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(X) f(X) -> n__f(X) f(f(a())) -> c(n__f(g(f(a())))) - Signature: {activate/1,f/1} / {a/0,c/1,g/1,n__f/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f} and constructors {a,c,g,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: none Following symbols are considered usable: {activate,f} TcT has computed the following interpretation: p(a) = [6] p(activate) = [8] x1 + [8] p(c) = [1] x1 + [0] p(f) = [1] x1 + [1] p(g) = [0] p(n__f) = [1] x1 + [0] Following rules are strictly oriented: activate(X) = [8] X + [8] > [1] X + [0] = X activate(n__f(X)) = [8] X + [8] > [1] X + [1] = f(X) f(X) = [1] X + [1] > [1] X + [0] = n__f(X) f(f(a())) = [8] > [0] = c(n__f(g(f(a())))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))