WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(a()) -> a() mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) - Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,f,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(a__f) = {1} Following symbols are considered usable: {a__f,mark} TcT has computed the following interpretation: p(a) = [8] p(a__f) = [1] x1 + [9] p(f) = [1] x1 + [8] p(g) = [8] p(mark) = [2] x1 + [0] Following rules are strictly oriented: a__f(X) = [1] X + [9] > [1] X + [8] = f(X) a__f(f(a())) = [25] > [17] = a__f(g(f(a()))) mark(a()) = [16] > [8] = a() mark(f(X)) = [2] X + [16] > [2] X + [9] = a__f(mark(X)) mark(g(X)) = [16] > [8] = g(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))