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: 1
     enrichment: match-dp
     automaton:
      final states: {7}
      transitions:
       f0(9,9) -> 10,8
       f0(10,9) -> 9*
       f{#,1}(11,9) -> 7*
       a0() -> 9*
       f{#,0}(9,8) -> 7*
       f30() -> 8*
       a1() -> 11*
     problem:
      DPs:
       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))
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        f0(6,5) -> 4*
        f0(6,4) -> 4*
        f0(3,6) -> 4*
        f0(5,3) -> 6*
        f0(3,2) -> 4*
        f0(3,3) -> 5*
        a0() -> 3*
        f{#,0}(6,4) -> 1*
        f100() -> 2*
      problem:
       DPs:
        
       TRS:
        f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
      Qed