YES

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

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