YES

Problem:
 sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
 sum(cons(0(),x),y) -> sum(x,y)
 sum(nil(),y) -> y
 weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
 weight(cons(n,nil())) -> n

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                  [1 2]     [1]
   [weight](x0) = [0 1]x0 + [1],
   
           [1]
   [nil] = [0],
   
         [1]
   [0] = [0],
   
                   [1 0]       
   [sum](x0, x1) = [0 0]x0 + x1,
   
                         [1 0]     [1]
   [cons](x0, x1) = x0 + [1 1]x1 + [0],
   
                  [3]
   [s](x0) = x0 + [0]
  orientation:
                                     [1 0]    [1 0]    [1 0]    [5]        [1 0]    [1 0]    [1 0]    [5]                              
   sum(cons(s(n),x),cons(m,y)) = m + [0 0]n + [0 0]x + [1 1]y + [0] >= m + [0 0]n + [0 0]x + [1 1]y + [0] = sum(cons(n,x),cons(s(m),y))
   
                        [1 0]        [2]    [1 0]                
   sum(cons(0(),x),y) = [0 0]x + y + [0] >= [0 0]x + y = sum(x,y)
   
                      [1]         
   sum(nil(),y) = y + [0] >= y = y
   
                               [3 2]    [1 2]    [5 2]    [5]    [1 0]    [1 0]    [4 2]    [5]                                             
   weight(cons(n,cons(m,x))) = [1 1]m + [0 1]n + [2 1]x + [2] >= [0 0]m + [0 0]n + [1 1]x + [1] = weight(sum(cons(n,cons(m,x)),cons(0(),x)))
   
                           [1 2]    [5]         
   weight(cons(n,nil())) = [0 1]n + [2] >= n = n
  problem:
   sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
   weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                   [1 2]  
    [weight](x0) = [0 0]x0,
    
          [0]
    [0] = [0],
    
                    [1 1]     [1 0]  
    [sum](x0, x1) = [0 0]x0 + [0 0]x1,
    
                     [1 0]     [1 1]  
    [cons](x0, x1) = [1 0]x0 + [2 0]x1,
    
              [1 0]     [3]
    [s](x0) = [0 0]x0 + [0]
   orientation:
                                  [1 0]    [2 0]    [3 1]    [1 1]    [6]    [1 0]    [2 0]    [3 1]    [1 1]    [3]                              
    sum(cons(s(n),x),cons(m,y)) = [0 0]m + [0 0]n + [0 0]x + [0 0]y + [0] >= [0 0]m + [0 0]n + [0 0]x + [0 0]y + [0] = sum(cons(n,x),cons(s(m),y))
    
                                [6 0]    [3 0]    [7 5]     [4 0]    [2 0]    [6 4]                                              
    weight(cons(n,cons(m,x))) = [0 0]m + [0 0]n + [0 0]x >= [0 0]m + [0 0]n + [0 0]x = weight(sum(cons(n,cons(m,x)),cons(0(),x)))
   problem:
    weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                    [1 1]  
     [weight](x0) = [0 0]x0,
     
           [0]
     [0] = [0],
     
                     [1 0]     [1 0]  
     [sum](x0, x1) = [0 0]x0 + [0 0]x1,
     
                      [2 2]     [2 0]     [0]
     [cons](x0, x1) = [0 0]x0 + [1 0]x1 + [1]
    orientation:
                                 [6 6]    [2 2]    [6 0]    [1]    [4 4]    [2 2]    [6 0]                                              
     weight(cons(n,cons(m,x))) = [0 0]m + [0 0]n + [0 0]x + [0] >= [0 0]m + [0 0]n + [0 0]x = weight(sum(cons(n,cons(m,x)),cons(0(),x)))
    problem:
     
    Qed