YES

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

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())),x)
   f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
  TRS:
   f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
  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())),x)
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
   TRS:
    f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
   graph:
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),x)
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
   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())),x)
     f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
    TRS:
     f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
    graph:
     
    Qed