YES

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

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