YES Problem: b(a(a(a(b(a(a(x1))))))) -> a(a(a(b(b(a(a(a(b(x1))))))))) Proof: DP Processor: DPs: b#(a(a(a(b(a(a(x1))))))) -> b#(x1) b#(a(a(a(b(a(a(x1))))))) -> b#(a(a(a(b(x1))))) b#(a(a(a(b(a(a(x1))))))) -> b#(b(a(a(a(b(x1)))))) TRS: b(a(a(a(b(a(a(x1))))))) -> a(a(a(b(b(a(a(a(b(x1))))))))) Arctic Interpretation Processor: dimension: 2 interpretation: [b#](x0) = [-& 0 ]x0 + [3], [-& -2] [0] [b](x0) = [-& -2]x0 + [0], [0 0] [2] [a](x0) = [2 0]x0 + [0] orientation: b#(a(a(a(b(a(a(x1))))))) = [4 4]x1 + [6] >= [-& 0 ]x1 + [3] = b#(x1) b#(a(a(a(b(a(a(x1))))))) = [4 4]x1 + [6] >= [-& 2 ]x1 + [4] = b#(a(a(a(b(x1))))) b#(a(a(a(b(a(a(x1))))))) = [4 4]x1 + [6] >= [-& 0 ]x1 + [3] = b#(b(a(a(a(b(x1)))))) [2 2] [4] [-& 0 ] [4] b(a(a(a(b(a(a(x1))))))) = [2 2]x1 + [4] >= [-& 2 ]x1 + [4] = a(a(a(b(b(a(a(a(b(x1))))))))) problem: DPs: TRS: b(a(a(a(b(a(a(x1))))))) -> a(a(a(b(b(a(a(a(b(x1))))))))) Qed