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