YES

Problem:
 f(f(a(),x),a()) -> f(a(),f(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#(f(a(),f(a(),a())),x)
   f#(f(a(),x),a()) -> f#(a(),f(f(a(),f(a(),a())),x))
  TRS:
   f(f(a(),x),a()) -> f(a(),f(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#(f(a(),f(a(),a())),x)
    f#(f(a(),x),a()) -> f#(a(),f(f(a(),f(a(),a())),x))
   TRS:
    f(f(a(),x),a()) -> f(a(),f(f(a(),f(a(),a())),x))
   graph:
    f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x) ->
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(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(),a())),x) ->
    f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
    f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x) ->
    f#(f(a(),x),a()) -> f#(a(),f(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(),a())),x)
    TRS:
     f(f(a(),x),a()) -> f(a(),f(f(a(),f(a(),a())),x))
    Usable Rule Processor:
     DPs:
      f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
     TRS:
      
     Bounds Processor:
      bound: 1
      enrichment: match-dp
      automaton:
       final states: {4}
       transitions:
        f{#,1}(9,5) -> 4*
        f1(7,7) -> 8*
        f1(7,8) -> 9*
        a1() -> 7*
        f{#,0}(6,3) -> 4*
        f0(1,2) -> 2*
        f0(2,1) -> 2*
        f0(1,1) -> 5,2
        f0(1,5) -> 6*
        f0(2,2) -> 2*
        a0() -> 1*
        1 -> 3*
        2 -> 3*
      problem:
       DPs:
        
       TRS:
        
      Qed