YES

Problem:
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 +(x,+(y,z)) -> +(+(x,y),z)
 f(g(f(x))) -> f(h(s(0()),x))
 f(g(h(x,y))) -> f(h(s(x),y))
 f(h(x,h(y,z))) -> f(h(+(x,y),z))

Proof:
 DP Processor:
  DPs:
   +#(x,s(y)) -> +#(x,y)
   +#(s(x),y) -> +#(x,y)
   +#(x,+(y,z)) -> +#(x,y)
   +#(x,+(y,z)) -> +#(+(x,y),z)
   f#(g(f(x))) -> f#(h(s(0()),x))
   f#(g(h(x,y))) -> f#(h(s(x),y))
   f#(h(x,h(y,z))) -> +#(x,y)
   f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
  TRS:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   +(x,+(y,z)) -> +(+(x,y),z)
   f(g(f(x))) -> f(h(s(0()),x))
   f(g(h(x,y))) -> f(h(s(x),y))
   f(h(x,h(y,z))) -> f(h(+(x,y),z))
  Usable Rule Processor:
   DPs:
    +#(x,s(y)) -> +#(x,y)
    +#(s(x),y) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z)
    f#(g(f(x))) -> f#(h(s(0()),x))
    f#(g(h(x,y))) -> f#(h(s(x),y))
    f#(h(x,h(y,z))) -> +#(x,y)
    f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
   TRS:
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    +(0(),y) -> y
    +(s(x),y) -> s(+(x,y))
    +(x,+(y,z)) -> +(+(x,y),z)
   CDG Processor:
    DPs:
     +#(x,s(y)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z)
     f#(g(f(x))) -> f#(h(s(0()),x))
     f#(g(h(x,y))) -> f#(h(s(x),y))
     f#(h(x,h(y,z))) -> +#(x,y)
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     +(x,+(y,z)) -> +(+(x,y),z)
    graph:
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z)) ->
     f#(h(x,h(y,z))) -> +#(x,y)
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z)) ->
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     f#(g(h(x,y))) -> f#(h(s(x),y)) -> f#(h(x,h(y,z))) -> +#(x,y)
     f#(g(h(x,y))) -> f#(h(s(x),y)) ->
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     f#(g(f(x))) -> f#(h(s(0()),x)) -> f#(h(x,h(y,z))) -> +#(x,y)
     f#(g(f(x))) -> f#(h(s(0()),x)) -> f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     +#(s(x),y) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,s(y)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    Restore Modifier:
     DPs:
      +#(x,s(y)) -> +#(x,y)
      +#(s(x),y) -> +#(x,y)
      +#(x,+(y,z)) -> +#(x,y)
      +#(x,+(y,z)) -> +#(+(x,y),z)
      f#(g(f(x))) -> f#(h(s(0()),x))
      f#(g(h(x,y))) -> f#(h(s(x),y))
      f#(h(x,h(y,z))) -> +#(x,y)
      f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     TRS:
      +(x,0()) -> x
      +(x,s(y)) -> s(+(x,y))
      +(0(),y) -> y
      +(s(x),y) -> s(+(x,y))
      +(x,+(y,z)) -> +(+(x,y),z)
      f(g(f(x))) -> f(h(s(0()),x))
      f(g(h(x,y))) -> f(h(s(x),y))
      f(h(x,h(y,z))) -> f(h(+(x,y),z))
     SCC Processor:
      #sccs: 2
      #rules: 5
      #arcs: 26/64
      DPs:
       f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       +(x,+(y,z)) -> +(+(x,y),z)
       f(g(f(x))) -> f(h(s(0()),x))
       f(g(h(x,y))) -> f(h(s(x),y))
       f(h(x,h(y,z))) -> f(h(+(x,y),z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0,
        
