MAYBE

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:
 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(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))
  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(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))
   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)
   CDG 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(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))
    graph:
     top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
     top#(ok(X)) -> top#(active(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X)
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X)))
     top#(ok(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     top#(ok(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     top#(ok(X)) -> active#(X) -> active#(length1(X)) -> length#(X)
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
     top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(length(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(length1(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(from(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(length1(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(length1(X)) -> proper#(X) ->
     proper#(s(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(length1(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(length1(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(length1(X)) -> length1#(proper(X)) ->
     length1#(ok(X)) -> length1#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(from(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(length(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(length(X)) -> proper#(X) ->
     proper#(s(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(length(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(length(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(length(X)) -> length#(proper(X)) ->
     length#(ok(X)) -> length#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length1(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length1(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(length(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(length1(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
     proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
     proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(from(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(from(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(length(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) ->
     proper#(length(X)) -> length#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(length1(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) ->
     proper#(length1(X)) -> length1#(proper(X))
     proper#(from(X)) -> from#(proper(X)) ->
     from#(mark(X)) -> from#(X)
     proper#(from(X)) -> from#(proper(X)) -> from#(ok(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#(mark(X1),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#(mark(X1),X2) -> cons#(X1,X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
     from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
     from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
     from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
     s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(ok(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#(cons(X1,X2)) -> cons#(active(X1),X2) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> s#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> from#(s(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(length1(X)) -> length#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> from#(active(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
     active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
     active#(s(X)) -> active#(X) -> active#(from(X)) -> s#(X)
     active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
     active#(s(X)) -> active#(X) ->
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(s(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     active#(s(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(s(X)) -> active#(X) -> active#(length1(X)) -> length#(X)
     active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
     active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(s(X)) -> active#(X) ->
     active#(s(X)) -> s#(active(X))
     active#(from(X)) -> cons#(X,from(s(X))) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     active#(from(X)) -> cons#(X,from(s(X))) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X)
     active#(from(X)) -> from#(s(X)) ->
     from#(ok(X)) -> from#(X)
     active#(from(X)) -> from#(active(X)) ->
     from#(mark(X)) -> from#(X)
     active#(from(X)) -> from#(active(X)) -> from#(ok(X)) -> from#(X)
     active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     active#(from(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     active#(from(X)) -> active#(X) -> active#(from(X)) -> s#(X)
     active#(from(X)) -> active#(X) ->
     active#(from(X)) -> from#(s(X))
     active#(from(X)) -> active#(X) ->
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(from(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> length1#(Y)
     active#(from(X)) -> active#(X) ->
     active#(length(cons(X,Y))) -> s#(length1(Y))
     active#(from(X)) -> active#(X) ->
     active#(length1(X)) -> length#(X)
     active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X)
     active#(from(X)) -> active#(X) ->
     active#(from(X)) -> from#(active(X))
     active#(from(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> active#(X1)
     active#(from(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    SCC Processor:
     #sccs: 8
     #rules: 19
     #arcs: 170/1225
     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(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))
     Open
     
     DPs:
      proper#(length1(X)) -> proper#(X)
      proper#(length(X)) -> proper#(X)
      proper#(s(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(from(X)) -> proper#(X)
     TRS:
      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))
     Open
     
     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(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))
     Open
     
     DPs:
      length1#(ok(X)) -> length1#(X)
     TRS:
      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))
     Open
     
     DPs:
      length#(ok(X)) -> length#(X)
     TRS:
      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))
     Open
     
     DPs:
      from#(ok(X)) -> from#(X)
      from#(mark(X)) -> from#(X)
     TRS:
      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))
     Open
     
     DPs:
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
      cons#(mark(X1),X2) -> cons#(X1,X2)
     TRS:
      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))
     Open
     
     DPs:
      s#(ok(X)) -> s#(X)
      s#(mark(X)) -> s#(X)
     TRS:
      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))
     Open