YES

Problem:
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(length(nil())) -> mark(0())
 active(length(cons(X,Y))) -> mark(s(length1(Y)))
 active(length1(X)) -> mark(length(X))
 active(from(X)) -> from(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(s(X)) -> s(active(X))
 from(mark(X)) -> mark(from(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 s(mark(X)) -> mark(s(X))
 proper(from(X)) -> from(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(s(X)) -> s(proper(X))
 proper(length(X)) -> length(proper(X))
 proper(nil()) -> ok(nil())
 proper(0()) -> ok(0())
 proper(length1(X)) -> length1(proper(X))
 from(ok(X)) -> ok(from(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 s(ok(X)) -> ok(s(X))
 length(ok(X)) -> ok(length(X))
 length1(ok(X)) -> ok(length1(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 1]  
   [mark](x0) = [0 0]x0,
   
                   [1 0]     [0]
   [length1](x0) = [2 0]x0 + [2],
   
                  [2 1]  
   [active](x0) = [0 0]x0,
   
                         [1 0]  
   [cons](x0, x1) = x0 + [0 0]x1,
   
           [0]
   [nil] = [0],
   
              [2 0]  
   [ok](x0) = [0 1]x0,
   
                  
   [from](x0) = x0,
   
         [0]
   [0] = [0],
   
               [1 1]     [0]
   [top](x0) = [0 0]x0 + [2],
   
                    
   [proper](x0) = x0,
   
                  [2 0]     [0]
   [length](x0) = [0 0]x0 + [2],
   
               
   [s](x0) = x0
  orientation:
                     [2 1]     [2 1]                            
   active(from(X)) = [0 0]X >= [0 0]X = mark(cons(X,from(s(X))))
   
                           [2]    [0]            
   active(length(nil())) = [0] >= [0] = mark(0())
   
                               [4 0]    [4 0]    [2]    [3 0]    [2]                      
   active(length(cons(X,Y))) = [0 0]X + [0 0]Y + [0] >= [0 0]Y + [0] = mark(s(length1(Y)))
   
                        [4 0]    [2]    [2 0]    [2]                  
   active(length1(X)) = [0 0]X + [0] >= [0 0]X + [0] = mark(length(X))
   
                     [2 1]     [2 1]                   
   active(from(X)) = [0 0]X >= [0 0]X = from(active(X))
   
                         [2 1]     [2 0]      [2 1]     [1 0]                        
   active(cons(X1,X2)) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = cons(active(X1),X2)
   
                  [2 1]     [2 1]                
   active(s(X)) = [0 0]X >= [0 0]X = s(active(X))
   
                   [1 1]     [1 1]                 
   from(mark(X)) = [0 0]X >= [0 0]X = mark(from(X))
   
                       [1 1]     [1 0]      [1 1]     [1 0]                      
   cons(mark(X1),X2) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = mark(cons(X1,X2))
   
                [1 1]     [1 1]              
   s(mark(X)) = [0 0]X >= [0 0]X = mark(s(X))
   
                                             
   proper(from(X)) = X >= X = from(proper(X))
   
                              [1 0]           [1 0]                                
   proper(cons(X1,X2)) = X1 + [0 0]X2 >= X1 + [0 0]X2 = cons(proper(X1),proper(X2))
   
                                       
   proper(s(X)) = X >= X = s(proper(X))
   
                       [2 0]    [0]    [2 0]    [0]                    
   proper(length(X)) = [0 0]X + [2] >= [0 0]X + [2] = length(proper(X))
   
                   [0]    [0]            
   proper(nil()) = [0] >= [0] = ok(nil())
   
                 [0]    [0]          
   proper(0()) = [0] >= [0] = ok(0())
   
                        [1 0]    [0]    [1 0]    [0]                     
   proper(length1(X)) = [2 0]X + [2] >= [2 0]X + [2] = length1(proper(X))
   
                 [2 0]     [2 0]               
   from(ok(X)) = [0 1]X >= [0 1]X = ok(from(X))
   
                         [2 0]     [2 0]      [2 0]     [2 0]                    
   cons(ok(X1),ok(X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = ok(cons(X1,X2))
   
