YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
   f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
  TRS:
   f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
  EDG Processor:
   DPs:
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
   TRS:
    f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
   graph:
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x) ->
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x) ->
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/4
    DPs:
     f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
    TRS:
     f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
    Usable Rule Processor:
     DPs:
      f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
     TRS:
      f3(x,y) -> x
      f3(x,y) -> y
     Bounds Processor:
      bound: 5
      enrichment: roof
      automaton:
       final states: {6}
       transitions:
        f{#,4}(18,16) -> 6*
        f4(16,17) -> 18*
        a4() -> 17*
        f{#,5}(20,18) -> 6*
        f5(18,19) -> 20*
        f{#,0}(5,5) -> 6*
        a5() -> 19*
        f0(5,5) -> 5*
        a0() -> 5*
        f30(5,5) -> 5*
        f{#,1}(10,5) -> 6*
        f1(5,9) -> 10*
        a1() -> 9*
        f{#,2}(12,10) -> 6*
        f2(10,11) -> 12*
        a2() -> 11*
        f{#,3}(16,12) -> 6*
        f3(12,15) -> 16*
        a3() -> 15*
      problem:
       DPs:
        
       TRS:
        f3(x,y) -> x
        f3(x,y) -> y
      Qed