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:
   [s](x0) = x0 + 1,
   
   [0] = 0,
   
   [plus](x0, x1) = x0 + x1 + 2,
   
   [sum](x0) = x0,
   
   [cons](x0, x1) = x0 + x1 + 2,
   
   [app](x0, x1) = x0 + x1 + 1,
   
   [nil] = 0
  orientation:
   app(nil(),k) = k + 1 >= k = k
   
   app(l,nil()) = l + 1 >= l = l
   
   app(cons(x,l),k) = k + l + x + 3 >= k + l + x + 3 = cons(x,app(l,k))
   
   sum(cons(x,nil())) = x + 2 >= x + 2 = cons(x,nil())
   
   sum(cons(x,cons(y,l))) = l + x + y + 4 >= l + x + y + 4 = sum(cons(plus(x,y),l))
   
   sum(app(l,cons(x,cons(y,k)))) = k + l + x + y + 5 >= k + l + x + y + 5 = sum(app(l,sum(cons(x,cons(y,k)))))
   
   plus(0(),y) = y + 2 >= y = y
   
   plus(s(x),y) = x + y + 3 >= x + y + 3 = 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:
    [s](x0) = x0 + 3,
    
    [plus](x0, x1) = x0 + x1,
    
    [sum](x0) = x0,
    
    [cons](x0, x1) = 2x0 + x1 + 1,
    
    [app](x0, x1) = 2x0 + x1 + 1,
    
    [nil] = 7
   orientation:
    app(cons(x,l),k) = k + 2l + 4x + 3 >= k + 2l + 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 + 2 >= l + 2x + 2y + 1 = sum(cons(plus(x,y),l))
    
    sum(app(l,cons(x,cons(y,k)))) = k + 2l + 2x + 2y + 3 >= k + 2l + 2x + 2y + 3 = sum(app(l,sum(cons(x,cons(y,k)))))
    
    plus(s(x),y) = x + y + 3 >= x + y + 3 = 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)))))
    plus(s(x),y) -> s(plus(x,y))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [s](x0) = x0 + 4,
     
     [plus](x0, x1) = 6x0 + x1,
     
     [sum](x0) = x0,
     
     [cons](x0, x1) = 5x0 + 4x1 + 1,
     
     [app](x0, x1) = x0 + x1 + 3,
     
     [nil] = 2
    orientation:
     sum(cons(x,nil())) = 5x + 9 >= 5x + 9 = cons(x,nil())
     
     sum(app(l,cons(x,cons(y,k)))) = 16k + l + 5x + 20y + 8 >= 16k + l + 5x + 20y + 8 = sum(app(l,sum(cons(x,cons(y,k)))))
     
     plus(s(x),y) = 6x + y + 24 >= 6x + y + 4 = 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]
                  [0 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 0 0]     [1],
      
              [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())
                           [0 0 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)))))
                                      [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]                                     
     problem:
      sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
     DP Processor:
      DPs:
       sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
       sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
      TRS:
       sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
      EDG Processor:
       DPs:
        sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
        sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
       TRS:
        sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
       graph:
        
       Qed