YES

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