YES

Problem:
 a__f(0()) -> cons(0(),f(s(0())))
 a__f(s(0())) -> a__f(a__p(s(0())))
 a__p(s(X)) -> mark(X)
 mark(f(X)) -> a__f(mark(X))
 mark(p(X)) -> a__p(mark(X))
 mark(0()) -> 0()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 a__f(X) -> f(X)
 a__p(X) -> p(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 1 0]     [1 0 0]  
   [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                    [0 1 0]     [0 0 0]  ,
   
                     [1]
   [a__f](x0) = x0 + [1]
                     [1],
   
                  [0]
   [f](x0) = x0 + [1]
                  [1],
   
                [1 1 0]  
   [a__p](x0) = [0 0 1]x0
                [0 1 0]  ,
   
         [0]
   [0] = [0]
         [0],
   
             [1 1 0]  
   [p](x0) = [0 0 1]x0
             [0 1 0]  ,
   
                [1 1 0]  
   [mark](x0) = [0 0 1]x0
                [0 1 0]  ,
   
             [1 0 0]  
   [s](x0) = [0 1 1]x0
             [0 1 1]  
  orientation:
               [1]    [0]                      
   a__f(0()) = [1] >= [0] = cons(0(),f(s(0())))
               [1]    [0]                      
   
                  [1]    [1]                     
   a__f(s(0())) = [1] >= [1] = a__f(a__p(s(0())))
                  [1]    [1]                     
   
                [1 1 1]     [1 1 0]           
   a__p(s(X)) = [0 1 1]X >= [0 0 1]X = mark(X)
                [0 1 1]     [0 1 0]           
   
                [1 1 0]    [1]    [1 1 0]    [1]                
   mark(f(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = a__f(mark(X))
                [0 1 0]    [1]    [0 1 0]    [1]                
   
                [1 1 1]     [1 1 1]                 
   mark(p(X)) = [0 1 0]X >= [0 1 0]X = a__p(mark(X))
                [0 0 1]     [0 0 1]                 
   
               [0]    [0]      
   mark(0()) = [0] >= [0] = 0()
               [0]    [0]      
   
                       [1 1 1]     [1 0 0]      [1 1 1]     [1 0 0]                      
   mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(mark(X1),X2)
                       [0 0 1]     [0 0 0]      [0 0 1]     [0 0 0]                      
   
                [1 1 1]     [1 1 0]              
   mark(s(X)) = [0 1 1]X >= [0 1 1]X = s(mark(X))
                [0 1 1]     [0 1 1]              
   
                 [1]        [0]       
   a__f(X) = X + [1] >= X + [1] = f(X)
                 [1]        [1]       
   
             [1 1 0]     [1 1 0]        
   a__p(X) = [0 0 1]X >= [0 0 1]X = p(X)
             [0 1 0]     [0 1 0]        
  problem:
   a__f(s(0())) -> a__f(a__p(s(0())))
   a__p(s(X)) -> mark(X)
   mark(f(X)) -> a__f(mark(X))
   mark(p(X)) -> a__p(mark(X))
   mark(0()) -> 0()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   a__p(X) -> p(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cons](x0, x1) = x0 + x1 + 2,
    
    [a__f](x0) = 2x0 + 2,
    
    [f](x0) = 2x0 + 1,
    
    [a__p](x0) = x0,
    
    [0] = 0,
    
    [p](x0) = x0,
    
    [mark](x0) = 2x0,
    
    [s](x0) = 2x0
   orientation:
    a__f(s(0())) = 2 >= 2 = a__f(a__p(s(0())))
    
    a__p(s(X)) = 2X >= 2X = mark(X)
    
    mark(f(X)) = 4X + 2 >= 4X + 2 = a__f(mark(X))
    
    mark(p(X)) = 2X >= 2X = a__p(mark(X))
    
    mark(0()) = 0 >= 0 = 0()
    
    mark(cons(X1,X2)) = 2X1 + 2X2 + 4 >= 2X1 + X2 + 2 = cons(mark(X1),X2)
    
    mark(s(X)) = 4X >= 4X = s(mark(X))
    
    a__p(X) = X >= X = p(X)
   problem:
    a__f(s(0())) -> a__f(a__p(s(0())))
    a__p(s(X)) -> mark(X)
    mark(f(X)) -> a__f(mark(X))
    mark(p(X)) -> a__p(mark(X))
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    a__p(X) -> p(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 1 0]  
     [a__f](x0) = [0 0 0]x0
                  [0 0 0]  ,
     
               [1 1 0]  
     [f](x0) = [1 1 0]x0
               [0 0 0]  ,
     
                  [1 0 0]  
     [a__p](x0) = [1 0 0]x0
                  [0 0 1]  ,
     
           [0]
     [0] = [0]
           [0],
     
               [1 0 0]  
     [p](x0) = [1 0 0]x0
               [0 0 1]  ,
     
                  [1 0 0]     [0]
     [mark](x0) = [0 1 0]x0 + [0]
                  [1 0 0]     [1],
     
               [1 1 0]     [0]
     [s](x0) = [1 0 0]x0 + [1]
               [1 0 0]     [1]
    orientation:
                    [1]    [0]                     
     a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0())))
                    [0]    [0]                     
     
