YES Problem: f(a(),f(f(a(),a()),x)) -> f(f(a(),a()),f(a(),f(a(),x))) Proof: DP Processor: DPs: f#(a(),f(f(a(),a()),x)) -> f#(a(),x) f#(a(),f(f(a(),a()),x)) -> f#(a(),f(a(),x)) f#(a(),f(f(a(),a()),x)) -> f#(f(a(),a()),f(a(),f(a(),x))) TRS: f(a(),f(f(a(),a()),x)) -> f(f(a(),a()),f(a(),f(a(),x))) Matrix Interpretation Processor: dim=2 interpretation: [f#](x0, x1) = [0 1]x1, [3 0] [0 2] [1] [f](x0, x1) = [2 0]x0 + [0 1]x1 + [0], [0] [a] = [0] orientation: f#(a(),f(f(a(),a()),x)) = [0 1]x + [2] >= [0 1]x = f#(a(),x) f#(a(),f(f(a(),a()),x)) = [0 1]x + [2] >= [0 1]x = f#(a(),f(a(),x)) f#(a(),f(f(a(),a()),x)) = [0 1]x + [2] >= [0 1]x = f#(f(a(),a()),f(a(),f(a(),x))) [0 2] [5] [0 2] [4] f(a(),f(f(a(),a()),x)) = [0 1]x + [2] >= [0 1]x + [2] = f(f(a(),a()),f(a(),f(a(),x))) problem: DPs: TRS: f(a(),f(f(a(),a()),x)) -> f(f(a(),a()),f(a(),f(a(),x))) Qed