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))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [plus](x0, x1) = x0 + x1,
   
   [app](x0, x1) = 2x0 + x1 + 1,
   
   [sum](x0) = x0,
   
   [0] = 2,
   
   [nil] = 0,
   
   [s](x0) = x0 + 4,
   
   [cons](x0, x1) = x0 + x1
  orientation:
   app(nil(),k) = k + 1 >= k = k
   
   app(l,nil()) = 2l + 1 >= l = l
   
   app(cons(x,l),k) = k + 2l + 2x + 1 >= k + 2l + x + 1 = cons(x,app(l,k))
   
   sum(cons(x,nil())) = x >= x = 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)))) = k + 2l + x + y + 1 >= k + 2l + x + y + 1 = sum(app(l,sum(cons(x,cons(y,k)))))
   
   plus(0(),y) = y + 2 >= y = y
   
   plus(s(x),y) = x + y + 4 >= x + y + 4 = s(plus(x,y))
  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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [plus](x0, x1) = x0 + x1,
    
    [app](x0, x1) = x0 + x1,
    
    [sum](x0) = x0,
    
    [nil] = 6,
    
    [s](x0) = x0,
    
    [cons](x0, x1) = 2x0 + x1 + 2
   orientation:
    app(cons(x,l),k) = k + l + 2x + 2 >= k + l + 2x + 2 = cons(x,app(l,k))
    
    sum(cons(x,nil())) = 2x + 8 >= 2x + 8 = cons(x,nil())
    
    sum(cons(x,cons(y,l))) = l + 2x + 2y + 4 >= l + 2x + 2y + 2 = sum(cons(plus(x,y),l))
    
    sum(app(l,cons(x,cons(y,k)))) = k + l + 2x + 2y + 4 >= k + l + 2x + 2y + 4 = sum(app(l,sum(cons(x,cons(y,k)))))
    
    plus(s(x),y) = x + y >= x + y = s(plus(x,y))
   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=1
    
    interpretation:
     [plus](x0, x1) = 4x0 + 2x1 + 2,
     
     [app](x0, x1) = x0 + x1,
     
     [sum](x0) = x0,
     
     [nil] = 0,
     
     [s](x0) = x0 + 4,
     
     [cons](x0, x1) = 4x0 + x1
    orientation:
     app(cons(x,l),k) = k + l + 4x >= k + l + 4x = cons(x,app(l,k))
     
     sum(cons(x,nil())) = 4x >= 4x = cons(x,nil())
     
     sum(app(l,cons(x,cons(y,k)))) = k + l + 4x + 4y >= k + l + 4x + 4y = sum(app(l,sum(cons(x,cons(y,k)))))
     
     plus(s(x),y) = 4x + 2y + 18 >= 4x + 2y + 6 = s(plus(x,y))
    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)))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 1 1]     [1 1 0]     [0]
      [app](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1]
                      [0 0 1]     [0 0 0]     [0],
      
                  [1 0 0]     [0]
      [sum](x0) = [0 0 0]x0 + [1]
                  [0 0 1]     [0],
      
              [0]
      [nil] = [0]
              [0],
      
                       [1 0 1]     [1 0 0]     [0]
      [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [0]
                       [0 0 0]     [0 0 0]     [1]
     orientation:
                         [1 1 0]    [1 1 1]    [1 0 1]    [1]    [1 1 0]    [1 1 1]    [1 0 1]    [0]                   
      app(cons(x,l),k) = [0 0 0]k + [0 1 1]l + [0 0 0]x + [1] >= [0 0 0]k + [0 1 1]l + [0 0 0]x + [1] = 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 1]    [0]    [1 0 1]    [0]                
      sum(cons(x,nil())) = [0 0 0]x + [1] >= [0 0 0]x + [0] = cons(x,nil())
                           [0 0 0]    [1]    [0 0 0]    [1]                
      
                                      [1 1 1]    [1 1 1]    [1 0 1]    [1 0 1]    [1]    [1 0 0]    [1 1 1]    [1 0 1]    [1 0 1]    [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)))))
                                      [0 0 0]    [0 0 1]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 1]    [0 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)))))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                       [1 0 1]     [1 0 0]     [1]
       [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                       [0 0 0]     [0 0 0]     [1],
       
                   [1 1 0]  
       [sum](x0) = [0 1 0]x0
                   [0 1 0]  ,
       
               [0]
       [nil] = [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]  
      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())
                            [0 0 0]    [1]    [0 0 0]    [0]                
       
                                       [1 1 1]    [1 0 1]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 1]    [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 + [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]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                                     
      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]     [1 0 1]  
        [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                        [0 0 0]     [0 0 0]  ,
        
                    [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 + [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