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:
 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)
   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(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))
    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(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))
      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=3
      
      usable rules:
       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))
       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:
       [top#](x0) = [0 1 0]x0,
       
                    
       [ok](x0) = x0
                    ,
       
                      [0 0 1]  
       [proper](x0) = [0 1 0]x0
                      [1 0 0]  ,
       
                       [0 0 0]     [0]
       [length1](x0) = [1 0 1]x0 + [1]
                       [0 0 0]     [0],
       
             [0]
       [0] = [0]
             [0],
       
                      [0 0 0]  
       [length](x0) = [1 0 1]x0
                      [0 0 0]  ,
       
               [1]
       [nil] = [0]
               [1],
       
                    [0 0 0]     [0]
       [mark](x0) = [0 1 0]x0 + [1]
                    [0 0 0]     [0],
       
                             [1 0 0]     [1]
       [cons](x0, x1) = x0 + [0 0 0]x1 + [0]
                             [0 0 1]     [1],
       
                 [0 0 0]  
       [s](x0) = [0 1 0]x0
                 [0 0 0]  ,
       
                        
       [active](x0) = x0
                        ,
       
                    [0 0 0]     [0]
       [from](x0) = [0 1 0]x0 + [1]
                    [0 0 0]     [0]
      orientation:
       top#(ok(X)) = [0 1 0]X >= [0 1 0]X = top#(active(X))
       
       top#(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X = top#(proper(X))
       
                         [0 0 0]    [0]    [0 0 0]    [0]                           
       active(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(cons(X,from(s(X))))
                         [0 0 0]    [0]    [0 0 0]    [0]                           
       
                               [0]    [0]            
       active(length(nil())) = [2] >= [1] = mark(0())
                               [0]    [0]            
       
                                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0]                      
       active(length(cons(X,Y))) = [1 0 1]X + [1 0 1]Y + [2] >= [1 0 1]Y + [2] = mark(s(length1(Y)))
                                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0]                      
       
                            [0 0 0]    [0]    [0 0 0]    [0]                  
       active(length1(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = mark(length(X))
                            [0 0 0]    [0]    [0 0 0]    [0]                  
       
                         [0 0 0]    [0]    [0 0 0]    [0]                  
       active(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = from(active(X))
                         [0 0 0]    [0]    [0 0 0]    [0]                  
       
                                  [1 0 0]     [1]         [1 0 0]     [1]                      
       active(cons(X1,X2)) = X1 + [0 0 0]X2 + [0] >= X1 + [0 0 0]X2 + [0] = cons(active(X1),X2)
                                  [0 0 1]     [1]         [0 0 1]     [1]                      
       
                      [0 0 0]     [0 0 0]                
       active(s(X)) = [0 1 0]X >= [0 1 0]X = s(active(X))
                      [0 0 0]     [0 0 0]                
       
                    [0 0 0]    [0]    [0 0 0]    [0]             
       s(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(s(X))
                    [0 0 0]    [0]    [0 0 0]    [0]             
       
                  [0 0 0]     [0 0 0]            
       s(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(s(X))
                  [0 0 0]     [0 0 0]            
       
                       [0 0 0]    [0]    [0 0 0]    [0]                
       from(mark(X)) = [0 1 0]X + [2] >= [0 1 0]X + [2] = mark(from(X))
                       [0 0 0]    [0]    [0 0 0]    [0]                
       
                     [0 0 0]    [0]    [0 0 0]    [0]              
       from(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(from(X))
                     [0 0 0]    [0]    [0 0 0]    [0]              
       
                           [0 0 0]     [1 0 0]     [1]    [0 0 0]     [0]                    
       cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [1] = mark(cons(X1,X2))
                           [0 0 0]     [0 0 1]     [1]    [0 0 0]     [0]                    
       
                                  [1 0 0]     [1]         [1 0 0]     [1]                  
       cons(ok(X1),ok(X2)) = X1 + [0 0 0]X2 + [0] >= X1 + [0 0 0]X2 + [0] = ok(cons(X1,X2))
                                  [0 0 1]     [1]         [0 0 1]     [1]                  
       
                        [0 0 0]    [0]    [0 0 0]    [0]                 
       length1(ok(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = ok(length1(X))
                        [0 0 0]    [0]    [0 0 0]    [0]                 
       
