YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(x,a())
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(f(a(),a()),f(x,a()))
   f#(f(a(),x),a()) -> f#(f(f(a(),a()),f(x,a())),a())
  TRS:
   f(f(a(),x),a()) -> f(f(f(a(),a()),f(x,a())),a())
  EDG Processor:
   DPs:
    f#(f(a(),x),a()) -> f#(x,a())
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(f(a(),a()),f(x,a()))
    f#(f(a(),x),a()) -> f#(f(f(a(),a()),f(x,a())),a())
   TRS:
    f(f(a(),x),a()) -> f(f(f(a(),a()),f(x,a())),a())
   graph:
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(x,a())
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,a()) ->
    f#(f(a(),x),a()) -> f#(f(a(),a()),f(x,a()))
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(f(f(a(),a()),f(x,a())),a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(f(a(),x),a()) -> f#(x,a())
    TRS:
     f(f(a(),x),a()) -> f(f(f(a(),a()),f(x,a())),a())
    KBO Processor:
     argument filtering:
      pi(a) = []
      pi(f) = [1]
      pi(f#) = 0
     weight function:
      w0 = 1
      w(f#) = w(f) = w(a) = 1
     precedence:
      f# ~ f ~ a
     problem:
      DPs:
       
      TRS:
       f(f(a(),x),a()) -> f(f(f(a(),a()),f(x,a())),a())
     Qed