YES

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

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