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(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g} + 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}, uargs(f) = {1} Following symbols are considered usable: {activate,c,d,f,g,h} TcT has computed the following interpretation: p(activate) = [5] x1 + [4] p(c) = [5] x1 + [6] p(d) = [1] x1 + [1] p(f) = [1] x1 + [9] p(g) = [3] p(h) = [8] x1 + [8] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [2] p(n__g) = [0] Following rules are strictly oriented: activate(X) = [5] X + [4] > [1] X + [0] = X activate(n__d(X)) = [5] X + [4] > [1] X + [1] = d(X) activate(n__f(X)) = [5] X + [14] > [5] X + [13] = f(activate(X)) activate(n__g(X)) = [4] > [3] = g(X) c(X) = [5] X + [6] > [5] X + [5] = d(activate(X)) d(X) = [1] X + [1] > [1] X + [0] = n__d(X) f(X) = [1] X + [9] > [1] X + [2] = n__f(X) f(f(X)) = [1] X + [18] > [16] = c(n__f(n__g(n__f(X)))) g(X) = [3] > [0] = n__g(X) h(X) = [8] X + [8] > [5] X + [6] = c(n__d(X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))