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: 1
     enrichment: match
     automaton:
      final states: {5}
      transitions:
       f1(12,9) -> 12,4
       f1(9,9) -> 10*
       f1(9,11) -> 12*
       f1(10,4) -> 11*
       f1(10,10) -> 11*
       f1(10,12) -> 11*
       a1() -> 9*
       f{#,1}(9,11) -> 5*
       f{#,0}(4,4) -> 5*
       a0() -> 4*
       f0(4,4) -> 4*
     problem:
      DPs:
       
      TRS:
       f(a(),f(x,a())) -> f(f(a(),f(f(a(),a()),x)),a())
     Qed