YES

Problem:
 f(0()) -> s(0())
 f(s(0())) -> s(s(0()))
 f(s(0())) -> *(s(s(0())),f(0()))
 f(+(x,s(0()))) -> +(s(s(0())),f(x))
 f(+(x,y)) -> *(f(x),f(y))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 0]     [1 1 1]  
   [+](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                 [0 0 1]     [0 0 0]  ,
   
                 [1 1 0]     [1 0 0]  
   [*](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
             [1 0 0]     [0]
   [s](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1],
   
             [1 0 1]     [0]
   [f](x0) = [0 1 0]x0 + [0]
             [0 0 0]     [1],
   
         [0]
   [0] = [0]
         [1]
  orientation:
            [1]    [0]         
   f(0()) = [0] >= [0] = s(0())
            [1]    [1]         
   
               [1]    [0]            
   f(s(0())) = [0] >= [0] = s(s(0()))
               [1]    [1]            
   
               [1]    [1]                      
   f(s(0())) = [0] >= [0] = *(s(s(0())),f(0()))
               [1]    [0]                      
   
                    [1 1 1]    [1]    [1 1 1]    [1]                    
   f(+(x,s(0()))) = [0 1 0]x + [0] >= [0 0 0]x + [0] = +(s(s(0())),f(x))
                    [0 0 0]    [1]    [0 0 0]    [1]                    
   
               [1 1 1]    [1 1 1]    [0]    [1 1 1]    [1 0 1]                
   f(+(x,y)) = [0 1 0]x + [0 0 0]y + [0] >= [0 1 0]x + [0 0 0]y = *(f(x),f(y))
               [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]                
  problem:
   f(s(0())) -> *(s(s(0())),f(0()))
   f(+(x,s(0()))) -> +(s(s(0())),f(x))
   f(+(x,y)) -> *(f(x),f(y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 1 1]     [1 0 1]  
    [+](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                  [1 0 1]     [0 1 0]  ,
    
                  [1 0 1]     [1 0 0]  
    [*](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                  [0 0 1]     [0 0 0]  ,
    
              [1 0 0]  
    [s](x0) = [0 0 1]x0
              [0 0 0]  ,
    
              [1 1 0]  
    [f](x0) = [1 0 0]x0
              [0 0 1]  ,
    
          [0]
    [0] = [0]
          [1]
   orientation:
                [1]    [0]                      
    f(s(0())) = [0] >= [0] = *(s(s(0())),f(0()))
                [0]    [0]                      
    
                     [1 1 1]    [1]    [1 1 1]                     
    f(+(x,s(0()))) = [1 1 1]x + [0] >= [1 0 0]x = +(s(s(0())),f(x))
                     [1 0 1]    [1]    [1 0 0]                     
    
                [1 1 1]    [1 1 1]     [1 1 1]    [1 1 0]                
    f(+(x,y)) = [1 1 1]x + [1 0 1]y >= [0 0 0]x + [1 0 0]y = *(f(x),f(y))
                [1 0 1]    [0 1 0]     [0 0 1]    [0 0 0]                
   problem:
    f(+(x,y)) -> *(f(x),f(y))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + x1 + 2,
     
     [*](x0, x1) = x0 + x1,
     
     [f](x0) = x0 + 1
    orientation:
     f(+(x,y)) = x + y + 3 >= x + y + 2 = *(f(x),f(y))
    problem:
     
    Qed