              [2 0]     [2 0]            
   s(ok(X)) = [0 1]X >= [0 1]X = ok(s(X))
   
                   [4 0]    [0]    [4 0]    [0]                
   length(ok(X)) = [0 0]X + [2] >= [0 0]X + [2] = ok(length(X))
   
                    [2 0]    [0]    [2 0]    [0]                 
   length1(ok(X)) = [4 0]X + [2] >= [2 0]X + [2] = ok(length1(X))
   
                  [1 1]    [0]    [1 1]    [0]                 
   top(mark(X)) = [0 0]X + [2] >= [0 0]X + [2] = top(proper(X))
   
                [2 1]    [0]    [2 1]    [0]                 
   top(ok(X)) = [0 0]X + [2] >= [0 0]X + [2] = top(active(X))
  problem:
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(length(cons(X,Y))) -> mark(s(length1(Y)))
   active(length1(X)) -> mark(length(X))
   active(from(X)) -> from(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(s(X)) -> s(active(X))
   from(mark(X)) -> mark(from(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   s(mark(X)) -> mark(s(X))
   proper(from(X)) -> from(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(length(X)) -> length(proper(X))
   proper(nil()) -> ok(nil())
   proper(0()) -> ok(0())
   proper(length1(X)) -> length1(proper(X))
   from(ok(X)) -> ok(from(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   s(ok(X)) -> ok(s(X))
   length(ok(X)) -> ok(length(X))
   length1(ok(X)) -> ok(length1(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  DP Processor:
   DPs:
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(length(cons(X,Y))) -> length1#(Y)
    active#(length(cons(X,Y))) -> s#(length1(Y))
    active#(length1(X)) -> length#(X)
    active#(from(X)) -> active#(X)
    active#(from(X)) -> from#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    from#(mark(X)) -> from#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    s#(mark(X)) -> s#(X)
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(length(X)) -> proper#(X)
    proper#(length(X)) -> length#(proper(X))
    proper#(length1(X)) -> proper#(X)
    proper#(length1(X)) -> length1#(proper(X))
    from#(ok(X)) -> from#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    s#(ok(X)) -> s#(X)
    length#(ok(X)) -> length#(X)
    length1#(ok(X)) -> length1#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(length(cons(X,Y))) -> mark(s(length1(Y)))
    active(length1(X)) -> mark(length(X))
    active(from(X)) -> from(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(s(X)) -> s(active(X))
    from(mark(X)) -> mark(from(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    s(mark(X)) -> mark(s(X))
    proper(from(X)) -> from(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(s(X)) -> s(proper(X))
    proper(length(X)) -> length(proper(X))
    proper(nil()) -> ok(nil())
    proper(0()) -> ok(0())
    proper(length1(X)) -> length1(proper(X))
    from(ok(X)) -> ok(from(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    s(ok(X)) -> ok(s(X))
    length(ok(X)) -> ok(length(X))
    length1(ok(X)) -> ok(length1(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   TDG Processor:
    DPs:
     active#(from(X)) -> s#(X)
     active#(from(X)) -> from#(s(X))
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(length(cons(X,Y))) -> length1#(Y)
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(length1(X)) -> length#(X)
     active#(from(X)) -> active#(X)
     active#(from(X)) -> from#(active(X))
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     from#(mark(X)) -> from#(X)
     cons#(mark(X1),X2) -> cons#(X1,X2)
     s#(mark(X)) -> s#(X)
     proper#(from(X)) -> proper#(X)
     proper#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(length(X)) -> proper#(X)
     proper#(length(X)) -> length#(proper(X))
     proper#(length1(X)) -> proper#(X)
     proper#(length1(X)) -> length1#(proper(X))
     from#(ok(X)) -> from#(X)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     s#(ok(X)) -> s#(X)
     length#(ok(X)) -> length#(X)
     length1#(ok(X)) -> length1#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(length(cons(X,Y))) -> mark(s(length1(Y)))
     active(length1(X)) -> mark(length(X))
     active(from(X)) -> from(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(s(X)) -> s(active(X))
     from(mark(X)) -> mark(from(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     s(mark(X)) -> mark(s(X))
     proper(from(X)) -> from(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(s(X)) -> s(proper(X))
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(0()) -> ok(0())
     proper(length1(X)) -> length1(proper(X))
     from(ok(X)) -> ok(from(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     s(ok(X)) -> ok(s(X))
     length(ok(X)) -> ok(length(X))
     length1(ok(X)) -> ok(length1(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    graph:
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     top#(ok(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(length1(X)) -> length#(X)
     top#(ok(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     top#(ok(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X)))
