YES

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

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