MAYBE

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:
 RT Transformation Processor:
  strict:
   +(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))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [h](x0, x1) = x0 + x1 + 10,
    
    [g](x0) = x0 + 23,
    
    [f](x0) = x0 + 1,
    
    [s](x0) = x0 + 9,
    
    [+](x0, x1) = x0 + x1 + 21,
    
    [0] = 13
   orientation:
    +(x,0()) = x + 34 >= x = x
    
    +(x,s(y)) = x + y + 30 >= x + y + 30 = s(+(x,y))
    
    +(0(),y) = y + 34 >= y = y
    
    +(s(x),y) = x + y + 30 >= x + y + 30 = s(+(x,y))
    
    +(x,+(y,z)) = x + y + z + 42 >= x + y + z + 42 = +(+(x,y),z)
    
    f(g(f(x))) = x + 25 >= x + 33 = f(h(s(0()),x))
    
    f(g(h(x,y))) = x + y + 34 >= x + y + 20 = f(h(s(x),y))
    
    f(h(x,h(y,z))) = x + y + z + 21 >= x + y + z + 32 = f(h(+(x,y),z))
   problem:
    strict:
     +(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))
    weak:
     +(x,0()) -> x
     +(0(),y) -> y
     f(g(h(x,y))) -> f(h(s(x),y))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [h](x0, x1) = x0 + x1 + 19,
     
     [g](x0) = x0 + 1,
     
     [f](x0) = x0 + 17,
     
     [s](x0) = x0 + 1,
     
     [+](x0, x1) = x0 + x1 + 16,
     
     [0] = 13
    orientation:
     +(x,s(y)) = x + y + 17 >= x + y + 17 = s(+(x,y))
     
     +(s(x),y) = x + y + 17 >= x + y + 17 = s(+(x,y))
     
     +(x,+(y,z)) = x + y + z + 32 >= x + y + z + 32 = +(+(x,y),z)
     
     f(g(f(x))) = x + 35 >= x + 50 = f(h(s(0()),x))
     
     f(h(x,h(y,z))) = x + y + z + 55 >= x + y + z + 52 = f(h(+(x,y),z))
     
     +(x,0()) = x + 29 >= x = x
     
     +(0(),y) = y + 29 >= y = y
     
     f(g(h(x,y))) = x + y + 37 >= x + y + 37 = f(h(s(x),y))
    problem:
     strict:
      +(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))
     weak:
      f(h(x,h(y,z))) -> f(h(+(x,y),z))
      +(x,0()) -> x
      +(0(),y) -> y
      f(g(h(x,y))) -> f(h(s(x),y))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [h](x0, x1) = x0 + x1 + 9,
      
      [g](x0) = x0 + 26,
      
      [f](x0) = x0 + 18,
      
      [s](x0) = x0 + 4,
      
      [+](x0, x1) = x0 + x1,
      
      [0] = 30
     orientation:
      +(x,s(y)) = x + y + 4 >= x + y + 4 = s(+(x,y))
      
      +(s(x),y) = x + y + 4 >= x + y + 4 = s(+(x,y))
      
      +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
      
      f(g(f(x))) = x + 62 >= x + 61 = f(h(s(0()),x))
      
      f(h(x,h(y,z))) = x + y + z + 36 >= x + y + z + 27 = f(h(+(x,y),z))
      
      +(x,0()) = x + 30 >= x = x
      
      +(0(),y) = y + 30 >= y = y
      
      f(g(h(x,y))) = x + y + 53 >= x + y + 31 = f(h(s(x),y))
     problem:
      strict:
       +(x,s(y)) -> s(+(x,y))
       +(s(x),y) -> s(+(x,y))
       +(x,+(y,z)) -> +(+(x,y),z)
      weak:
       f(g(f(x))) -> f(h(s(0()),x))
       f(h(x,h(y,z))) -> f(h(+(x,y),z))
       +(x,0()) -> x
       +(0(),y) -> y
       f(g(h(x,y))) -> f(h(s(x),y))
     Matrix Interpretation Processor:
      dimension: 2
      interpretation:
                          [1 2]     [0]
       [h](x0, x1) = x0 + [0 1]x1 + [7],
       
