YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(a(),x)
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
  TRS:
   f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   TRS:
    f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(a(),x) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
     f#(x,f(a(),a())) -> f#(a(),x)
    TRS:
     f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
    Bounds Processor:
     bound: 2
     enrichment: match
     automaton:
      final states: {5}
      transitions:
       f1(13,11) -> 4*
       f1(10,13) -> 11*
       f1(13,12) -> 11*
       f1(10,4) -> 11*
       f1(10,10) -> 12*
       f1(12,10) -> 13*
       a1() -> 10*
       f{#,1}(13,11) -> 5*
       f{#,1}(10,13) -> 5*
       f{#,1}(13,12) -> 5*
       f{#,1}(10,4) -> 5*
       f{#,1}(10,10) -> 5*
       f2(14,14) -> 16*
       f2(16,14) -> 17*
       f2(17,15) -> 11*
       f2(14,13) -> 15*
       f{#,0}(4,4) -> 5*
       a2() -> 14*
       f0(4,4) -> 4*
       f{#,2}(17,15) -> 5*
       f{#,2}(14,13) -> 5*
       a0() -> 4*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
     Qed