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