        [h](x0, x1) = x1 + 1,
        
        [g](x0) = x0 + 1,
        
        [f](x0) = x0,
        
        [s](x0) = 0,
        
        [+](x0, x1) = x0 + x1,
        
        [0] = 0
       orientation:
        f#(h(x,h(y,z))) = z + 2 >= z + 1 = f#(h(+(x,y),z))
        
        +(x,0()) = x >= x = x
        
        +(x,s(y)) = x >= 0 = s(+(x,y))
        
        +(0(),y) = y >= y = y
        
        +(s(x),y) = y >= 0 = s(+(x,y))
        
        +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
        
        f(g(f(x))) = x + 1 >= x + 1 = f(h(s(0()),x))
        
        f(g(h(x,y))) = y + 2 >= y + 1 = f(h(s(x),y))
        
        f(h(x,h(y,z))) = z + 2 >= z + 1 = f(h(+(x,y),z))
       problem:
        DPs:
         
        TRS:
         +(x,0()) -> x
         +(x,s(y)) -> s(+(x,y))
         +(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         +(x,+(y,z)) -> +(+(x,y),z)
         f(g(f(x))) -> f(h(s(0()),x))
         f(g(h(x,y))) -> f(h(s(x),y))
         f(h(x,h(y,z))) -> f(h(+(x,y),z))
       Qed
      
      DPs:
       +#(x,+(y,z)) -> +#(+(x,y),z)
       +#(x,+(y,z)) -> +#(x,y)
       +#(s(x),y) -> +#(x,y)
       +#(x,s(y)) -> +#(x,y)
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       +(x,+(y,z)) -> +(+(x,y),z)
       f(g(f(x))) -> f(h(s(0()),x))
       f(g(h(x,y))) -> f(h(s(x),y))
       f(h(x,h(y,z))) -> f(h(+(x,y),z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x1,
        
        [h](x0, x1) = 1,
        
        [g](x0) = 0,
        
        [f](x0) = 0,
        
        [s](x0) = x0 + 1,
        
        [+](x0, x1) = x0 + x1,
        
        [0] = 0
       orientation:
        +#(x,+(y,z)) = y + z >= z = +#(+(x,y),z)
        
        +#(x,+(y,z)) = y + z >= y = +#(x,y)
        
        +#(s(x),y) = y >= y = +#(x,y)
        
        +#(x,s(y)) = y + 1 >= y = +#(x,y)
        
        +(x,0()) = x >= x = x
        
        +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
        
        +(0(),y) = y >= y = y
        
        +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
        
        +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
        
        f(g(f(x))) = 0 >= 0 = f(h(s(0()),x))
        
        f(g(h(x,y))) = 0 >= 0 = f(h(s(x),y))
        
        f(h(x,h(y,z))) = 0 >= 0 = f(h(+(x,y),z))
       problem:
        DPs:
         +#(x,+(y,z)) -> +#(+(x,y),z)
         +#(x,+(y,z)) -> +#(x,y)
         +#(s(x),y) -> +#(x,y)
        TRS:
         +(x,0()) -> x
         +(x,s(y)) -> s(+(x,y))
         +(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         +(x,+(y,z)) -> +(+(x,y),z)
         f(g(f(x))) -> f(h(s(0()),x))
         f(g(h(x,y))) -> f(h(s(x),y))
         f(h(x,h(y,z))) -> f(h(+(x,y),z))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [+#](x0, x1) = x0 + x1,
         
         [h](x0, x1) = 1,
         
         [g](x0) = 1,
         
         [f](x0) = x0 + 1,
         
         [s](x0) = x0 + 1,
         
         [+](x0, x1) = x0 + x1,
         
         [0] = 0
        orientation:
         +#(x,+(y,z)) = x + y + z >= x + y + z = +#(+(x,y),z)
         
         +#(x,+(y,z)) = x + y + z >= x + y = +#(x,y)
         
         +#(s(x),y) = x + y + 1 >= x + y = +#(x,y)
         
