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: 4
      enrichment: top-dp
      automaton:
       final states: {5}
       transitions:
        a3() -> 19*
        f{#,1}(12,10) -> 5*
        f{#,4}(26,20) -> 5*
        f1(10,11) -> 12*
        f4(20,25) -> 26*
        a1() -> 11*
        a4() -> 25*
        f{#,2}(18,12) -> 5*
        f2(12,17) -> 18*
        f{#,0}(10,7) -> 5*
        f{#,0}(10,9) -> 5*
        f{#,0}(10,8) -> 5*
        f{#,0}(10,10) -> 5*
        a2() -> 17*
        f0(8,7) -> 7*
        f0(8,9) -> 7*
        f0(9,8) -> 10*
        f0(9,10) -> 7*
        f0(10,7) -> 7*
        f0(10,9) -> 7*
        f0(7,7) -> 7*
        f0(7,9) -> 7*
        f0(8,8) -> 10*
        f0(8,10) -> 7*
        f0(9,7) -> 7*
        f0(9,9) -> 7*
        f0(10,8) -> 10*
        f0(10,10) -> 7*
        f0(7,8) -> 10*
        f0(7,10) -> 7*
        f{#,3}(20,18) -> 5*
        a0() -> 8*
        f3(18,19) -> 20*
        f30(8,7) -> 9*
        f30(8,9) -> 9*
        f30(9,8) -> 9*
        f30(9,10) -> 9*
        f30(10,7) -> 9*
        f30(10,9) -> 9*
        f30(7,7) -> 9*
        f30(7,9) -> 9*
        f30(8,8) -> 9*
        f30(8,10) -> 9*
        f30(9,7) -> 9*
        f30(9,9) -> 9*
        f30(10,8) -> 9*
        f30(10,10) -> 9*
        f30(7,8) -> 9*
        f30(7,10) -> 9*
        7 -> 9*
        8 -> 9*
        10 -> 9*
      problem:
       DPs:
        
       TRS:
        f3(x,y) -> x
        f3(x,y) -> y
      Qed