WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {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(g) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = [4] x1 + [9] p(g) = [1] x1 + [1] Following rules are strictly oriented: f(g(x)) = [4] x + [13] > [4] x + [11] = g(g(f(x))) f(g(x)) = [4] x + [13] > [1] x + [3] = g(g(g(x))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))