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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f#](x0) = 3x0 + 1/2,
    
    [+#](x0, x1) = 1/2x0 + 3/2x1,
    
    [h](x0, x1) = 1/2x0 + 3x1 + 2,
    
    [g](x0) = x0 + 3,
    
    [f](x0) = 3x0 + 2,
    
    [s](x0) = x0 + 3,
    
    [+](x0, x1) = x0 + 3x1 + 3,
    
    [0] = 0
   orientation:
    +#(x,s(y)) = 1/2x + 3/2y + 9/2 >= 1/2x + 3/2y = +#(x,y)
    
    +#(s(x),y) = 1/2x + 3/2y + 3/2 >= 1/2x + 3/2y = +#(x,y)
    
    +#(x,+(y,z)) = 1/2x + 3/2y + 9/2z + 9/2 >= 1/2x + 3/2y = +#(x,y)
    
    +#(x,+(y,z)) = 1/2x + 3/2y + 9/2z + 9/2 >= 1/2x + 3/2y + 3/2z + 3/2 = +#(+(x,y),z)
    
    f#(g(f(x))) = 9x + 31/2 >= 9x + 11 = f#(h(s(0()),x))
    
    f#(g(h(x,y))) = 3/2x + 9y + 31/2 >= 3/2x + 9y + 11 = f#(h(s(x),y))
    
    f#(h(x,h(y,z))) = 3/2x + 9/2y + 27z + 49/2 >= 1/2x + 3/2y = +#(x,y)
    
    f#(h(x,h(y,z))) = 3/2x + 9/2y + 27z + 49/2 >= 3/2x + 9/2y + 9z + 11 = f#(h(+(x,y),z))
    
    +(x,0()) = x + 3 >= x = x
    
    +(x,s(y)) = x + 3y + 12 >= x + 3y + 6 = s(+(x,y))
    
    +(0(),y) = 3y + 3 >= y = y
    
    +(s(x),y) = x + 3y + 6 >= x + 3y + 6 = s(+(x,y))
    
    +(x,+(y,z)) = x + 3y + 9z + 12 >= x + 3y + 3z + 6 = +(+(x,y),z)
    
    f(g(f(x))) = 9x + 17 >= 9x + 25/2 = f(h(s(0()),x))
    
    f(g(h(x,y))) = 3/2x + 9y + 17 >= 3/2x + 9y + 25/2 = f(h(s(x),y))
    
    f(h(x,h(y,z))) = 3/2x + 9/2y + 27z + 26 >= 3/2x + 9/2y + 9z + 25/2 = 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