YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
   f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
     f#(x,f(a(),y)) -> f#(a(),x)
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {14}
      transitions:
       a1() -> 31*
       f50() -> 15*
       f1(31,37) -> 38*
       f1(38,22) -> 16*
       f1(31,31) -> 36*
       f{#,0}(16,15) -> 14*
       h1(36) -> 37*
       f0(16,16) -> 21*
       f0(16,22) -> 16*
       f0(16,15) -> 15*
       a0() -> 16*
       h0(21) -> 22*
       f{#,1}(31,16) -> 14*
       f{#,1}(38,22) -> 14*
       f{#,1}(31,31) -> 14*
     problem:
      DPs:
       f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
       f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
      TRS:
       f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
     Semantic Labeling Processor:
      dimension: 1
      usable rules:
       f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
      interpretation:
       [h](x0) = 1,
       
       [f](x0, x1) = x1 + 1,
       
       [a] = 1
       labeled:
       usable (for model):
       argument filtering:
        pi(a) = []
        pi(f) = [1]
        pi(h) = []
        pi(f#) = 1
      precedence:
       f# ~ h ~ f ~ a
      problem:
       DPs:
        f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
      Restore Modifier:
       DPs:
        f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
       Semantic Labeling Processor:
        dimension: 2
        usable rules:
         
        interpretation:
                   [1 1]     [1]
         [h](x0) = [0 0]x0 + [0],
         
                       [0 0]     [0 1]  
         [f](x0, x1) = [1 0]x0 + [1 1]x1,
         
               [1]
         [a] = [0]
         labeled:
          f#
          f
         usable (for model):
          f#
          f
          a
          h
         argument filtering:
          pi(a) = []
          pi(f) = 1
          pi(h) = []
          pi(f#) = []
        precedence:
         f# ~ h ~ f ~ a
        problem:
         DPs:
          
         TRS:
          f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
        Qed