YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),f(a(),x)) -> f#(a(),a())
   f#(a(),f(a(),x)) -> f#(f(a(),a()),a())
   f#(a(),f(a(),x)) -> f#(x,f(f(a(),a()),a()))
   f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a())))
  TRS:
   f(a(),f(a(),x)) -> f(a(),f(x,f(f(a(),a()),a())))
  EDG Processor:
   DPs:
    f#(a(),f(a(),x)) -> f#(a(),a())
    f#(a(),f(a(),x)) -> f#(f(a(),a()),a())
    f#(a(),f(a(),x)) -> f#(x,f(f(a(),a()),a()))
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a())))
   TRS:
    f(a(),f(a(),x)) -> f(a(),f(x,f(f(a(),a()),a())))
   graph:
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a()))) ->
    f#(a(),f(a(),x)) -> f#(a(),a())
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a()))) ->
    f#(a(),f(a(),x)) -> f#(f(a(),a()),a())
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a()))) ->
    f#(a(),f(a(),x)) -> f#(x,f(f(a(),a()),a()))
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a()))) ->
    f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a())))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(a(),f(a(),x)) -> f#(a(),f(x,f(f(a(),a()),a())))
    TRS:
     f(a(),f(a(),x)) -> f(a(),f(x,f(f(a(),a()),a())))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {5}
      transitions:
       f1(4,12) -> 13*
       f1(10,13) -> 4*
       f1(11,10) -> 12*
       f1(13,12) -> 13*
       f1(10,10) -> 11*
       f1(12,12) -> 13*
       a1() -> 10*
       f{#,1}(10,13) -> 5*
       f{#,0}(4,4) -> 5*
       a0() -> 4*
       f0(4,4) -> 4*
     problem:
      DPs:
       
      TRS:
       f(a(),f(a(),x)) -> f(a(),f(x,f(f(a(),a()),a())))
     Qed