YES

Problem:
 f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
   f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
     f#(x,f(a(),y)) -> f#(a(),x)
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f#](x0, x1) = 2x0 + 2x1,
      
      [h](x0) = 0,
      
      [f](x0, x1) = 4x1 + 3,
      
      [a] = 0
     orientation:
      f#(x,f(a(),y)) = 2x + 8y + 6 >= 2y + 6 = f#(f(a(),h(f(a(),x))),y)
      
      f#(x,f(a(),y)) = 2x + 8y + 6 >= 8y + 6 = f#(a(),f(f(a(),h(f(a(),x))),y))
      
      f#(x,f(a(),y)) = 2x + 8y + 6 >= 2x = f#(a(),x)
      
      f(x,f(a(),y)) = 16y + 15 >= 16y + 15 = f(a(),f(f(a(),h(f(a(),x))),y))
     problem:
      DPs:
       f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
       f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
      TRS:
       f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1,
       
       [h](x0) = 0,
       
       [f](x0, x1) = 1x1,
       
       [a] = 0
      orientation:
       f#(x,f(a(),y)) = 1y >= y = f#(f(a(),h(f(a(),x))),y)
       
       f#(x,f(a(),y)) = 1y >= 1y = f#(a(),f(f(a(),h(f(a(),x))),y))
       
       f(x,f(a(),y)) = 2y >= 2y = f(a(),f(f(a(),h(f(a(),x))),y))
      problem:
       DPs:
        f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
      Matrix Interpretation Processor: dim=2
       
       interpretation:
        [f#](x0, x1) = [2 0]x0 + [1 0]x1,
        
                  [0]
        [h](x0) = [0],
        
                      [0 1]     [3 0]  
        [f](x0, x1) = [2 0]x0 + [0 0]x1,
        
              [0]
        [a] = [1]
       orientation:
        f#(x,f(a(),y)) = [2 0]x + [3 0]y + [1] >= [3 0]y = f#(a(),f(f(a(),h(f(a(),x))),y))
        
                        [0 1]    [9 0]    [3]    [9 0]    [1]                                 
        f(x,f(a(),y)) = [2 0]x + [0 0]y + [0] >= [0 0]y + [0] = f(a(),f(f(a(),h(f(a(),x))),y))
       problem:
        DPs:
         
        TRS:
         f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
       Qed