YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),y) -> f#(h(a()),a())
   f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
   f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
   f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
  TRS:
   f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
  EDG Processor:
   DPs:
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
   TRS:
    f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
   graph:
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
     f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    TRS:
     f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
    Bounds Processor:
     bound: 2
     enrichment: match
     automaton:
      final states: {6}
      transitions:
       f1(12,14) -> 15*
       f1(15,5) -> 5,16
       f1(15,15) -> 16,5,15
       f1(5,15) -> 5,16
       f1(13,12) -> 14*
       f1(5,16) -> 5*
       f1(21,5) -> 5,16
       f1(16,5) -> 5*
       f1(21,15) -> 5,16,15
       f1(16,15) -> 5,15
       a1() -> 12*
       h1(12) -> 13*
       f{#,1}(15,15) -> 6*
       f{#,1}(5,15) -> 6*
       f{#,1}(16,16) -> 6*
       f{#,1}(15,16) -> 6*
       f{#,1}(5,16) -> 6*
       f{#,1}(21,5) -> 6*
       f{#,1}(21,15) -> 6*
       f{#,1}(16,15) -> 6*
       f2(18,17) -> 19*
       f2(14,20) -> 21*
       f2(15,21) -> 16,5,15
       f2(5,21) -> 5,16
       f2(17,19) -> 20*
       f2(21,21) -> 16,15,5
       f{#,0}(5,5) -> 6*
       a2() -> 17*
       f0(5,5) -> 5*
       h2(17) -> 18*
       a0() -> 5*
       f{#,2}(14,20) -> 6*
       f{#,2}(15,21) -> 6*
       f{#,2}(21,21) -> 6*
       f{#,2}(16,21) -> 6*
       h0(5) -> 5*
     problem:
      DPs:
       
      TRS:
       f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
     Qed