YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),a()) -> f#(a(),a())
   f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
   f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),a())
   f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x)
  TRS:
   f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),a()),x)
  EDG Processor:
   DPs:
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
    f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x)
   TRS:
    f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),a()),x)
   graph:
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x) ->
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x) ->
    f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x) ->
    f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x) ->
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x)
   CDG Processor:
    DPs:
     f#(f(x,a()),a()) -> f#(a(),a())
     f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
     f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),a())
     f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),a()),x)
    TRS:
     f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),a()),x)
    graph:
     
    Qed