YES
Time: 0.106868
TRS:
 {  +(x, +(y, z)) -> +(+(x, y), z),
        +(x, 0()) -> x,
        +(x, s y) -> s +(x, y),
        +(0(), y) -> y,
        +(s x, y) -> s +(x, y),
  f h(x, h(y, z)) -> f h(+(x, y), z),
          f g f x -> f h(s 0(), x),
      f g h(x, y) -> f h(s x, y)}
 DP:
  DP:
   {  +#(x, +(y, z)) -> +#(x, y),
      +#(x, +(y, z)) -> +#(+(x, y), z),
          +#(x, s y) -> +#(x, y),
          +#(s x, y) -> +#(x, y),
    f# h(x, h(y, z)) -> +#(x, y),
    f# h(x, h(y, z)) -> f# h(+(x, y), z),
            f# g f x -> f# h(s 0(), x),
        f# g h(x, y) -> f# h(s x, y)}
  TRS:
  {  +(x, +(y, z)) -> +(+(x, y), z),
         +(x, 0()) -> x,
         +(x, s y) -> s +(x, y),
         +(0(), y) -> y,
         +(s x, y) -> s +(x, y),
   f h(x, h(y, z)) -> f h(+(x, y), z),
           f g f x -> f h(s 0(), x),
       f g h(x, y) -> f h(s x, y)}
  EDG:
   {(+#(x, s y) -> +#(x, y), +#(s x, y) -> +#(x, y))
    (+#(x, s y) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (+#(x, s y) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z))
    (+#(x, s y) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y))
    (f# h(x, h(y, z)) -> +#(x, y), +#(s x, y) -> +#(x, y))
    (f# h(x, h(y, z)) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (f# h(x, h(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z))
    (f# h(x, h(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y))
    (f# g f x -> f# h(s 0(), x), f# g h(x, y) -> f# h(s x, y))
    (f# g f x -> f# h(s 0(), x), f# g f x -> f# h(s 0(), x))
    (f# g f x -> f# h(s 0(), x), 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))
    (+#(x, +(y, z)) -> +#(+(x, y), z), +#(s x, y) -> +#(x, y))
    (+#(x, +(y, z)) -> +#(+(x, y), z), +#(x, s y) -> +#(x, y))
    (+#(x, +(y, z)) -> +#(+(x, y), z), +#(x, +(y, z)) -> +#(+(x, y), z))
    (+#(x, +(y, z)) -> +#(+(x, y), z), +#(x, +(y, z)) -> +#(x, y))
    (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 h(x, y) -> f# h(s x, y), f# g f x -> f# h(s 0(), x))
    (f# g h(x, y) -> f# h(s x, y), f# g h(x, y) -> f# h(s x, y))
    (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)) -> f# h(+(x, y), z), f# g f x -> f# h(s 0(), x))
    (f# h(x, h(y, z)) -> f# h(+(x, y), z), f# g h(x, y) -> f# h(s x, y))
    (+#(s x, y) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y))
    (+#(s x, y) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z))
    (+#(s x, y) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (+#(s x, y) -> +#(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))
    (+#(x, +(y, z)) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (+#(x, +(y, z)) -> +#(x, y), +#(s x, y) -> +#(x, y))}
   STATUS:
    arrows: 0.500000
    SCCS (2):
     Scc:
      {f# h(x, h(y, z)) -> f# h(+(x, y), z),
               f# g f x -> f# h(s 0(), x),
           f# g h(x, y) -> f# h(s x, y)}
     Scc:
      {+#(x, +(y, z)) -> +#(x, y),
       +#(x, +(y, z)) -> +#(+(x, y), z),
           +#(x, s y) -> +#(x, y),
           +#(s x, y) -> +#(x, y)}
     
