YES

Problem:
 app(nil(),k) -> k
 app(l,nil()) -> l
 app(cons(x,l),k) -> cons(x,app(l,k))
 sum(cons(x,nil())) -> cons(x,nil())
 sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
 sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
 pred(cons(s(x),nil())) -> cons(x,nil())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [pred](x0) = x0,
   
   [s](x0) = x0,
   
   [0] = 4,
   
   [plus](x0, x1) = x0 + x1,
   
   [sum](x0) = x0,
   
   [cons](x0, x1) = x0 + x1,
   
   [app](x0, x1) = 4x0 + 2x1,
   
   [nil] = 1
  orientation:
   app(nil(),k) = 2k + 4 >= k = k
   
   app(l,nil()) = 4l + 2 >= l = l
   
   app(cons(x,l),k) = 2k + 4l + 4x >= 2k + 4l + x = cons(x,app(l,k))
   
   sum(cons(x,nil())) = x + 1 >= x + 1 = cons(x,nil())
   
   sum(cons(x,cons(y,l))) = l + x + y >= l + x + y = sum(cons(plus(x,y),l))
   
   sum(app(l,cons(x,cons(y,k)))) = 2k + 4l + 2x + 2y >= 2k + 4l + 2x + 2y = sum(app(l,sum(cons(x,cons(y,k)))))
   
   plus(0(),y) = y + 4 >= y = y
   
   plus(s(x),y) = x + y >= x + y = s(plus(x,y))
   
   sum(plus(cons(0(),x),cons(y,l))) = l + x + y + 4 >= l + x + y = pred(sum(cons(s(x),cons(y,l))))
   
   pred(cons(s(x),nil())) = x + 1 >= x + 1 = cons(x,nil())
  problem:
   app(cons(x,l),k) -> cons(x,app(l,k))
   sum(cons(x,nil())) -> cons(x,nil())
   sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
   sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
   plus(s(x),y) -> s(plus(x,y))
   pred(cons(s(x),nil())) -> cons(x,nil())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]  
    [pred](x0) = [0 0 0]x0
                 [1 0 0]  ,
    
              [1 1 0]     [1]
    [s](x0) = [0 0 0]x0 + [1]
              [1 0 0]     [0],
    
                     [1 0 0]     [1 0 0]  
    [plus](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 1 1]     [1 1 1]  ,
    
                [1 1 0]     [0]
    [sum](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1],
    
                     [1 0 0]     [1 0 0]     [0]
    [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [0]
                     [0 0 0]     [0 0 0]     [1],
    
                         [1 0 0]  
    [app](x0, x1) = x0 + [0 1 0]x1
                         [0 0 0]  ,
    
            [0]
    [nil] = [0]
            [0]
   orientation:
                       [1 0 0]    [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [1 0 0]    [0]                   
    app(cons(x,l),k) = [0 1 0]k + [0 1 1]l + [0 0 0]x + [0] >= [0 1 0]k + [0 1 1]l + [0 0 0]x + [0] = cons(x,app(l,k))
                       [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                   
    
                         [1 0 0]    [0]    [1 0 0]    [0]                
    sum(cons(x,nil())) = [0 0 0]x + [0] >= [0 0 0]x + [0] = cons(x,nil())
                         [0 0 0]    [1]    [0 0 0]    [1]                
    
                             [1 1 1]    [1 0 0]    [1 0 0]    [1]    [1 1 1]    [1 0 0]    [1 0 0]    [0]                         
    sum(cons(x,cons(y,l))) = [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] = sum(cons(plus(x,y),l))
                             [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                         
    
                                    [1 1 1]    [1 1 0]    [1 0 0]    [1 0 0]    [1]    [1 1 1]    [1 1 0]    [1 0 0]    [1 0 0]    [1]                                     
    sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] = sum(app(l,sum(cons(x,cons(y,k)))))
                                    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                                     
    
                   [1 1 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [1]               
    plus(s(x),y) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = s(plus(x,y))
                   [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 0 0]    [0]               
    
                             [1 1 0]    [1]    [1 0 0]    [0]                
    pred(cons(s(x),nil())) = [0 0 0]x + [0] >= [0 0 0]x + [0] = cons(x,nil())
                             [1 1 0]    [1]    [0 0 0]    [1]                
   problem:
    app(cons(x,l),k) -> cons(x,app(l,k))
    sum(cons(x,nil())) -> cons(x,nil())
    sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
    plus(s(x),y) -> s(plus(x,y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 
     [s](x0) = x0
                 ,
     