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
     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#(length1(X)) -> length1#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(length1(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(length(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#(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#(from(X)) -> from#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(s(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(length1(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(from(X)) -> proper#(X)
     proper#(length1(X)) -> length1#(proper(X)) ->
     length1#(ok(X)) -> length1#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(s(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(length(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(from(X)) -> proper#(X)
     proper#(length(X)) -> length#(proper(X)) ->
     length#(ok(X)) -> length#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length1(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length(X)) -> proper#(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#(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#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length1(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length(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#(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#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     proper#(s(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(length1(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(length(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#(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#(from(X)) -> from#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(from(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#(length1(X)) -> length1#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(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#(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#(from(X)) -> from#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(from(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)
     length#(ok(X)) -> length#(X) -> length#(ok(X)) -> length#(X)
     length1#(ok(X)) -> length1#(X) ->
     length1#(ok(X)) -> length1#(X)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(mark(X1),X2) -> cons#(X1,X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     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#(length1(X)) -> length#(X) ->
     length#(ok(X)) -> length#(X)
     active#(length(cons(X,Y))) -> length1#(Y) ->
     length1#(ok(X)) -> length1#(X)
     active#(length(cons(X,Y))) -> s#(length1(Y)) ->
     s#(ok(X)) -> s#(X)
     active#(length(cons(X,Y))) -> s#(length1(Y)) ->
     s#(mark(X)) -> s#(X)
     active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     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#(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)) -> from#(active(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length1(X)) -> length#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     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)
     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#(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)) -> from#(active(X))
     active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     active#(s(X)) -> active#(X) -> active#(length1(X)) -> length#(X)
     active#(s(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(s(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     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#(ok(X1),ok(X2)) -> cons#(X1,X2)
     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#(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)) -> from#(active(X))
     active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     active#(from(X)) -> active#(X) ->
     active#(length1(X)) -> length#(X)
     active#(from(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(from(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     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)
    SCC Processor:
     #sccs: 8
     #rules: 19
     #arcs: 171/1225
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Usable Rule Processor:
      DPs:
       top#(ok(X)) -> top#(active(X))
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(length(cons(X,Y))) -> mark(s(length1(Y)))
       active(length1(X)) -> mark(length(X))
       active(from(X)) -> from(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(s(X)) -> s(active(X))
       s(mark(X)) -> mark(s(X))
       s(ok(X)) -> ok(s(X))
       from(mark(X)) -> mark(from(X))
       from(ok(X)) -> ok(from(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       length1(ok(X)) -> ok(length1(X))
       length(ok(X)) -> ok(length(X))
       proper(from(X)) -> from(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(0()) -> ok(0())
       proper(length1(X)) -> length1(proper(X))
      Matrix Interpretation Processor: dim=2
       
