YES

Problem:
 active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 2nd(mark(X)) -> 2nd(X)
 2nd(active(X)) -> 2nd(X)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 from(mark(X)) -> from(X)
 from(active(X)) -> from(X)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)

Proof:
 DP Processor:
  DPs:
   active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y)
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(from(X)) -> mark#(cons(X,from(s(X))))
   mark#(2nd(X)) -> mark#(X)
   mark#(2nd(X)) -> 2nd#(mark(X))
   mark#(2nd(X)) -> active#(2nd(mark(X)))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
   mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> from#(mark(X))
   mark#(from(X)) -> active#(from(mark(X)))
   mark#(s(X)) -> mark#(X)
   mark#(s(X)) -> s#(mark(X))
   mark#(s(X)) -> active#(s(mark(X)))
   2nd#(mark(X)) -> 2nd#(X)
   2nd#(active(X)) -> 2nd#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   cons#(X1,mark(X2)) -> cons#(X1,X2)
   cons#(active(X1),X2) -> cons#(X1,X2)
   cons#(X1,active(X2)) -> cons#(X1,X2)
   from#(mark(X)) -> from#(X)
   from#(active(X)) -> from#(X)
   s#(mark(X)) -> s#(X)
   s#(active(X)) -> s#(X)
  TRS:
   active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
   active(from(X)) -> mark(cons(X,from(s(X))))
   mark(2nd(X)) -> active(2nd(mark(X)))
   mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
   mark(from(X)) -> active(from(mark(X)))
   mark(s(X)) -> active(s(mark(X)))
   2nd(mark(X)) -> 2nd(X)
   2nd(active(X)) -> 2nd(X)
   cons(mark(X1),X2) -> cons(X1,X2)
   cons(X1,mark(X2)) -> cons(X1,X2)
   cons(active(X1),X2) -> cons(X1,X2)
   cons(X1,active(X2)) -> cons(X1,X2)
   from(mark(X)) -> from(X)
   from(active(X)) -> from(X)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
  Matrix Interpretation Processor: dim=2
   
   usable rules:
    active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
    active(from(X)) -> mark(cons(X,from(s(X))))
    mark(2nd(X)) -> active(2nd(mark(X)))
    mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    mark(from(X)) -> active(from(mark(X)))
    mark(s(X)) -> active(s(mark(X)))
    2nd(mark(X)) -> 2nd(X)
    2nd(active(X)) -> 2nd(X)
    cons(mark(X1),X2) -> cons(X1,X2)
    cons(X1,mark(X2)) -> cons(X1,X2)
    cons(active(X1),X2) -> cons(X1,X2)
    cons(X1,active(X2)) -> cons(X1,X2)
    from(mark(X)) -> from(X)
    from(active(X)) -> from(X)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
   interpretation:
    [2nd#](x0) = [0 1]x0 + [1],
    
    [cons#](x0, x1) = [0 1]x0 + [0 2]x1,
    
    [from#](x0) = [0 2]x0,
    
    [s#](x0) = [0 1]x0,
    
    [mark#](x0) = [2 2]x0,
    
    [active#](x0) = [1 0]x0,
    
              [1 1]     [0]
    [s](x0) = [0 0]x0 + [1],
    
                 [2 2]     [3]
    [from](x0) = [0 0]x0 + [0],
    
                 [0 0]     [0]
    [mark](x0) = [2 2]x0 + [1],
    
                   [0 0]     [0]
    [active](x0) = [1 1]x0 + [1],
    
                [1 1]     [0]
    [2nd](x0) = [0 0]x0 + [3],
    
                     [0 0]     [0 0]     [0]
    [cons](x0, x1) = [1 1]x0 + [0 2]x1 + [1]
   orientation:
    active#(2nd(cons(X,cons(Y,Z)))) = [1 1]X + [2 2]Y + [0 4]Z + [3] >= [2 2]Y = mark#(Y)
    
    active#(from(X)) = [2 2]X + [3] >= [0 1]X = s#(X)
    
    active#(from(X)) = [2 2]X + [3] >= [2] = from#(s(X))
    
    active#(from(X)) = [2 2]X + [3] >= [0 1]X = cons#(X,from(s(X)))
    
    active#(from(X)) = [2 2]X + [3] >= [2 2]X + [2] = mark#(cons(X,from(s(X))))
    
    mark#(2nd(X)) = [2 2]X + [6] >= [2 2]X = mark#(X)
    
    mark#(2nd(X)) = [2 2]X + [6] >= [2 2]X + [2] = 2nd#(mark(X))
    
    mark#(2nd(X)) = [2 2]X + [6] >= [2 2]X + [1] = active#(2nd(mark(X)))
    
    mark#(cons(X1,X2)) = [2 2]X1 + [0 4]X2 + [2] >= [2 2]X1 = mark#(X1)
    
    mark#(cons(X1,X2)) = [2 2]X1 + [0 4]X2 + [2] >= [2 2]X1 + [0 2]X2 + [1] = cons#(mark(X1),X2)
    
    mark#(cons(X1,X2)) = [2 2]X1 + [0 4]X2 + [2] >= [0] = active#(cons(mark(X1),X2))
    
    mark#(from(X)) = [4 4]X + [6] >= [2 2]X = mark#(X)
    
    mark#(from(X)) = [4 4]X + [6] >= [4 4]X + [2] = from#(mark(X))
    
    mark#(from(X)) = [4 4]X + [6] >= [4 4]X + [5] = active#(from(mark(X)))
    
    mark#(s(X)) = [2 2]X + [2] >= [2 2]X = mark#(X)
    
    mark#(s(X)) = [2 2]X + [2] >= [2 2]X + [1] = s#(mark(X))
    
    mark#(s(X)) = [2 2]X + [2] >= [2 2]X + [1] = active#(s(mark(X)))
    
