YES

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

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