WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,y) -> g(x,y) g(h(x),y) -> h(f(x,y)) g(h(x),y) -> h(g(x,y)) - Signature: {f/2,g/2} / {h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {h} + 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(h) = {1} Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(f) = [4] x1 + [2] p(g) = [4] x1 + [1] p(h) = [1] x1 + [1] Following rules are strictly oriented: f(x,y) = [4] x + [2] > [4] x + [1] = g(x,y) g(h(x),y) = [4] x + [5] > [4] x + [3] = h(f(x,y)) g(h(x),y) = [4] x + [5] > [4] x + [2] = h(g(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))