                      [1 0 0]       
     [plus](x0, x1) = [1 0 0]x0 + x1
                      [0 0 0]       ,
     
                 [1 0 0]  
     [sum](x0) = [0 1 0]x0
                 [0 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 1 1]     [0],
     
                     [1 1 1]     [1 1 0]  
     [app](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 0 1]     [0 1 0]  ,
     
             [1]
     [nil] = [0]
             [0]
    orientation:
                        [1 1 0]    [1 1 1]    [1 1 0]    [1]    [1 1 0]    [1 1 1]    [1 0 0]    [0]                   
     app(cons(x,l),k) = [0 0 0]k + [0 0 0]l + [0 1 0]x + [1] >= [0 0 0]k + [0 0 0]l + [0 1 0]x + [1] = cons(x,app(l,k))
                        [0 1 0]    [0 1 1]    [0 0 0]    [0]    [0 1 0]    [0 1 1]    [0 0 0]    [0]                   
     
                          [1 0 0]    [1]    [1 0 0]    [1]                
     sum(cons(x,nil())) = [0 1 0]x + [1] >= [0 1 0]x + [1] = cons(x,nil())
                          [0 0 0]    [0]    [0 0 0]    [0]                
     
                                     [1 0 0]    [1 1 1]    [1 1 0]    [1 0 0]    [1]    [1 0 0]    [1 1 1]    [1 1 0]    [1 0 0]    [1]                                     
     sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 1 0]l + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]k + [0 1 0]l + [0 0 0]x + [0 0 0]y + [0] = sum(app(l,sum(cons(x,cons(y,k)))))
                                     [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                                     
     
                    [1 0 0]         [1 0 0]                    
     plus(s(x),y) = [1 0 0]x + y >= [1 0 0]x + y = s(plus(x,y))
                    [0 0 0]         [0 0 0]                    
    problem:
     sum(cons(x,nil())) -> cons(x,nil())
     sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
     plus(s(x),y) -> s(plus(x,y))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [s](x0) = x0 + 3,
      
      [plus](x0, x1) = 3x0 + x1 + 2,
      
      [sum](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [app](x0, x1) = 4x0 + x1,
      
      [nil] = 4
     orientation:
      sum(cons(x,nil())) = x + 4 >= x + 4 = cons(x,nil())
      
      sum(app(l,cons(x,cons(y,k)))) = k + 4l + x + y >= k + 4l + x + y = sum(app(l,sum(cons(x,cons(y,k)))))
      
      plus(s(x),y) = 3x + y + 11 >= 3x + y + 5 = s(plus(x,y))
     problem:
      sum(cons(x,nil())) -> cons(x,nil())
      sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                   [1 1 0]     [0]
       [sum](x0) = [0 0 0]x0 + [1]
                   [1 0 0]     [1],
       
                        [1 1 0]     [1 1 0]  
       [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                        [0 0 0]     [0 0 0]  ,
       
                       [1 0 0]     [1 0 0]     [0]
       [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                       [0 0 0]     [0 1 0]     [0],
       
               [0]
       [nil] = [0]
               [1]
      orientation:
                            [1 1 0]    [1]    [1 1 0]    [0]                
       sum(cons(x,nil())) = [0 0 0]x + [1] >= [0 0 0]x + [1] = cons(x,nil())
                            [1 1 0]    [1]    [0 0 0]    [0]                
       
                                       [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]                                     
       sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [1] = sum(app(l,sum(cons(x,cons(y,k)))))
                                       [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 0]    [1 1 0]    [1 1 0]    [1]                                     
      problem:
       sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                    [1 0 0]  
        [sum](x0) = [0 0 0]x0
                    [0 0 0]  ,
        
                         [1 0 0]     [1 0 0]     [0]
        [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                         [0 0 0]     [0 0 0]     [0],
        
                        [1 0 0]     [1 1 0]     [0]
        [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                        [0 0 0]     [0 0 0]     [1]
       orientation:
                                        [1 0 0]    [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1 0 0]    [1 0 0]                                      
        sum(app(l,cons(x,cons(y,k)))) = [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]k + [0 0 0]l + [0 0 0]x + [0 0 0]y = sum(app(l,sum(cons(x,cons(y,k)))))
                                        [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]                                      
       problem:
        
       Qed