YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [top](x0) = 2x0 + 2,
   
   [ok](x0) = 5x0 + 1,
   
   [proper](x0) = x0,
   
   [s](x0) = x0,
   
   [from](x0) = x0,
   
   [mark](x0) = x0,
   
   [active](x0) = 5x0,
   
   [2nd](x0) = x0,
   
   [cons](x0, x1) = x0 + 4x1
  orientation:
   active(2nd(cons(X,cons(Y,Z)))) = 5X + 20Y + 80Z >= Y = mark(Y)
   
   active(from(X)) = 5X >= 5X = mark(cons(X,from(s(X))))
   
   active(2nd(X)) = 5X >= 5X = 2nd(active(X))
   
   active(cons(X1,X2)) = 5X1 + 20X2 >= 5X1 + 4X2 = cons(active(X1),X2)
   
   active(from(X)) = 5X >= 5X = from(active(X))
   
   active(s(X)) = 5X >= 5X = s(active(X))
   
   2nd(mark(X)) = X >= X = mark(2nd(X))
   
   cons(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = mark(cons(X1,X2))
   
   from(mark(X)) = X >= X = mark(from(X))
   
   s(mark(X)) = X >= X = mark(s(X))
   
   proper(2nd(X)) = X >= X = 2nd(proper(X))
   
   proper(cons(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = cons(proper(X1),proper(X2))
   
   proper(from(X)) = X >= X = from(proper(X))
   
   proper(s(X)) = X >= X = s(proper(X))
   
   2nd(ok(X)) = 5X + 1 >= 5X + 1 = ok(2nd(X))
   
   cons(ok(X1),ok(X2)) = 5X1 + 20X2 + 5 >= 5X1 + 20X2 + 1 = ok(cons(X1,X2))
   
   from(ok(X)) = 5X + 1 >= 5X + 1 = ok(from(X))
   
   s(ok(X)) = 5X + 1 >= 5X + 1 = ok(s(X))
   
   top(mark(X)) = 2X + 2 >= 2X + 2 = top(proper(X))
   
   top(ok(X)) = 10X + 4 >= 10X + 2 = top(active(X))
  problem:
   active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(2nd(X)) -> 2nd(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(from(X)) -> from(active(X))
   active(s(X)) -> s(active(X))
   2nd(mark(X)) -> mark(2nd(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   2nd(ok(X)) -> ok(2nd(X))
   from(ok(X)) -> ok(from(X))
   s(ok(X)) -> ok(s(X))
   top(mark(X)) -> top(proper(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = x0,
    
    [ok](x0) = x0,
    
    [proper](x0) = x0,
    
    [s](x0) = x0,
    
    [from](x0) = 4x0,
    
    [mark](x0) = x0,
    
    [active](x0) = 2x0,
    
    [2nd](x0) = 2x0 + 4,
    
    [cons](x0, x1) = 2x0 + x1
   orientation:
    active(2nd(cons(X,cons(Y,Z)))) = 8X + 8Y + 4Z + 8 >= Y = mark(Y)
    
    active(from(X)) = 8X >= 6X = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 4X + 8 >= 4X + 4 = 2nd(active(X))
    
    active(cons(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = cons(active(X1),X2)
    
    active(from(X)) = 8X >= 8X = from(active(X))
    
    active(s(X)) = 2X >= 2X = s(active(X))
    
    2nd(mark(X)) = 2X + 4 >= 2X + 4 = mark(2nd(X))
    
    cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(cons(X1,X2))
    
    from(mark(X)) = 4X >= 4X = mark(from(X))
    
    s(mark(X)) = X >= X = mark(s(X))
    
    proper(2nd(X)) = 2X + 4 >= 2X + 4 = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 4X >= 4X = from(proper(X))
    
    proper(s(X)) = X >= X = s(proper(X))
    
    2nd(ok(X)) = 2X + 4 >= 2X + 4 = ok(2nd(X))
    
    from(ok(X)) = 4X >= 4X = ok(from(X))
    
    s(ok(X)) = X >= X = ok(s(X))
    
