YES

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

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