       usable rules:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        s(mark(X)) -> mark(s(X))
        s(ok(X)) -> ok(s(X))
        from(mark(X)) -> mark(from(X))
        from(ok(X)) -> ok(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        length1(ok(X)) -> ok(length1(X))
        length(ok(X)) -> ok(length(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
       interpretation:
                          [0]
        [mark](x0) = x0 + [2],
        
                        [2 0]     [2]
        [length1](x0) = [3 0]x0 + [2],
        
                            [2]
        [active](x0) = x0 + [0],
        
                              [2 0]     [2]
        [cons](x0, x1) = x0 + [0 0]x1 + [0],
        
        [top#](x0) = [0 2]x0,
        
                [0]
        [nil] = [0],
        
                     
        [ok](x0) = x0,
        
                          [0]
        [from](x0) = x0 + [2],
        
              [0]
        [0] = [0],
        
                         
        [proper](x0) = x0,
        
                       [2 0]  
        [length](x0) = [3 0]x0,
        
                  [0 0]  
        [s](x0) = [0 2]x0
       orientation:
        top#(ok(X)) = [0 2]X >= [0 2]X = top#(active(X))
        
        top#(mark(X)) = [0 2]X + [4] >= [0 2]X = top#(proper(X))
        
                              [2]        [2]                           
        active(from(X)) = X + [2] >= X + [2] = mark(cons(X,from(s(X))))
        
                                    [2 0]    [4 0]    [6]    [0 0]    [0]                      
        active(length(cons(X,Y))) = [3 0]X + [6 0]Y + [6] >= [6 0]Y + [6] = mark(s(length1(Y)))
        
                             [2 0]    [4]    [2 0]    [0]                  
        active(length1(X)) = [3 0]X + [2] >= [3 0]X + [2] = mark(length(X))
        
                              [2]        [2]                  
        active(from(X)) = X + [2] >= X + [2] = from(active(X))
        
                                   [2 0]     [4]         [2 0]     [4]                      
        active(cons(X1,X2)) = X1 + [0 0]X2 + [0] >= X1 + [0 0]X2 + [0] = cons(active(X1),X2)
        
                       [0 0]    [2]    [0 0]                
        active(s(X)) = [0 2]X + [0] >= [0 2]X = s(active(X))
        
                     [0 0]    [0]    [0 0]    [0]             
        s(mark(X)) = [0 2]X + [4] >= [0 2]X + [2] = mark(s(X))
        
                   [0 0]     [0 0]            
        s(ok(X)) = [0 2]X >= [0 2]X = ok(s(X))
        
                            [0]        [0]                
        from(mark(X)) = X + [4] >= X + [4] = mark(from(X))
        
                          [0]        [0]              
        from(ok(X)) = X + [2] >= X + [2] = ok(from(X))
        
                                 [2 0]     [2]         [2 0]     [2]                    
        cons(mark(X1),X2) = X1 + [0 0]X2 + [2] >= X1 + [0 0]X2 + [2] = mark(cons(X1,X2))
        
                                   [2 0]     [2]         [2 0]     [2]                  
        cons(ok(X1),ok(X2)) = X1 + [0 0]X2 + [0] >= X1 + [0 0]X2 + [0] = ok(cons(X1,X2))
        
                         [2 0]    [2]    [2 0]    [2]                 
        length1(ok(X)) = [3 0]X + [2] >= [3 0]X + [2] = ok(length1(X))
        
                        [2 0]     [2 0]                 
        length(ok(X)) = [3 0]X >= [3 0]X = ok(length(X))
        
                              [0]        [0]                  
        proper(from(X)) = X + [2] >= X + [2] = from(proper(X))
        
                                   [2 0]     [2]         [2 0]     [2]                              
        proper(cons(X1,X2)) = X1 + [0 0]X2 + [0] >= X1 + [0 0]X2 + [0] = cons(proper(X1),proper(X2))
        
                       [0 0]     [0 0]                
        proper(s(X)) = [0 2]X >= [0 2]X = s(proper(X))
        
                            [2 0]     [2 0]                     
        proper(length(X)) = [3 0]X >= [3 0]X = length(proper(X))
        
                        [0]    [0]            
        proper(nil()) = [0] >= [0] = ok(nil())
        
                      [0]    [0]          
        proper(0()) = [0] >= [0] = ok(0())
        
