YES Problem: g(x,y) -> x g(x,y) -> y f(s(x),y,y) -> f(y,x,s(x)) Proof: DP Processor: DPs: f#(s(x),y,y) -> f#(y,x,s(x)) TRS: g(x,y) -> x g(x,y) -> y f(s(x),y,y) -> f(y,x,s(x)) Arctic Interpretation Processor: dimension: 1 interpretation: [f#](x0, x1, x2) = 2x0 + 5x1 + x2, [f](x0, x1, x2) = 2x0 + 4x1 + x2 + -12, [s](x0) = 4x0, [g](x0, x1) = x0 + x1 + 0 orientation: f#(s(x),y,y) = 6x + 5y >= 5x + 2y = f#(y,x,s(x)) g(x,y) = x + y + 0 >= x = x g(x,y) = x + y + 0 >= y = y f(s(x),y,y) = 6x + 4y + -12 >= 4x + 2y + -12 = f(y,x,s(x)) problem: DPs: TRS: g(x,y) -> x g(x,y) -> y f(s(x),y,y) -> f(y,x,s(x)) Qed