WORST_CASE(?,O(n^2)) * Step 1: MI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {c,s} + Applied Processor: MI {miKind = Automaton Nothing, miDimension = 2, 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(c) = [1 0] x_1 + [7] [1 1] [6] p(f) = [2 0] x_1 + [1 3] x_2 + [4] [0 0] [0 0] [8] p(s) = [1 0] x_1 + [12] [0 0] [1] Following rules are strictly oriented: f(x,c(y)) = [2 0] x + [4 3] y + [29] [0 0] [0 0] [8] > [2 0] x + [3 3] y + [23] [0 0] [0 0] [8] = f(x,s(f(y,y))) f(s(x),y) = [2 0] x + [1 3] y + [28] [0 0] [0 0] [8] > [2 0] x + [1 0] y + [26] [0 0] [0 0] [8] = f(x,s(c(y))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^2))