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