YES(?,O(n^3)) Problem: f(x,f(f(a(),a()),a())) -> f(f(a(),f(a(),a())),x) Proof: Complexity Transformation Processor: strict: f(x,f(f(a(),a()),a())) -> f(f(a(),f(a(),a())),x) weak: Matrix Interpretation Processor: dimension: 3 max_matrix: [1 1 0] [0 1 1] [0 0 0] interpretation: [1 1 0] [1 1 0] [0] [f](x0, x1) = [0 1 1]x0 + [0 1 0]x1 + [0] [0 0 0] [0 0 0] [1], [0] [a] = [0] [0] orientation: [1 1 0] [1] [1 1 0] [0] f(x,f(f(a(),a()),a())) = [0 1 1]x + [1] >= [0 1 0]x + [1] = f(f(a(),f(a(),a())),x) [0 0 0] [1] [0 0 0] [1] problem: strict: weak: f(x,f(f(a(),a()),a())) -> f(f(a(),f(a(),a())),x) Qed