YES

Problem:
 a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
 a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
 a__from(X) -> cons(mark(X),from(s(X)))
 mark(2nd(X)) -> a__2nd(mark(X))
 mark(from(X)) -> a__from(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
 a__2nd(X) -> 2nd(X)
 a__from(X) -> from(X)

Proof:
 DP Processor:
  DPs:
   a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y)
   a__2nd#(cons(X,X1)) -> mark#(X1)
   a__2nd#(cons(X,X1)) -> mark#(X)
   a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1)))
   a__from#(X) -> mark#(X)
   mark#(2nd(X)) -> mark#(X)
   mark#(2nd(X)) -> a__2nd#(mark(X))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
   mark#(cons1(X1,X2)) -> mark#(X2)
   mark#(cons1(X1,X2)) -> mark#(X1)
  TRS:
   a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
   a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
   a__from(X) -> cons(mark(X),from(s(X)))
   mark(2nd(X)) -> a__2nd(mark(X))
   mark(from(X)) -> a__from(mark(X))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
   a__2nd(X) -> 2nd(X)
   a__from(X) -> from(X)
  Matrix Interpretation Processor: dim=2
   
   usable rules:
    a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
    a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
    a__from(X) -> cons(mark(X),from(s(X)))
    mark(2nd(X)) -> a__2nd(mark(X))
    mark(from(X)) -> a__from(mark(X))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
    a__2nd(X) -> 2nd(X)
    a__from(X) -> from(X)
   interpretation:
    [a__from#](x0) = [0 1]x0 + [1],
    
    [mark#](x0) = [0 1]x0,
    
    [a__2nd#](x0) = [2 2]x0,
    
                [2 2]     [0]
    [2nd](x0) = [2 2]x0 + [1],
    
                 [0 2]     [3]
    [from](x0) = [2 1]x0 + [2],
    
              [0 0]     [0]
    [s](x0) = [0 1]x0 + [1],
    
                    [0 2]     [3]
    [a__from](x0) = [2 1]x0 + [2],
    
                   
    [mark](x0) = x0,
    
                   [2 2]     [0]
    [a__2nd](x0) = [2 2]x0 + [1],
    
                      [0 0]     [0 0]     [0]
    [cons1](x0, x1) = [2 1]x0 + [0 1]x1 + [1],
    
                     [0 0]     [0 1]     [0]
    [cons](x0, x1) = [2 1]x0 + [0 0]x1 + [2]
   orientation:
    a__2nd#(cons1(X,cons(Y,Z))) = [4 2]X + [4 2]Y + [6] >= [0 1]Y = mark#(Y)
    
    a__2nd#(cons(X,X1)) = [4 2]X + [0 2]X1 + [4] >= [0 1]X1 = mark#(X1)
    
    a__2nd#(cons(X,X1)) = [4 2]X + [0 2]X1 + [4] >= [0 1]X = mark#(X)
    
    a__2nd#(cons(X,X1)) = [4 2]X + [0 2]X1 + [4] >= [4 2]X + [0 2]X1 + [2] = a__2nd#(cons1(mark(X),mark(X1)))
    
    a__from#(X) = [0 1]X + [1] >= [0 1]X = mark#(X)
    
    mark#(2nd(X)) = [2 2]X + [1] >= [0 1]X = mark#(X)
    
    mark#(2nd(X)) = [2 2]X + [1] >= [2 2]X = a__2nd#(mark(X))
    
    mark#(from(X)) = [2 1]X + [2] >= [0 1]X = mark#(X)
    
    mark#(from(X)) = [2 1]X + [2] >= [0 1]X + [1] = a__from#(mark(X))
    
    mark#(cons(X1,X2)) = [2 1]X1 + [2] >= [0 1]X1 = mark#(X1)
    
    mark#(s(X)) = [0 1]X + [1] >= [0 1]X = mark#(X)
    
    mark#(cons1(X1,X2)) = [2 1]X1 + [0 1]X2 + [1] >= [0 1]X2 = mark#(X2)
    
    mark#(cons1(X1,X2)) = [2 1]X1 + [0 1]X2 + [1] >= [0 1]X1 = mark#(X1)
    
                                 [4 2]    [4 2]    [6]               
    a__2nd(cons1(X,cons(Y,Z))) = [4 2]X + [4 2]Y + [7] >= Y = mark(Y)
    
                         [4 2]    [0 2]     [4]    [4 2]    [0 2]     [2]                                  
    a__2nd(cons(X,X1)) = [4 2]X + [0 2]X1 + [5] >= [4 2]X + [0 2]X1 + [3] = a__2nd(cons1(mark(X),mark(X1)))
    
                 [0 2]    [3]    [0 1]    [3]                           
    a__from(X) = [2 1]X + [2] >= [2 1]X + [2] = cons(mark(X),from(s(X)))
    
                   [2 2]    [0]    [2 2]    [0]                  
    mark(2nd(X)) = [2 2]X + [1] >= [2 2]X + [1] = a__2nd(mark(X))
    
                    [0 2]    [3]    [0 2]    [3]                   
    mark(from(X)) = [2 1]X + [2] >= [2 1]X + [2] = a__from(mark(X))
    
                        [0 0]     [0 1]     [0]    [0 0]     [0 1]     [0]                    
    mark(cons(X1,X2)) = [2 1]X1 + [0 0]X2 + [2] >= [2 1]X1 + [0 0]X2 + [2] = cons(mark(X1),X2)
    
                 [0 0]    [0]    [0 0]    [0]             
    mark(s(X)) = [0 1]X + [1] >= [0 1]X + [1] = s(mark(X))
    
                         [0 0]     [0 0]     [0]    [0 0]     [0 0]     [0]                           
    mark(cons1(X1,X2)) = [2 1]X1 + [0 1]X2 + [1] >= [2 1]X1 + [0 1]X2 + [1] = cons1(mark(X1),mark(X2))
    
                [2 2]    [0]    [2 2]    [0]         
    a__2nd(X) = [2 2]X + [1] >= [2 2]X + [1] = 2nd(X)
    
                 [0 2]    [3]    [0 2]    [3]          
    a__from(X) = [2 1]X + [2] >= [2 1]X + [2] = from(X)
   problem:
    DPs:
     
    TRS:
     a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
     a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
     a__from(X) -> cons(mark(X),from(s(X)))
     mark(2nd(X)) -> a__2nd(mark(X))
     mark(from(X)) -> a__from(mark(X))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
     a__2nd(X) -> 2nd(X)
     a__from(X) -> from(X)
   Qed