YES

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

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