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=3
  
  interpretation:
                 [1 1 1]     [1 0 0]  
   [h](x0, x1) = [0 0 0]x0 + [1 0 0]x1
                 [1 0 0]     [0 0 0]  ,
   
             [1 0 0]     [1]
   [g](x0) = [0 0 1]x0 + [1]
             [0 1 0]     [0],
   
             [1 0 0]  
   [f](x0) = [0 1 1]x0
             [1 0 0]  ,
   
             [1 0 0]  
   [s](x0) = [0 1 0]x0
             [0 0 0]  ,
   
                        
   [+](x0, x1) = x0 + x1
                        ,
   
         [1]
   [0] = [0]
         [0]
  orientation:
                  [1]         
   +(x,0()) = x + [0] >= x = x
                  [0]         
   
                   [1 0 0]     [1 0 0]    [1 0 0]             
   +(x,s(y)) = x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = s(+(x,y))
                   [0 0 0]     [0 0 0]    [0 0 0]             
   
                  [1]         
   +(0(),y) = y + [0] >= y = y
                  [0]         
   
               [1 0 0]         [1 0 0]    [1 0 0]             
   +(s(x),y) = [0 1 0]x + y >= [0 1 0]x + [0 1 0]y = s(+(x,y))
               [0 0 0]         [0 0 0]    [0 0 0]             
   
                                                     
   +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
                                                     
   
                [1 0 0]    [1]    [1 0 0]    [1]                 
   f(g(f(x))) = [1 1 1]x + [1] >= [1 0 0]x + [1] = f(h(s(0()),x))
                [1 0 0]    [1]    [1 0 0]    [1]                 
   
                  [1 1 1]    [1 0 0]    [1]    [1 1 0]    [1 0 0]                
   f(g(h(x,y))) = [1 0 0]x + [1 0 0]y + [1] >= [1 0 0]x + [1 0 0]y = f(h(s(x),y))
                  [1 1 1]    [1 0 0]    [1]    [1 1 0]    [1 0 0]                
   
                    [1 1 1]    [1 1 1]    [1 0 0]     [1 1 1]    [1 1 1]    [1 0 0]                  
   f(h(x,h(y,z))) = [1 0 0]x + [1 1 1]y + [1 0 0]z >= [1 0 0]x + [1 0 0]y + [1 0 0]z = f(h(+(x,y),z))
                    [1 1 1]    [1 1 1]    [1 0 0]     [1 1 1]    [1 1 1]    [1 0 0]                  
  problem:
   +(x,s(y)) -> s(+(x,y))
   +(s(x),y) -> s(+(x,y))
   +(x,+(y,z)) -> +(+(x,y),z)
   f(g(f(x))) -> f(h(s(0()),x))
   f(h(x,h(y,z))) -> f(h(+(x,y),z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h](x0, x1) = x0 + 2x1,
    
    [g](x0) = x0 + 2,
    
    [f](x0) = 4x0 + 2,
    
    [s](x0) = x0 + 1,
    
    [+](x0, x1) = x0 + x1,
    
    [0] = 0
   orientation:
    +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,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))) = 16x + 18 >= 8x + 6 = f(h(s(0()),x))
    
    f(h(x,h(y,z))) = 4x + 8y + 16z + 2 >= 4x + 4y + 8z + 2 = f(h(+(x,y),z))
   problem:
    +(x,s(y)) -> s(+(x,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:
     [h](x0, x1) = 2x0 + 4x1,
     
     [f](x0) = x0 + 6,
     
     [s](x0) = x0 + 1,
     
     [+](x0, x1) = x0 + 2x1
    orientation:
     +(x,s(y)) = x + 2y + 2 >= x + 2y + 1 = s(+(x,y))
     
     +(s(x),y) = x + 2y + 1 >= x + 2y + 1 = s(+(x,y))
     
     +(x,+(y,z)) = x + 2y + 4z >= x + 2y + 2z = +(+(x,y),z)
     
     f(h(x,h(y,z))) = 2x + 8y + 16z + 6 >= 2x + 4y + 4z + 6 = f(h(+(x,y),z))
    problem:
     +(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=3
     
     interpretation:
                    [1 0 1]     [1 0 1]     [0]
      [h](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [1],
      
                [1 1 0]  
      [f](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 1 0]  
      [s](x0) = [0 0 0]x0
                [0 0 1]  ,
      
                    [1 0 1]     [1 0 0]  
      [+](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  
     orientation:
                  [1 1 1]    [1 0 0]     [1 0 1]    [1 0 0]             
      +(s(x),y) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = s(+(x,y))
                  [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]             
      
                    [1 0 1]    [1 0 1]    [1 0 0]     [1 0 1]    [1 0 0]    [1 0 0]               
      +(x,+(y,z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z >= [0 0 0]x + [0 0 0]y + [0 0 0]z = +(+(x,y),z)
                    [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]               
      
                       [1 1 1]    [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 0]    [1 0 1]                  
      f(h(x,h(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z = f(h(+(x,y),z))
                       [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                  
     problem:
      +(s(x),y) -> s(+(x,y))
      +(x,+(y,z)) -> +(+(x,y),z)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [s](x0) = x0 + 6,
       
       [+](x0, x1) = x0 + 2x1 + 1
      orientation:
       +(s(x),y) = x + 2y + 7 >= x + 2y + 7 = s(+(x,y))
       
       +(x,+(y,z)) = x + 2y + 4z + 3 >= x + 2y + 2z + 2 = +(+(x,y),z)
      problem:
       +(s(x),y) -> s(+(x,y))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                       [0]
        [s](x0) = x0 + [1]
                       [1],
        
                      [1 1 0]     [1 0 0]  
        [+](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                      [0 1 0]     [0 0 0]  
       orientation:
                    [1 1 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [0]            
        +(s(x),y) = [0 0 1]x + [0 0 0]y + [1] >= [0 0 1]x + [0 0 0]y + [1] = s(+(x,y))
                    [0 1 0]    [0 0 0]    [1]    [0 1 0]    [0 0 0]    [1]            
       problem:
        
       Qed