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)
    Bounds Processor:
     bound: 4
     enrichment: top-dp
     automaton:
      final states: {4}
      transitions:
       f3(16,17) -> 18*
       a3() -> 17*
       f{#,4}(24,18) -> 4*
       f4(18,23) -> 24*
       f{#,0}(8,7) -> 4*
       f{#,0}(8,6) -> 4*
       f{#,0}(8,8) -> 4*
       a4() -> 23*
       f0(8,7) -> 6,8
       f0(6,6) -> 6*
       f0(6,8) -> 6*
       f0(7,7) -> 8*
       f0(8,6) -> 6*
       f0(8,8) -> 6*
       f0(6,7) -> 8*
       f0(7,6) -> 6*
       f0(7,8) -> 6*
       a0() -> 7*
       f{#,1}(10,8) -> 4*
       f1(8,9) -> 10*
       a1() -> 9*
       f{#,2}(16,10) -> 4*
       f2(10,15) -> 16*
       a2() -> 15*
       f{#,3}(18,16) -> 4*
     problem:
      DPs:
       
      TRS:
       f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
     Qed