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-dp
     automaton:
      final states: {16}
      transitions:
       f{#,1}(12,28) -> 16,14
       f{#,1}(28,29) -> 16,14
       f{#,1}(28,35) -> 14,15,16
       f{#,1}(14,28) -> 16,14
       f{#,1}(35,35) -> 14,15,16
       f{#,1}(35,41) -> 14,15,16
       f{#,1}(11,28) -> 16,14
       f{#,1}(28,28) -> 14,16,15
       f{#,1}(18,28) -> 16*
       f{#,1}(13,28) -> 16,14
       f{#,1}(29,35) -> 14,16,15
       f1(27,28) -> 35*
       f1(12,28) -> 29*
       f1(28,29) -> 29*
       f1(28,35) -> 41*
       f1(14,28) -> 29*
       f1(25,27) -> 28*
       f1(35,35) -> 41*
       f1(35,41) -> 29*
       f1(11,28) -> 29*
       f1(28,28) -> 41*
       f1(13,28) -> 29*
       f1(29,35) -> 29*
       f1(26,25) -> 27*
       a1() -> 25*
       h1(25) -> 26*
       f{#,2}(27,33) -> 16,14,15
       f{#,0}(13,11) -> 14*
       f{#,0}(13,13) -> 14*
       f{#,0}(14,12) -> 14*
       f{#,0}(14,14) -> 14*
       f{#,0}(15,19) -> 16*
       f{#,0}(11,12) -> 14*
       f{#,0}(11,14) -> 14*
       f{#,0}(12,11) -> 14*
       f{#,0}(12,13) -> 14*
       f{#,0}(13,12) -> 14*
       f{#,0}(13,14) -> 14*
       f{#,0}(14,11) -> 14*
       f{#,0}(19,13) -> 16*
       f{#,0}(14,13) -> 14*
       f{#,0}(11,11) -> 14*
       f{#,0}(11,13) -> 14*
       f{#,0}(12,12) -> 14*
       f{#,0}(12,14) -> 14*
       f2(31,30) -> 32*
       f2(30,32) -> 33*
       f0(12,14) -> 13*
       f0(12,18) -> 19*
       f0(13,11) -> 13*
       f0(18,13) -> 19*
       f0(13,13) -> 13*
       f0(14,12) -> 13*
       f0(14,14) -> 13*
       f0(11,12) -> 13*
       f0(11,14) -> 13*
       f0(12,11) -> 13*
       f0(12,13) -> 13*
       f0(13,12) -> 13*
       f0(13,14) -> 13*
       f0(14,11) -> 13*
       f0(14,13) -> 13*
       f0(11,11) -> 13*
       f0(11,13) -> 13*
       f0(17,12) -> 18*
       f0(12,12) -> 13*
       a2() -> 30*
       a0() -> 12*
       h2(30) -> 31*
       h0(12) -> 17,11
       h0(14) -> 11*
       h0(11) -> 11*
       h0(13) -> 11*
       11 -> 15*
       12 -> 15*
       13 -> 15*
       14 -> 15*
     problem:
      DPs:
       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()))))
     Restore Modifier:
      DPs:
       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()))))
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {5}
        transitions:
         f{#,1}(9,14) -> 5*
         f{#,1}(21,22) -> 5*
         f{#,1}(14,21) -> 5*
         f1(13,13) -> 22*
         f1(8,13) -> 21*
         f1(3,13) -> 14*
         f1(13,25) -> 21*
         f1(25,13) -> 21*
         f1(11,10) -> 12*
         f1(22,13) -> 14*
         f1(12,13) -> 13*
         f1(7,13) -> 25*
         f1(2,13) -> 14*
         f1(13,14) -> 14*
         f1(13,22) -> 14*
         f1(14,13) -> 14*
         f1(10,12) -> 13*
         f1(1,13) -> 14*
         a1() -> 10*
         h1(10) -> 11*
         f{#,0}(4,9) -> 5*
         f0(3,1) -> 3*
         f0(8,3) -> 9*
         f0(3,3) -> 3*
         f0(3,25) -> 9*
         f0(4,8) -> 9*
         f0(25,3) -> 9*
         f0(6,2) -> 7*
         f0(1,2) -> 3*
         f0(2,1) -> 3*
         f0(2,3) -> 3*
         f0(2,7) -> 8*
         f0(3,2) -> 3*
         f0(1,1) -> 3*
         f0(1,3) -> 3*
         f0(2,2) -> 3*
         a0() -> 2*
         h0(2) -> 6,1
         h0(1) -> 1*
         h0(3) -> 1*
         1 -> 4*
         2 -> 4*
         3 -> 4*
       problem:
        DPs:
         
        TRS:
         f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
       Qed