YES

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

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