WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,h(y,z)) -> h(g(x,y),z) g(f(x,y),z) -> f(x,g(y,z)) g(h(x,y),z) -> g(x,f(y,z)) - Signature: {g/2} / {f/2,h/2} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {f,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(f) = {2}, uargs(h) = {1} Following symbols are considered usable: {g} TcT has computed the following interpretation: p(f) = [1] x1 + [1] x2 + [1] p(g) = [8] x1 + [8] x2 + [8] p(h) = [1] x1 + [1] x2 + [2] Following rules are strictly oriented: g(x,h(y,z)) = [8] x + [8] y + [8] z + [24] > [8] x + [8] y + [1] z + [10] = h(g(x,y),z) g(f(x,y),z) = [8] x + [8] y + [8] z + [16] > [1] x + [8] y + [8] z + [9] = f(x,g(y,z)) g(h(x,y),z) = [8] x + [8] y + [8] z + [24] > [8] x + [8] y + [8] z + [16] = g(x,f(y,z)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))