                  [1 1 0]    [0]    [1 0 0]    [0]          
     a__p(s(X)) = [1 1 0]X + [0] >= [0 1 0]X + [0] = mark(X)
                  [1 0 0]    [1]    [1 0 0]    [1]          
     
                  [1 1 0]    [0]    [1 1 0]                 
     mark(f(X)) = [1 1 0]X + [0] >= [0 0 0]X = a__f(mark(X))
                  [1 1 0]    [1]    [0 0 0]                 
     
                  [1 0 0]    [0]    [1 0 0]    [0]                
     mark(p(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = a__p(mark(X))
                  [1 0 0]    [1]    [1 0 0]    [1]                
     
                 [0]    [0]      
     mark(0()) = [0] >= [0] = 0()
                 [1]    [0]      
     
                  [1 1 0]    [0]    [1 1 0]    [0]             
     mark(s(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = s(mark(X))
                  [1 1 0]    [1]    [1 0 0]    [1]             
     
               [1 0 0]     [1 0 0]        
     a__p(X) = [1 0 0]X >= [1 0 0]X = p(X)
               [0 0 1]     [0 0 1]        
    problem:
     a__p(s(X)) -> mark(X)
     mark(f(X)) -> a__f(mark(X))
     mark(p(X)) -> a__p(mark(X))
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__p(X) -> p(X)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                   [1 0 0]     [1]
      [a__f](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
      
                [1 0 0]     [0]
      [f](x0) = [0 0 0]x0 + [0]
                [0 0 1]     [1],
      
                   [1 0 0]  
      [a__p](x0) = [0 0 1]x0
                   [0 1 1]  ,
      
            [0]
      [0] = [0]
            [0],
      
                [1 0 0]  
      [p](x0) = [0 0 0]x0
                [0 0 1]  ,
      
                   [1 0 1]  
      [mark](x0) = [0 0 0]x0
                   [0 0 0]  ,
      
                [1 0 1]     [1]
      [s](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [0]
     orientation:
                   [1 0 1]    [1]    [1 0 1]           
      a__p(s(X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(X)
                   [0 0 0]    [0]    [0 0 0]           
      
                   [1 0 1]    [1]    [1 0 1]    [1]                
      mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X))
                   [0 0 0]    [0]    [0 0 0]    [0]                
      
                   [1 0 1]     [1 0 1]                 
      mark(p(X)) = [0 0 0]X >= [0 0 0]X = a__p(mark(X))
                   [0 0 0]     [0 0 0]                 
      
                  [0]    [0]      
      mark(0()) = [0] >= [0] = 0()
                  [0]    [0]      
      
                   [1 0 1]    [1]    [1 0 1]    [1]             
      mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(mark(X))
                   [0 0 0]    [0]    [0 0 0]    [0]             
      
                [1 0 0]     [1 0 0]        
      a__p(X) = [0 0 1]X >= [0 0 0]X = p(X)
                [0 1 1]     [0 0 1]        
     problem:
      mark(f(X)) -> a__f(mark(X))
      mark(p(X)) -> a__p(mark(X))
      mark(0()) -> 0()
      mark(s(X)) -> s(mark(X))
      a__p(X) -> p(X)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                    [1 0 0]  
       [a__f](x0) = [0 0 0]x0
                    [0 0 0]  ,
       
                 [1 1 0]     [1]
       [f](x0) = [0 0 0]x0 + [0]
                 [1 0 0]     [1],
       
                         [0]
       [a__p](x0) = x0 + [1]
                         [1],
       
             [0]
       [0] = [1]
             [1],
       
                      [0]
       [p](x0) = x0 + [1]
                      [1],
       
                    [1 1 0]  
       [mark](x0) = [0 0 1]x0
                    [0 1 0]  ,
       
                 [1 1 0]     [0]
       [s](x0) = [0 0 1]x0 + [1]
                 [0 1 0]     [1]
      orientation:
                    [1 1 0]    [1]    [1 1 0]                 
       mark(f(X)) = [1 0 0]X + [1] >= [0 0 0]X = a__f(mark(X))
                    [0 0 0]    [0]    [0 0 0]                 
       
                    [1 1 0]    [1]    [1 1 0]    [0]                
       mark(p(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = a__p(mark(X))
                    [0 1 0]    [1]    [0 1 0]    [1]                
       
                   [1]    [0]      
       mark(0()) = [1] >= [1] = 0()
                   [1]    [1]      
       
                    [1 1 1]    [1]    [1 1 1]    [0]             
       mark(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(mark(X))
                    [0 0 1]    [1]    [0 0 1]    [1]             
       
                     [0]        [0]       
       a__p(X) = X + [1] >= X + [1] = p(X)
                     [1]        [1]       
      problem:
       a__p(X) -> p(X)
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                     [1 0 0]     [1]
        [a__p](x0) = [0 0 0]x0 + [0]
                     [0 0 1]     [0],
        
                  [1 0 0]  
        [p](x0) = [0 0 0]x0
                  [0 0 0]  
       orientation:
                  [1 0 0]    [1]    [1 0 0]        
        a__p(X) = [0 0 0]X + [0] >= [0 0 0]X = p(X)
                  [0 0 1]    [0]    [0 0 0]        
       problem:
        
       Qed