YES

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

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