     SCC (3):
      Strict:
       {f# h(x, h(y, z)) -> f# h(+(x, y), z),
                f# g f x -> f# h(s 0(), x),
            f# g h(x, y) -> f# h(s x, y)}
      Weak:
      {  +(x, +(y, z)) -> +(+(x, y), z),
             +(x, 0()) -> x,
             +(x, s y) -> s +(x, y),
             +(0(), y) -> y,
             +(s x, y) -> s +(x, y),
       f h(x, h(y, z)) -> f h(+(x, y), z),
               f g f x -> f h(s 0(), x),
           f g h(x, y) -> f h(s x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [+](x0, x1) = x0 + x1 + 1,
        
        [h](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [f](x0) = 1,
        
        [g](x0) = x0 + 1,
        
        [0] = 1,
        
        [f#](x0) = x0
       Strict:
        f# g h(x, y) -> f# h(s x, y)
        1 + 0x + 0y >= 0 + 0x + 0y
        f# g f x -> f# h(s 0(), x)
        2 + 0x >= 0 + 0x
        f# h(x, h(y, z)) -> f# h(+(x, y), z)
        0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
       Weak:
        f g h(x, y) -> f h(s x, y)
        1 + 0x + 0y >= 1 + 0x + 0y
        f g f x -> f h(s 0(), x)
        1 + 0x >= 1 + 0x
        f h(x, h(y, z)) -> f h(+(x, y), z)
        1 + 0x + 0y + 0z >= 1 + 0x + 0y + 0z
        +(s x, y) -> s +(x, y)
        2 + 1x + 1y >= 2 + 1x + 1y
        +(0(), y) -> y
        2 + 1y >= 1y
        +(x, s y) -> s +(x, y)
        2 + 1x + 1y >= 2 + 1x + 1y
        +(x, 0()) -> x
        2 + 1x >= 1x
        +(x, +(y, z)) -> +(+(x, y), z)
        2 + 1x + 1y + 1z >= 2 + 1x + 1y + 1z
      SCCS (1):
       Scc:
        {f# h(x, h(y, z)) -> f# h(+(x, y), z)}
       
       SCC (1):
        Strict:
         {f# h(x, h(y, z)) -> f# h(+(x, y), z)}
        Weak:
        {  +(x, +(y, z)) -> +(+(x, y), z),
               +(x, 0()) -> x,
               +(x, s y) -> s +(x, y),
               +(0(), y) -> y,
               +(s x, y) -> s +(x, y),
         f h(x, h(y, z)) -> f h(+(x, y), z),
                 f g f x -> f h(s 0(), x),
             f g h(x, y) -> f h(s x, y)}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [+](x0, x1) = 0,
          
          [h](x0, x1) = x0 + 1,
          
          [s](x0) = 0,
          
          [f](x0) = 0,
          
          [g](x0) = 0,
          
          [0] = 0,
          
          [f#](x0) = x0 + 1
         Strict:
          f# h(x, h(y, z)) -> f# h(+(x, y), z)
          3 + 0x + 0y + 1z >= 2 + 0x + 0y + 1z
         Weak:
          f g h(x, y) -> f h(s x, y)
          0 + 0x + 0y >= 0 + 0x + 0y
          f g f x -> f h(s 0(), x)
          0 + 0x >= 0 + 0x
          f h(x, h(y, z)) -> f h(+(x, y), z)
          0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
          +(s x, y) -> s +(x, y)
          0 + 0x + 0y >= 0 + 0x + 0y
          +(0(), y) -> y
          0 + 0y >= 1y
          +(x, s y) -> s +(x, y)
          0 + 0x + 0y >= 0 + 0x + 0y
          +(x, 0()) -> x
          0 + 0x >= 1x
          +(x, +(y, z)) -> +(+(x, y), z)
          0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
        Qed
    
