YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(x,a())
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a()))
  TRS:
   f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(x,a()))
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(x,a())
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a()))
   TRS:
    f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(x,a()))
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a())) ->
    f#(x,f(a(),a())) -> f#(x,a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a())) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a())) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a()))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(x,a()))
    TRS:
     f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(x,a()))
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(6,2) -> 4*
       f0(5,2) -> 6*
       f0(3,2) -> 4*
       f0(2,2) -> 5*
       a0() -> 2*
       f{#,0}(6,4) -> 1*
       f30() -> 3*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(x,a()))
     Qed