    top(mark(X)) = X >= X = top(proper(X))
   problem:
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(from(X)) -> from(active(X))
    active(s(X)) -> s(active(X))
    2nd(mark(X)) -> mark(2nd(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    proper(2nd(X)) -> 2nd(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(s(X)) -> s(proper(X))
    2nd(ok(X)) -> ok(2nd(X))
    from(ok(X)) -> ok(from(X))
    s(ok(X)) -> ok(s(X))
    top(mark(X)) -> top(proper(X))
   DP Processor:
    DPs:
     active#(from(X)) -> s#(X)
     active#(from(X)) -> from#(s(X))
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(from(X)) -> active#(X)
     active#(from(X)) -> from#(active(X))
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     2nd#(mark(X)) -> 2nd#(X)
     cons#(mark(X1),X2) -> cons#(X1,X2)
     from#(mark(X)) -> from#(X)
     s#(mark(X)) -> s#(X)
     proper#(2nd(X)) -> proper#(X)
     proper#(2nd(X)) -> 2nd#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(from(X)) -> proper#(X)
     proper#(from(X)) -> from#(proper(X))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     2nd#(ok(X)) -> 2nd#(X)
     from#(ok(X)) -> from#(X)
     s#(ok(X)) -> s#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     2nd(ok(X)) -> ok(2nd(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     top(mark(X)) -> top(proper(X))
    TDG Processor:
     DPs:
      active#(from(X)) -> s#(X)
      active#(from(X)) -> from#(s(X))
      active#(from(X)) -> cons#(X,from(s(X)))
      active#(cons(X1,X2)) -> active#(X1)
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(from(X)) -> active#(X)
      active#(from(X)) -> from#(active(X))
      active#(s(X)) -> active#(X)
      active#(s(X)) -> s#(active(X))
      2nd#(mark(X)) -> 2nd#(X)
      cons#(mark(X1),X2) -> cons#(X1,X2)
      from#(mark(X)) -> from#(X)
      s#(mark(X)) -> s#(X)
      proper#(2nd(X)) -> proper#(X)
      proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(from(X)) -> proper#(X)
      proper#(from(X)) -> from#(proper(X))
      proper#(s(X)) -> proper#(X)
      proper#(s(X)) -> s#(proper(X))
      2nd#(ok(X)) -> 2nd#(X)
      from#(ok(X)) -> from#(X)
      s#(ok(X)) -> s#(X)
      top#(mark(X)) -> proper#(X)
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(from(X)) -> from(active(X))
      active(s(X)) -> s(active(X))
      2nd(mark(X)) -> mark(2nd(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      from(mark(X)) -> mark(from(X))
      s(mark(X)) -> mark(s(X))
      proper(2nd(X)) -> 2nd(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(from(X)) -> from(proper(X))
      proper(s(X)) -> s(proper(X))
      2nd(ok(X)) -> ok(2nd(X))
      from(ok(X)) -> ok(from(X))
      s(ok(X)) -> ok(s(X))
      top(mark(X)) -> top(proper(X))
     graph:
      top#(mark(X)) -> top#(proper(X)) ->
      top#(mark(X)) -> top#(proper(X))
      top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
      top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
      top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
      top#(mark(X)) -> proper#(X) ->
      proper#(from(X)) -> from#(proper(X))
      top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
      top#(mark(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
      top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
      top#(mark(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X))
      top#(mark(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X)
      proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
      proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
      proper#(s(X)) -> proper#(X) ->
      proper#(from(X)) -> from#(proper(X))
      proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
      proper#(s(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
      proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
      proper#(s(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(s(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X)
      proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
      proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
      proper#(from(X)) -> proper#(X) ->
      proper#(s(X)) -> s#(proper(X))
      proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
      proper#(from(X)) -> proper#(X) ->
      proper#(from(X)) -> from#(proper(X))
      proper#(from(X)) -> proper#(X) ->
      proper#(from(X)) -> proper#(X)
      proper#(from(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(from(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(from(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(from(X)) -> proper#(X) ->
      proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(from(X)) -> proper#(X) ->
      proper#(2nd(X)) -> proper#(X)
      proper#(from(X)) -> from#(proper(X)) ->
      from#(ok(X)) -> from#(X)
      proper#(from(X)) -> from#(proper(X)) ->
      from#(mark(X)) -> from#(X)
      proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
      proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
      proper#(2nd(X)) -> proper#(X) ->
      proper#(from(X)) -> from#(proper(X))
      proper#(2nd(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
      proper#(2nd(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(2nd(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(2nd(X)) -> proper#(X) ->
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(2nd(X)) -> proper#(X) ->
      proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(2nd(X)) -> proper#(X) ->
      proper#(2nd(X)) -> proper#(X)
      proper#(2nd(X)) -> 2nd#(proper(X)) ->
      2nd#(ok(X)) -> 2nd#(X)
      proper#(2nd(X)) -> 2nd#(proper(X)) ->
      2nd#(mark(X)) -> 2nd#(X)
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(s(X)) -> s#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(s(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(from(X)) -> from#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(from(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X2) ->
      proper#(2nd(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(s(X)) -> s#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(s(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(from(X)) -> from#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(from(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(2nd(X)) -> 2nd#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X1) ->
