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: 1
     enrichment: match
     automaton:
      final states: {9,8,1}
      transitions:
       f1(7,18) -> 7*
       f1(14,16) -> 17*
       f1(11,18) -> 13*
       f1(18,18) -> 13*
       f1(4,17) -> 18*
       f1(15,14) -> 16*
       f1(5,18) -> 13*
       a1() -> 14*
       h1(14) -> 15*
       f{#,1}(7,18) -> 8*
       f{#,1}(11,18) -> 8*
       f{#,1}(18,18) -> 8*
       f{#,1}(4,17) -> 8*
       f{#,1}(5,18) -> 8*
       f40() -> 6*
       f{#,0}(13,13) -> 8*
       f{#,0}(5,5) -> 1*
       f{#,0}(5,7) -> 8*
       f{#,0}(5,11) -> 1*
       f{#,0}(7,7) -> 1*
       f{#,0}(7,11) -> 8*
       f{#,0}(7,13) -> 1*
       f{#,0}(4,5) -> 8*
       f{#,0}(6,5) -> 8*
       f{#,0}(6,7) -> 1*
       f{#,0}(11,11) -> 8*
       f{#,0}(11,13) -> 1*
       f0(13,13) -> 9*
       f0(5,5) -> 13*
       f0(5,7) -> 7*
       f0(5,11) -> 13*
       f0(7,7) -> 9*
       f0(7,11) -> 7*
       f0(7,13) -> 9*
       f0(3,2) -> 4*
       f0(4,5) -> 11*
       f0(6,5) -> 7*
       f0(6,7) -> 9*
       f0(11,11) -> 13*
       f0(11,13) -> 7*
       f0(2,4) -> 5*
       a0() -> 2*
       h0(2) -> 3*
       1 -> 8*
       8 -> 1*
     problem:
      DPs:
       
      TRS:
       f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
     Qed