YES

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

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