    2nd#(mark(X)) = [2 2]X + [2] >= [0 1]X + [1] = 2nd#(X)
    
    2nd#(active(X)) = [1 1]X + [2] >= [0 1]X + [1] = 2nd#(X)
    
    cons#(mark(X1),X2) = [2 2]X1 + [0 2]X2 + [1] >= [0 1]X1 + [0 2]X2 = cons#(X1,X2)
    
    cons#(X1,mark(X2)) = [0 1]X1 + [4 4]X2 + [2] >= [0 1]X1 + [0 2]X2 = cons#(X1,X2)
    
    cons#(active(X1),X2) = [1 1]X1 + [0 2]X2 + [1] >= [0 1]X1 + [0 2]X2 = cons#(X1,X2)
    
    cons#(X1,active(X2)) = [0 1]X1 + [2 2]X2 + [2] >= [0 1]X1 + [0 2]X2 = cons#(X1,X2)
    
    from#(mark(X)) = [4 4]X + [2] >= [0 2]X = from#(X)
    
    from#(active(X)) = [2 2]X + [2] >= [0 2]X = from#(X)
    
    s#(mark(X)) = [2 2]X + [1] >= [0 1]X = s#(X)
    
    s#(active(X)) = [1 1]X + [1] >= [0 1]X = s#(X)
    
                                     [0 0]    [0 0]    [0 0]    [0]    [0 0]    [0]          
    active(2nd(cons(X,cons(Y,Z)))) = [1 1]X + [2 2]Y + [0 4]Z + [7] >= [2 2]Y + [1] = mark(Y)
    
                      [0 0]    [0]    [0 0]    [0]                           
    active(from(X)) = [2 2]X + [4] >= [2 2]X + [3] = mark(cons(X,from(s(X))))
    
                   [0 0]    [0]    [0 0]    [0]                       
    mark(2nd(X)) = [2 2]X + [7] >= [2 2]X + [5] = active(2nd(mark(X)))
    
                        [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]                            
    mark(cons(X1,X2)) = [2 2]X1 + [0 4]X2 + [3] >= [2 2]X1 + [0 2]X2 + [3] = active(cons(mark(X1),X2))
    
                    [0 0]    [0]    [0 0]    [0]                        
    mark(from(X)) = [4 4]X + [7] >= [4 4]X + [6] = active(from(mark(X)))
    
                 [0 0]    [0]    [0 0]    [0]                     
    mark(s(X)) = [2 2]X + [3] >= [2 2]X + [3] = active(s(mark(X)))
    
                   [2 2]    [1]    [1 1]    [0]         
    2nd(mark(X)) = [0 0]X + [3] >= [0 0]X + [3] = 2nd(X)
    
                     [1 1]    [1]    [1 1]    [0]         
    2nd(active(X)) = [0 0]X + [3] >= [0 0]X + [3] = 2nd(X)
    
                        [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]              
    cons(mark(X1),X2) = [2 2]X1 + [0 2]X2 + [2] >= [1 1]X1 + [0 2]X2 + [1] = cons(X1,X2)
    
                        [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]              
    cons(X1,mark(X2)) = [1 1]X1 + [4 4]X2 + [3] >= [1 1]X1 + [0 2]X2 + [1] = cons(X1,X2)
    
                          [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]              
    cons(active(X1),X2) = [1 1]X1 + [0 2]X2 + [2] >= [1 1]X1 + [0 2]X2 + [1] = cons(X1,X2)
    
                          [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]              
    cons(X1,active(X2)) = [1 1]X1 + [2 2]X2 + [3] >= [1 1]X1 + [0 2]X2 + [1] = cons(X1,X2)
    
                    [4 4]    [5]    [2 2]    [3]          
    from(mark(X)) = [0 0]X + [0] >= [0 0]X + [0] = from(X)
    
                      [2 2]    [5]    [2 2]    [3]          
    from(active(X)) = [0 0]X + [0] >= [0 0]X + [0] = from(X)
    
                 [2 2]    [1]    [1 1]    [0]       
    s(mark(X)) = [0 0]X + [1] >= [0 0]X + [1] = s(X)
    
                   [1 1]    [1]    [1 1]    [0]       
    s(active(X)) = [0 0]X + [1] >= [0 0]X + [1] = s(X)
   problem:
    DPs:
     
    TRS:
     active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
     active(from(X)) -> mark(cons(X,from(s(X))))
     mark(2nd(X)) -> active(2nd(mark(X)))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(from(X)) -> active(from(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     2nd(mark(X)) -> 2nd(X)
     2nd(active(X)) -> 2nd(X)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     from(mark(X)) -> from(X)
     from(active(X)) -> from(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
   Qed