      proper#(2nd(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
      cons#(mark(X1),X2) -> cons#(X1,X2)
      2nd#(ok(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X)
      2nd#(ok(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X)
      2nd#(mark(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X)
      2nd#(mark(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X)
      cons#(mark(X1),X2) -> cons#(X1,X2) ->
      cons#(mark(X1),X2) -> cons#(X1,X2)
      from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
      from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
      from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
      from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
      s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
      s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
      s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
      s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
      active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
      active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
      active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
      active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
      active#(s(X)) -> active#(X) ->
      active#(from(X)) -> from#(active(X))
      active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X)
      active#(s(X)) -> active#(X) ->
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
      active#(s(X)) -> active#(X) ->
      active#(from(X)) -> cons#(X,from(s(X)))
      active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
      active#(s(X)) -> active#(X) ->
      active#(from(X)) -> s#(X)
      active#(from(X)) -> cons#(X,from(s(X))) ->
      cons#(mark(X1),X2) -> cons#(X1,X2)
      active#(from(X)) -> from#(s(X)) -> from#(ok(X)) -> from#(X)
      active#(from(X)) -> from#(s(X)) ->
      from#(mark(X)) -> from#(X)
      active#(from(X)) -> from#(active(X)) ->
      from#(ok(X)) -> from#(X)
      active#(from(X)) -> from#(active(X)) -> from#(mark(X)) -> from#(X)
      active#(from(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
      active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
      active#(from(X)) -> active#(X) ->
      active#(s(X)) -> s#(active(X))
      active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X)
      active#(from(X)) -> active#(X) ->
      active#(from(X)) -> from#(active(X))
      active#(from(X)) -> active#(X) ->
      active#(from(X)) -> active#(X)
      active#(from(X)) -> active#(X) ->
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(from(X)) -> active#(X) ->
      active#(cons(X1,X2)) -> active#(X1)
      active#(from(X)) -> active#(X) ->
      active#(from(X)) -> cons#(X,from(s(X)))
      active#(from(X)) -> active#(X) ->
      active#(from(X)) -> from#(s(X))
      active#(from(X)) -> active#(X) ->
      active#(from(X)) -> s#(X)
      active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
      cons#(mark(X1),X2) -> cons#(X1,X2)
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(s(X)) -> s#(active(X))
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(s(X)) -> active#(X)
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(from(X)) -> from#(active(X))
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(from(X)) -> active#(X)
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(cons(X1,X2)) -> active#(X1)
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(from(X)) -> cons#(X,from(s(X)))
      active#(cons(X1,X2)) -> active#(X1) ->
      active#(from(X)) -> from#(s(X))
      active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X)
     SCC Processor:
      #sccs: 7
      #rules: 16
      #arcs: 113/729
      DPs:
       active#(s(X)) -> active#(X)
       active#(cons(X1,X2)) -> active#(X1)
       active#(from(X)) -> active#(X)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(active#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Bounds Processor:
       bound: 1
       enrichment: top-dp
       automaton:
        final states: {12}
        transitions:
         from0(11) -> 11*
         cons0(11,11) -> 11*
         s0(11) -> 11*
         2nd0(11) -> 11*
         ok0(11) -> 11*
         top0(11) -> 11*
         top{#,1}(17) -> 18*
         proper1(16) -> 17*
         s1(17) -> 17*
         from1(17) -> 17*
         cons1(17,17) -> 17*
         2nd1(17) -> 17*
         top{#,0}(11) -> 12*
         mark0(11) -> 11*
         proper0(11) -> 11*
         active0(11) -> 11*
         11 -> 16*
         18 -> 12*
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       proper#(2nd(X)) -> proper#(X)
       proper#(cons(X1,X2)) -> proper#(X2)
       proper#(cons(X1,X2)) -> proper#(X1)
       proper#(from(X)) -> proper#(X)
       proper#(s(X)) -> proper#(X)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(proper#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       s#(mark(X)) -> s#(X)
       s#(ok(X)) -> s#(X)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(s#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       from#(mark(X)) -> from#(X)
       from#(ok(X)) -> from#(X)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(from#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       cons#(mark(X1),X2) -> cons#(X1,X2)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(cons#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed
      
      DPs:
       2nd#(mark(X)) -> 2nd#(X)
       2nd#(ok(X)) -> 2nd#(X)
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       2nd(mark(X)) -> mark(2nd(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       proper(2nd(X)) -> 2nd(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       2nd(ok(X)) -> ok(2nd(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
      Subterm Criterion Processor:
       simple projection:
        pi(2nd#) = 0
       problem:
        DPs:
         
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         2nd(mark(X)) -> mark(2nd(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         proper(2nd(X)) -> 2nd(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         2nd(ok(X)) -> ok(2nd(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         top(mark(X)) -> top(proper(X))
       Qed