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: 5
     enrichment: roof
     automaton:
      final states: {5}
      transitions:
       f{#,5}(24,20) -> 5*
       f1(9,4) -> 4*
       f1(4,8) -> 9*
       f{#,3}(16,12) -> 5*
       a4() -> 19*
       f{#,1}(9,4) -> 5*
       a1() -> 8*
       f{#,0}(4,4) -> 5*
       a3() -> 15*
       f3(12,15) -> 16*
       f3(16,12) -> 4*
       a0() -> 4*
       f0(4,4) -> 4*
       f2(12,9) -> 4*
       f2(9,11) -> 12*
       f{#,2}(12,9) -> 5*
       a2() -> 11*
       f{#,4}(20,16) -> 5*
       f5(24,20) -> 4*
       f5(20,23) -> 24*
       a5() -> 23*
       f4(16,19) -> 20*
       f4(20,16) -> 4*
     problem:
      DPs:
       
      TRS:
       f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
     Qed