YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
   f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),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#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
     f#(x,f(a(),y)) -> f#(a(),x)
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
    Matrix Interpretation Processor: dim=2
     
     interpretation:
      [f#](x0, x1) = [0 2]x0 + [0 2]x1,
      
                [0]
      [h](x0) = [0],
      
                    [0 0]     [0 0]     [0]
      [f](x0, x1) = [1 0]x0 + [2 2]x1 + [1],
      
            [1]
      [a] = [0]
     orientation:
      f#(x,f(a(),y)) = [0 2]x + [4 4]y + [4] >= [0 2]y + [2] = f#(f(f(a(),x),h(a())),y)
      
      f#(x,f(a(),y)) = [0 2]x + [4 4]y + [4] >= [4 4]y + [2] = f#(a(),f(f(f(a(),x),h(a())),y))
      
      f#(x,f(a(),y)) = [0 2]x + [4 4]y + [4] >= [0 2]x = f#(a(),x)
      
                      [0 0]    [0 0]    [0]    [0 0]    [0]                                 
      f(x,f(a(),y)) = [1 0]x + [4 4]y + [5] >= [4 4]y + [4] = f(a(),f(f(f(a(),x),h(a())),y))
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
     Qed