YES

Problem:
 f(g(x,y),f(y,y)) -> f(g(y,x),y)

Proof:
 DP Processor:
  DPs:
   f#(g(x,y),f(y,y)) -> f#(g(y,x),y)
  TRS:
   f(g(x,y),f(y,y)) -> f(g(y,x),y)
  Usable Rule Processor:
   DPs:
    f#(g(x,y),f(y,y)) -> f#(g(y,x),y)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0, x1) = 1x0 + -4x1 + -16,
     
     [f](x0, x1) = 11x0 + x1 + 4,
     
     [g](x0, x1) = 1x0 + x1 + -7
    orientation:
     f#(g(x,y),f(y,y)) = 2x + 7y + 0 >= 1x + 2y + -6 = f#(g(y,x),y)
    problem:
     DPs:
      
     TRS:
      
    Qed