                             [2 0]    [2]    [2 0]    [2]                     
        proper(length1(X)) = [3 0]X + [2] >= [3 0]X + [2] = length1(proper(X))
       problem:
        DPs:
         top#(ok(X)) -> top#(active(X))
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(length(cons(X,Y))) -> mark(s(length1(Y)))
         active(length1(X)) -> mark(length(X))
         active(from(X)) -> from(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(s(X)) -> s(active(X))
         s(mark(X)) -> mark(s(X))
         s(ok(X)) -> ok(s(X))
         from(mark(X)) -> mark(from(X))
         from(ok(X)) -> ok(from(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         length1(ok(X)) -> ok(length1(X))
         length(ok(X)) -> ok(length(X))
         proper(from(X)) -> from(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(s(X)) -> s(proper(X))
         proper(length(X)) -> length(proper(X))
         proper(nil()) -> ok(nil())
         proper(0()) -> ok(0())
         proper(length1(X)) -> length1(proper(X))
       Restore Modifier:
        DPs:
         top#(ok(X)) -> top#(active(X))
        TRS:
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(length(cons(X,Y))) -> mark(s(length1(Y)))
         active(length1(X)) -> mark(length(X))
         active(from(X)) -> from(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(s(X)) -> s(active(X))
         from(mark(X)) -> mark(from(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         s(mark(X)) -> mark(s(X))
         proper(from(X)) -> from(proper(X))
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(s(X)) -> s(proper(X))
         proper(length(X)) -> length(proper(X))
         proper(nil()) -> ok(nil())
         proper(0()) -> ok(0())
         proper(length1(X)) -> length1(proper(X))
         from(ok(X)) -> ok(from(X))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         s(ok(X)) -> ok(s(X))
         length(ok(X)) -> ok(length(X))
         length1(ok(X)) -> ok(length1(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
        Subterm Criterion Processor:
         simple projection:
          pi(from) = [0,0]
          pi(active) = [0,0]
          pi(s) = 0
          pi(cons) = [1,1]
          pi(mark) = 0
          pi(length) = [0,0]
          pi(length1) = [0,0]
          pi(ok) = [0,0,0]
          pi(top#) = 0
         problem:
          DPs:
           
          TRS:
           active(from(X)) -> mark(cons(X,from(s(X))))
           active(length(cons(X,Y))) -> mark(s(length1(Y)))
           active(length1(X)) -> mark(length(X))
           active(from(X)) -> from(active(X))
           active(cons(X1,X2)) -> cons(active(X1),X2)
           active(s(X)) -> s(active(X))
           from(mark(X)) -> mark(from(X))
           cons(mark(X1),X2) -> mark(cons(X1,X2))
           s(mark(X)) -> mark(s(X))
           proper(from(X)) -> from(proper(X))
           proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
           proper(s(X)) -> s(proper(X))
           proper(length(X)) -> length(proper(X))
           proper(nil()) -> ok(nil())
           proper(0()) -> ok(0())
           proper(length1(X)) -> length1(proper(X))
           from(ok(X)) -> ok(from(X))
           cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
           s(ok(X)) -> ok(s(X))
           length(ok(X)) -> ok(length(X))
           length1(ok(X)) -> ok(length1(X))
           top(mark(X)) -> top(proper(X))
           top(ok(X)) -> top(active(X))
         Qed
     
     DPs:
      active#(from(X)) -> active#(X)
      active#(cons(X1,X2)) -> active#(X1)
      active#(s(X)) -> active#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(active#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      proper#(from(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(s(X)) -> proper#(X)
      proper#(length(X)) -> proper#(X)
      proper#(length1(X)) -> proper#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(proper#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      length1#(ok(X)) -> length1#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(length1#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      length#(ok(X)) -> length#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(length#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      s#(mark(X)) -> s#(X)
      s#(ok(X)) -> s#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(s#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      cons#(mark(X1),X2) -> cons#(X1,X2)
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      from#(mark(X)) -> from#(X)
      from#(ok(X)) -> from#(X)
     TRS:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(length(cons(X,Y))) -> mark(s(length1(Y)))
      active(length1(X)) -> mark(length(X))
      active(from(X)) -> from(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      from(mark(X)) -> mark(from(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      proper(from(X)) -> from(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      proper(0()) -> ok(0())
      proper(length1(X)) -> length1(proper(X))
      from(ok(X)) -> ok(from(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      length1(ok(X)) -> ok(length1(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(from#) = 0
      problem:
       DPs:
        
       TRS:
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(length(cons(X,Y))) -> mark(s(length1(Y)))
        active(length1(X)) -> mark(length(X))
        active(from(X)) -> from(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        from(mark(X)) -> mark(from(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        proper(from(X)) -> from(proper(X))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(0()) -> ok(0())
        proper(length1(X)) -> length1(proper(X))
        from(ok(X)) -> ok(from(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        length1(ok(X)) -> ok(length1(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed