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