activate) = [1] x1 + [8] p(c) = [1] x1 + [11] p(d) = [1] x1 + [2] p(f) = [1] x1 + [11] p(g) = [0] p(h) = [1] x1 + [15] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [5] Following rules are strictly oriented: activate(X) = [1] X + [8] > [1] X + [0] = X activate(n__d(X)) = [1] X + [8] > [1] X + [2] = d(X) activate(n__f(X)) = [1] X + [13] > [1] X + [11] = f(X) c(X) = [1] X + [11] > [1] X + [10] = d(activate(X)) d(X) = [1] X + [2] > [1] X + [0] = n__d(X) f(X) = [1] X + [11] > [1] X + [5] = n__f(X) f(f(X)) = [1] X + [22] > [16] = c(n__f(g(n__f(X)))) h(X) = [1] X + [15] > [1] X + [11] = c(n__d(X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))