YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(x,f(a(),a()))
   f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
  TRS:
   f(f(a(),x),a()) -> f(f(x,f(a(),a())),a())
  EDG Processor:
   DPs:
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
   TRS:
    f(f(a(),x),a()) -> f(f(x,f(a(),a())),a())
   graph:
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(x,f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) -> f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
    TRS:
     f(f(a(),x),a()) -> f(f(x,f(a(),a())),a())
    Usable Rule Processor:
     DPs:
      f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
     TRS:
      
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        f30() -> 4*
        f{#,0}(5,2) -> 1*
        f0(3,3) -> 5*
        f0(4,3) -> 5*
        f0(2,2) -> 3*
        a0() -> 2*
      problem:
       DPs:
        
       TRS:
        
      Qed