                 [1 2]     [9]
       [g](x0) = [0 1]x0 + [9],
       
                      [0]
       [f](x0) = x0 + [8],
       
                      [2]
       [s](x0) = x0 + [0],
       
                          [1 1]     [0]
       [+](x0, x1) = x0 + [0 1]x1 + [2],
       
             [0]
       [0] = [5]
      orientation:
                       [1 1]    [2]        [1 1]    [2]            
       +(x,s(y)) = x + [0 1]y + [2] >= x + [0 1]y + [2] = s(+(x,y))
       
                       [1 1]    [2]        [1 1]    [2]            
       +(s(x),y) = x + [0 1]y + [2] >= x + [0 1]y + [2] = s(+(x,y))
       
                         [1 1]    [1 2]    [2]        [1 1]    [1 1]    [0]              
       +(x,+(y,z)) = x + [0 1]y + [0 1]z + [4] >= x + [0 1]y + [0 1]z + [4] = +(+(x,y),z)
       
                    [1 2]    [25]    [1 2]    [2 ]                 
       f(g(f(x))) = [0 1]x + [25] >= [0 1]x + [20] = f(h(s(0()),x))
       
                            [1 2]    [1 4]    [14]        [1 1]    [1 2]    [0 ]                 
       f(h(x,h(y,z))) = x + [0 1]y + [0 1]z + [22] >= x + [0 1]y + [0 1]z + [17] = f(h(+(x,y),z))
       
                      [5]         
       +(x,0()) = x + [7] >= x = x
       
                  [1 1]    [0]         
       +(0(),y) = [0 1]y + [7] >= y = y
       
                      [1 2]    [1 4]    [23]        [1 2]    [2 ]               
       f(g(h(x,y))) = [0 1]x + [0 1]y + [24] >= x + [0 1]y + [15] = f(h(s(x),y))
      problem:
       strict:
        +(x,s(y)) -> s(+(x,y))
        +(s(x),y) -> s(+(x,y))
       weak:
        +(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))
        +(x,0()) -> x
        +(0(),y) -> y
        f(g(h(x,y))) -> f(h(s(x),y))
      Matrix Interpretation Processor:
       dimension: 2
       interpretation:
                           [1 4]     [3]
        [h](x0, x1) = x0 + [0 1]x1 + [0],
        
                  [1 1]     [12]
        [g](x0) = [0 1]x0 + [4 ],
        
                  [1 4]  
        [f](x0) = [0 1]x0,
        
                       [0]
        [s](x0) = x0 + [1],
        
                           [1 4]     [1]
        [+](x0, x1) = x0 + [0 1]x1 + [0],
        
              [13]
        [0] = [2 ]
       orientation:
                        [1 4]    [5]        [1 4]    [1]            
        +(x,s(y)) = x + [0 1]y + [1] >= x + [0 1]y + [1] = s(+(x,y))
        
                        [1 4]    [1]        [1 4]    [1]            
        +(s(x),y) = x + [0 1]y + [1] >= x + [0 1]y + [1] = s(+(x,y))
        
                          [1 4]    [1 8]    [2]        [1 4]    [1 4]    [2]              
        +(x,+(y,z)) = x + [0 1]y + [0 1]z + [0] >= x + [0 1]y + [0 1]z + [0] = +(+(x,y),z)
        
                     [1 9]    [28]    [1 8]    [28]                 
        f(g(f(x))) = [0 1]x + [4 ] >= [0 1]x + [3 ] = f(h(s(0()),x))
        
                         [1 4]    [1 8]    [1  12]    [6]    [1 4]    [1 8]    [1 8]    [4]                 
        f(h(x,h(y,z))) = [0 1]x + [0 1]y + [0  1 ]z + [0] >= [0 1]x + [0 1]y + [0 1]z + [0] = f(h(+(x,y),z))
        
                       [22]         
        +(x,0()) = x + [2 ] >= x = x
        
                   [1 4]    [14]         
        +(0(),y) = [0 1]y + [2 ] >= y = y
        
                       [1 5]    [1 9]    [31]    [1 4]    [1 8]    [7]               
        f(g(h(x,y))) = [0 1]x + [0 1]y + [4 ] >= [0 1]x + [0 1]y + [1] = f(h(s(x),y))
       problem:
        strict:
         +(s(x),y) -> s(+(x,y))
        weak:
         +(x,s(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))
         +(x,0()) -> x
         +(0(),y) -> y
         f(g(h(x,y))) -> f(h(s(x),y))
       Open