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)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     +(x,+(y,z)) -> +(+(x,y),z)
    interpretation:
     [f#](x0) = x0 + 1,
     
     [+#](x0, x1) = x0 + 3x1,
     
     [h](x0, x1) = x0 + 4x1 + 6,
     
     [g](x0) = x0 + 3,
     
     [f](x0) = 4x0 + 7,
     
     [s](x0) = x0 + 1,
     
     [+](x0, x1) = x0 + 3x1 + 1,
     
     [0] = 0
    orientation:
     +#(x,s(y)) = x + 3y + 3 >= x + 3y = +#(x,y)
     
     +#(s(x),y) = x + 3y + 1 >= x + 3y = +#(x,y)
     
     +#(x,+(y,z)) = x + 3y + 9z + 3 >= x + 3y = +#(x,y)
     
     +#(x,+(y,z)) = x + 3y + 9z + 3 >= x + 3y + 3z + 1 = +#(+(x,y),z)
     
     f#(g(f(x))) = 4x + 11 >= 4x + 8 = f#(h(s(0()),x))
     
     f#(g(h(x,y))) = x + 4y + 10 >= x + 4y + 8 = f#(h(s(x),y))
     
     f#(h(x,h(y,z))) = x + 4y + 16z + 31 >= x + 3y = +#(x,y)
     
     f#(h(x,h(y,z))) = x + 4y + 16z + 31 >= x + 3y + 4z + 8 = f#(h(+(x,y),z))
     
     +(x,0()) = x + 1 >= x = x
     
     +(x,s(y)) = x + 3y + 4 >= x + 3y + 2 = s(+(x,y))
     
     +(0(),y) = 3y + 1 >= y = y
     
     +(s(x),y) = x + 3y + 2 >= x + 3y + 2 = s(+(x,y))
     
     +(x,+(y,z)) = x + 3y + 9z + 4 >= x + 3y + 3z + 2 = +(+(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)
    Qed