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: 2
     enrichment: match
     automaton:
      final states: {3}
      transitions:
       f1(8,1) -> 9*
       f1(8,7) -> 9*
       f1(9,6) -> 7,1
       f1(6,6) -> 8*
       f1(1,6) -> 7*
       f1(2,6) -> 7*
       a1() -> 6*
       f{#,1}(9,6) -> 3*
       f2(9,18) -> 19*
       f2(20,19) -> 21*
       f2(21,18) -> 7*
       f2(18,18) -> 20*
       f{#,0}(1,2) -> 3*
       f{#,0}(2,1) -> 3*
       f{#,0}(1,1) -> 3*
       f{#,0}(2,2) -> 3*
       a2() -> 18*
       f0(1,2) -> 1*
       f0(2,1) -> 1*
       f0(1,1) -> 1*
       f0(2,2) -> 1*
       a0() -> 2*
     problem:
      DPs:
       
      TRS:
       f(f(x,a()),a()) -> f(f(f(a(),a()),f(x,a())),a())
     Qed