YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),a()) -> f#(a(),a())
   f#(f(x,a()),a()) -> f#(f(a(),a()),f(x,a()))
   f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a())
  TRS:
   f(f(x,a()),a()) -> f(f(f(a(),a()),f(x,a())),a())
  EDG Processor:
   DPs:
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(f(a(),a()),f(x,a()))
    f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a())
   TRS:
    f(f(x,a()),a()) -> f(f(f(a(),a()),f(x,a())),a())
   graph:
    f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a()) ->
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a()) ->
    f#(f(x,a()),a()) -> f#(f(a(),a()),f(x,a()))
    f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a()) ->
    f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(f(x,a()),a()) -> f#(f(f(a(),a()),f(x,a())),a())
    TRS:
     f(f(x,a()),a()) -> f(f(f(a(),a()),f(x,a())),a())
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(6,2) -> 4*
       f0(5,4) -> 6*
       f0(3,2) -> 4*
       f0(2,2) -> 5*
       a0() -> 2*
       f30() -> 3*
       f{#,0}(6,2) -> 1*
     problem:
      DPs:
       
      TRS:
       f(f(x,a()),a()) -> f(f(f(a(),a()),f(x,a())),a())
     Qed