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())
    Usable Rule Processor:
     DPs:
      f#(a(),f(x,a())) -> f#(a(),f(f(a(),a()),x))
     TRS:
      
     Bounds Processor:
      bound: 1
      enrichment: match-dp
      automaton:
       final states: {4}
       transitions:
        f{#,1}(7,9) -> 4*
        a1() -> 7*
        f1(8,5) -> 9*
        f1(7,7) -> 8*
        f{#,0}(2,6) -> 4*
        a0() -> 2*
        f0(5,3) -> 6*
        f0(1,2) -> 1*
        f0(2,1) -> 1*
        f0(1,1) -> 1*
        f0(2,2) -> 5,1
        1 -> 3*
        2 -> 3*
      problem:
       DPs:
        
       TRS:
        
      Qed