         +(x,0()) = x >= x = x
         
         +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
         
         +(0(),y) = y >= y = y
         
         +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
         
         +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
         
         f(g(f(x))) = 2 >= 2 = f(h(s(0()),x))
         
         f(g(h(x,y))) = 2 >= 2 = f(h(s(x),y))
         
         f(h(x,h(y,z))) = 2 >= 2 = f(h(+(x,y),z))
        problem:
         DPs:
          +#(x,+(y,z)) -> +#(+(x,y),z)
          +#(x,+(y,z)) -> +#(x,y)
         TRS:
          +(x,0()) -> x
          +(x,s(y)) -> s(+(x,y))
          +(0(),y) -> y
          +(s(x),y) -> s(+(x,y))
          +(x,+(y,z)) -> +(+(x,y),z)
          f(g(f(x))) -> f(h(s(0()),x))
          f(g(h(x,y))) -> f(h(s(x),y))
          f(h(x,h(y,z))) -> f(h(+(x,y),z))
        Matrix Interpretation Processor:
         dimension: 1
         interpretation:
          [+#](x0, x1) = x0 + x1,
          
          [h](x0, x1) = x1 + 1,
          
          [g](x0) = x0,
          
          [f](x0) = x0 + 1,
          
          [s](x0) = x0 + 1,
          
          [+](x0, x1) = x0 + x1 + 1,
          
          [0] = 0
         orientation:
          +#(x,+(y,z)) = x + y + z + 1 >= x + y + z + 1 = +#(+(x,y),z)
          
          +#(x,+(y,z)) = x + y + z + 1 >= x + y = +#(x,y)
          
          +(x,0()) = x + 1 >= x = x
          
          +(x,s(y)) = x + y + 2 >= x + y + 2 = s(+(x,y))
          
          +(0(),y) = y + 1 >= y = y
          
          +(s(x),y) = x + y + 2 >= x + y + 2 = s(+(x,y))
          
          +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
          
          f(g(f(x))) = x + 2 >= x + 2 = f(h(s(0()),x))
          
          f(g(h(x,y))) = y + 2 >= y + 2 = f(h(s(x),y))
          
          f(h(x,h(y,z))) = z + 3 >= z + 2 = f(h(+(x,y),z))
         problem:
          DPs:
           +#(x,+(y,z)) -> +#(+(x,y),z)
          TRS:
           +(x,0()) -> x
           +(x,s(y)) -> s(+(x,y))
           +(0(),y) -> y
           +(s(x),y) -> s(+(x,y))
           +(x,+(y,z)) -> +(+(x,y),z)
           f(g(f(x))) -> f(h(s(0()),x))
           f(g(h(x,y))) -> f(h(s(x),y))
           f(h(x,h(y,z))) -> f(h(+(x,y),z))
         Matrix Interpretation Processor:
          dimension: 1
          interpretation:
           [+#](x0, x1) = x1,
           
           [h](x0, x1) = 0,
           
           [g](x0) = 0,
           
           [f](x0) = 0,
           
           [s](x0) = x0,
           
           [+](x0, x1) = x0 + x1 + 1,
           
           [0] = 0
          orientation:
           +#(x,+(y,z)) = y + z + 1 >= z = +#(+(x,y),z)
           
           +(x,0()) = x + 1 >= x = x
           
           +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
           
           +(0(),y) = y + 1 >= y = y
           
           +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
           
           +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
           
           f(g(f(x))) = 0 >= 0 = f(h(s(0()),x))
           
           f(g(h(x,y))) = 0 >= 0 = f(h(s(x),y))
           
           f(h(x,h(y,z))) = 0 >= 0 = f(h(+(x,y),z))
          problem:
           DPs:
            
           TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            +(x,+(y,z)) -> +(+(x,y),z)
            f(g(f(x))) -> f(h(s(0()),x))
            f(g(h(x,y))) -> f(h(s(x),y))
            f(h(x,h(y,z))) -> f(h(+(x,y),z))
          Qed