YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(a(),x)
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
  TRS:
   f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   TRS:
    f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(a(),x) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   CDG Processor:
    DPs:
     f#(x,f(a(),a())) -> f#(a(),x)
     f#(x,f(a(),a())) -> f#(f(a(),a()),a())
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
    TRS:
     f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
    graph:
     f#(x,f(a(),a())) -> f#(a(),x) ->
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
     f#(x,f(a(),a())) -> f#(a(),x) ->
     f#(x,f(a(),a())) -> f#(f(a(),a()),a())
     f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(a(),x)
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 3/9
     DPs:
      f#(x,f(a(),a())) -> f#(a(),x)
     TRS:
      f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
     Matrix Interpretation Processor: dim=2
      
      interpretation:
       [f#](x0, x1) = [2 0]x0 + [1 0]x1,
       
                     [0 1]  
       [f](x0, x1) = [0 0]x0,
       
             [0]
       [a] = [2]
      orientation:
       f#(x,f(a(),a())) = [2 0]x + [2] >= [1 0]x = f#(a(),x)
       
                         [0 1]     [0]                                
       f(x,f(a(),a())) = [0 0]x >= [0] = f(f(f(a(),a()),a()),f(a(),x))
      problem:
       DPs:
        
       TRS:
        f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
      Qed