    SCC (4):
     Strict:
      {+#(x, +(y, z)) -> +#(x, y),
       +#(x, +(y, z)) -> +#(+(x, y), z),
           +#(x, s y) -> +#(x, y),
           +#(s x, y) -> +#(x, y)}
     Weak:
     {  +(x, +(y, z)) -> +(+(x, y), z),
            +(x, 0()) -> x,
            +(x, s y) -> s +(x, y),
            +(0(), y) -> y,
            +(s x, y) -> s +(x, y),
      f h(x, h(y, z)) -> f h(+(x, y), z),
              f g f x -> f h(s 0(), x),
          f g h(x, y) -> f h(s x, y)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [+](x0, x1) = x0 + x1 + 1,
       
       [h](x0, x1) = x0,
       
       [s](x0) = x0 + 1,
       
       [f](x0) = 0,
       
       [g](x0) = 0,
       
       [0] = 0,
       
       [+#](x0, x1) = x0 + x1 + 1
      Strict:
       +#(s x, y) -> +#(x, y)
       2 + 1x + 1y >= 1 + 1x + 1y
       +#(x, s y) -> +#(x, y)
       2 + 1x + 1y >= 1 + 1x + 1y
       +#(x, +(y, z)) -> +#(+(x, y), z)
       2 + 1x + 1y + 1z >= 2 + 1x + 1y + 1z
       +#(x, +(y, z)) -> +#(x, y)
       2 + 1x + 1y + 1z >= 1 + 1x + 1y
      Weak:
       f g h(x, y) -> f h(s x, y)
       0 + 0x + 0y >= 0 + 0x + 0y
       f g f x -> f h(s 0(), x)
       0 + 0x >= 0 + 0x
       f h(x, h(y, z)) -> f h(+(x, y), z)
       0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
       +(s x, y) -> s +(x, y)
       2 + 1x + 1y >= 2 + 1x + 1y
       +(0(), y) -> y
       1 + 1y >= 1y
       +(x, s y) -> s +(x, y)
       2 + 1x + 1y >= 2 + 1x + 1y
       +(x, 0()) -> x
       1 + 1x >= 1x
       +(x, +(y, z)) -> +(+(x, y), z)
       2 + 1x + 1y + 1z >= 2 + 1x + 1y + 1z
     SCCS (1):
      Scc:
       {+#(x, +(y, z)) -> +#(+(x, y), z)}
      
      SCC (1):
       Strict:
        {+#(x, +(y, z)) -> +#(+(x, y), z)}
       Weak:
       {  +(x, +(y, z)) -> +(+(x, y), z),
              +(x, 0()) -> x,
              +(x, s y) -> s +(x, y),
              +(0(), y) -> y,
              +(s x, y) -> s +(x, y),
        f h(x, h(y, z)) -> f h(+(x, y), z),
                f g f x -> f h(s 0(), x),
            f g h(x, y) -> f h(s x, y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [+](x0, x1) = x0 + 1,
         
         [h](x0, x1) = 0,
         
         [s](x0) = x0 + 1,
         
         [f](x0) = 0,
         
         [g](x0) = 0,
         
         [0] = 1,
         
         [+#](x0, x1) = x0
        Strict:
         +#(x, +(y, z)) -> +#(+(x, y), z)
         1 + 0x + 0y + 1z >= 0 + 0x + 0y + 1z
        Weak:
         f g h(x, y) -> f h(s x, y)
         0 + 0x + 0y >= 0 + 0x + 0y
         f g f x -> f h(s 0(), x)
         0 + 0x >= 0 + 0x
         f h(x, h(y, z)) -> f h(+(x, y), z)
         0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
         +(s x, y) -> s +(x, y)
         1 + 0x + 1y >= 2 + 0x + 1y
         +(0(), y) -> y
         1 + 1y >= 1y
         +(x, s y) -> s +(x, y)
         2 + 0x + 1y >= 2 + 0x + 1y
         +(x, 0()) -> x
         2 + 0x >= 1x
         +(x, +(y, z)) -> +(+(x, y), z)
         2 + 0x + 0y + 1z >= 1 + 0x + 0y + 1z
       Qed