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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 2x0 + 1,
   
   [+](x0, x1) = x0 + x1,
   
   [f](x0) = 2x0 + 1,
   
   [h](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [s](x0) = x0
  orientation:
   +(x,0()) = x >= x = x
   
   +(x,s(y)) = x + y >= x + y = s(+(x,y))
   
   +(0(),y) = y >= y = y
   
   +(s(x),y) = x + y >= x + y = s(+(x,y))
   
   +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
   
   f(g(f(x))) = 8x + 7 >= 2x + 1 = f(h(s(0()),x))
   
   f(g(h(x,y))) = 16x + 4y + 3 >= 8x + 2y + 1 = f(h(s(x),y))
   
   f(h(x,h(y,z))) = 8x + 8y + 2z + 1 >= 8x + 8y + 2z + 1 = f(h(+(x,y),z))
  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(h(x,h(y,z))) -> f(h(+(x,y),z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = x0 + 4x1,
    
    [f](x0) = x0 + 6,
    
    [h](x0, x1) = 4x0 + 4x1 + 1,
    
    [0] = 3,
    
    [s](x0) = x0 + 2
   orientation:
    +(x,0()) = x + 12 >= x = x
    
    +(x,s(y)) = x + 4y + 8 >= x + 4y + 2 = s(+(x,y))
    
    +(0(),y) = 4y + 3 >= y = y
    
    +(s(x),y) = x + 4y + 2 >= x + 4y + 2 = s(+(x,y))
    
    +(x,+(y,z)) = x + 4y + 16z >= x + 4y + 4z = +(+(x,y),z)
    
    f(h(x,h(y,z))) = 4x + 16y + 16z + 11 >= 4x + 16y + 4z + 7 = f(h(+(x,y),z))
   problem:
    +(s(x),y) -> s(+(x,y))
    +(x,+(y,z)) -> +(+(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + 2x1 + 5,
     
     [s](x0) = x0
    orientation:
     +(s(x),y) = x + 2y + 5 >= x + 2y + 5 = s(+(x,y))
     
     +(x,+(y,z)) = x + 2y + 4z + 15 >= x + 2y + 2z + 10 = +(+(x,y),z)
    problem:
     +(s(x),y) -> s(+(x,y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 1 0]     [1 0 0]  
      [+](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                    [0 1 1]     [1 0 0]  ,
      
                [1 0 0]     [0]
      [s](x0) = [0 1 0]x0 + [1]
                [1 0 0]     [0]
     orientation:
                  [1 1 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [0]            
      +(s(x),y) = [0 1 0]x + [0 0 0]y + [1] >= [0 1 0]x + [0 0 0]y + [1] = s(+(x,y))
                  [1 1 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [0]            
     problem:
      
     Qed