YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),f(x,a())) -> f#(a(),a())
   f#(a(),f(x,a())) -> f#(f(a(),a()),a())
   f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a()))
   f#(a(),f(x,a())) -> f#(a(),f(x,f(f(a(),a()),a())))
  TRS:
   f(a(),f(x,a())) -> f(a(),f(x,f(f(a(),a()),a())))
  EDG Processor:
   DPs:
    f#(a(),f(x,a())) -> f#(a(),a())
    f#(a(),f(x,a())) -> f#(f(a(),a()),a())
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a()))
    f#(a(),f(x,a())) -> f#(a(),f(x,f(f(a(),a()),a())))
   TRS:
    f(a(),f(x,a())) -> f(a(),f(x,f(f(a(),a()),a())))
   graph:
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a())) ->
    f#(a(),f(x,a())) -> f#(a(),a())
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a())) ->
    f#(a(),f(x,a())) -> f#(f(a(),a()),a())
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a())) ->
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a()))
    f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a())) ->
    f#(a(),f(x,a())) -> f#(a(),f(x,f(f(a(),a()),a())))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(a(),f(x,a())) -> f#(x,f(f(a(),a()),a()))
    TRS:
     f(a(),f(x,a())) -> f(a(),f(x,f(f(a(),a()),a())))
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(3,2) -> 4*
       f0(2,2) -> 3*
       a0() -> 2*
       f{#,0}(3,4) -> 1*
       f{#,0}(5,4) -> 1*
       f30() -> 5*
     problem:
      DPs:
       
      TRS:
       f(a(),f(x,a())) -> f(a(),f(x,f(f(a(),a()),a())))
     Qed