WORST_CASE(?,O(n^3)) * Step 1: MI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: h(f(x,y)) -> f(y,f(h(h(x)),a())) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: MI {miKind = Automaton Nothing, miDimension = 3, miUArgs = NoUArgs, miURules = NoURules, miSelector = Nothing} + Details: We apply a matrix interpretation of kind Automaton Nothing: Following symbols are considered usable: all TcT has computed the following interpretation: p(a) = [0] [0] [0] p(f) = [1 0 0] [1 0 0] [0] [0 0 0] x_1 + [0 1 1] x_2 + [1] [0 1 1] [0 0 0] [1] p(h) = [1 0 2] [0] [0 0 3] x_1 + [0] [0 1 0] [0] Following rules are strictly oriented: h(f(x,y)) = [1 2 2] [1 0 0] [2] [0 3 3] x + [0 0 0] y + [3] [0 0 0] [0 1 1] [1] > [1 2 2] [1 0 0] [0] [0 3 3] x + [0 0 0] y + [3] [0 0 0] [0 1 1] [1] = f(y,f(h(h(x)),a())) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^3))