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))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = 2x0 + -2x1 + -16,
       
       [f](x0, x1) = -8x0 + -4x1 + 9,
       
       [a] = 0
      orientation:
       f#(x,f(a(),a())) = 2x + 7 >= -2x + 2 = f#(a(),x)
       
       f(x,f(a(),a())) = -8x + 9 >= -8x + 9 = 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