YES

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

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#(a(),f(a(),f(f(a(),a()),x)))
  TRS:
   f(a(),f(x,a())) -> f(a(),f(a(),f(f(a(),a()),x)))
  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#(a(),f(a(),f(f(a(),a()),x)))
   TRS:
    f(a(),f(x,a())) -> f(a(),f(a(),f(f(a(),a()),x)))
   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#(a(),f(a(),f(f(a(),a()),x)))
   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(a(),f(a(),f(f(a(),a()),x)))
    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:
       f(a(),f(x,a())) -> f(a(),f(a(),f(f(a(),a()),x)))
     Qed