                       [0 0 0]     [0 0 0]                 
       length(ok(X)) = [1 0 1]X >= [1 0 1]X = ok(length(X))
                       [0 0 0]     [0 0 0]                 
       
                         [0 0 0]    [0]    [0 0 0]    [0]                  
       proper(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = from(proper(X))
                         [0 0 0]    [0]    [0 0 0]    [0]                  
       
                             [0 0 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                              
       proper(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = cons(proper(X1),proper(X2))
                             [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]     [1]                              
       
                      [0 0 0]     [0 0 0]                
       proper(s(X)) = [0 1 0]X >= [0 1 0]X = s(proper(X))
                      [0 0 0]     [0 0 0]                
       
                           [0 0 0]     [0 0 0]                     
       proper(length(X)) = [1 0 1]X >= [1 0 1]X = length(proper(X))
                           [0 0 0]     [0 0 0]                     
       
                       [1]    [1]            
       proper(nil()) = [0] >= [0] = ok(nil())
                       [1]    [1]            
       
                     [0]    [0]          
       proper(0()) = [0] >= [0] = ok(0())
                     [0]    [0]          
       
                            [0 0 0]    [0]    [0 0 0]    [0]                     
       proper(length1(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = length1(proper(X))
                            [0 0 0]    [0]    [0 0 0]    [0]                     
      problem:
       DPs:
        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))
        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(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))
       Usable Rule Processor:
        DPs:
         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))
         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))
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          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))
          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))
         interpretation:
          [top#](x0) = x0 + 0,
          
          [ok](x0) = x0 + 5,
          
          [length1](x0) = x0 + 3,
          
          [0] = 0,
          
          [length](x0) = x0 + 2,
          
          [nil] = 0,
          
          [mark](x0) = 1,
          
          [cons](x0, x1) = x0 + 0,
          
          [s](x0) = x0 + 2,
          
          [active](x0) = 4,
          
          [from](x0) = x0 + 0
         orientation:
          top#(ok(X)) = X + 5 >= 4 = top#(active(X))
          
          active(from(X)) = 4 >= 1 = mark(cons(X,from(s(X))))
          
          active(length(nil())) = 4 >= 1 = mark(0())
          
          active(length(cons(X,Y))) = 4 >= 1 = mark(s(length1(Y)))
          
          active(length1(X)) = 4 >= 1 = mark(length(X))
          
          active(from(X)) = 4 >= 4 = from(active(X))
          
          active(cons(X1,X2)) = 4 >= 4 = cons(active(X1),X2)
          
          active(s(X)) = 4 >= 4 = s(active(X))
          
          s(mark(X)) = 2 >= 1 = mark(s(X))
          
          s(ok(X)) = X + 5 >= X + 5 = ok(s(X))
          
          from(mark(X)) = 1 >= 1 = mark(from(X))
          
          from(ok(X)) = X + 5 >= X + 5 = ok(from(X))
          
          cons(mark(X1),X2) = 1 >= 1 = mark(cons(X1,X2))
          
          cons(ok(X1),ok(X2)) = X1 + 5 >= X1 + 5 = ok(cons(X1,X2))
          
          length1(ok(X)) = X + 5 >= X + 5 = ok(length1(X))
          
          length(ok(X)) = X + 5 >= X + 5 = ok(length(X))
         problem:
          DPs:
           
          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))
           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))
         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(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))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      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))
     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(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))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      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))
     Qed
    
    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))
    Subterm Criterion Processor:
     simple projection:
      pi(length1#) = 0
     problem:
      DPs:
       
      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))
     Qed
    
    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))
    Subterm Criterion Processor:
     simple projection:
      pi(length#) = 0
     problem:
      DPs:
       
      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))
     Qed
    
    DPs:
     s#(mark(X)) -> s#(X)
     s#(ok(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))
    Subterm Criterion Processor:
     simple projection:
      pi(s#) = 0
     problem:
      DPs:
       
      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))
     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(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))
    Subterm Criterion Processor:
     simple projection:
      pi(cons#) = 1
     problem:
      DPs:
       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))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 0
      problem:
       DPs:
        
       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))
      Qed
    
    DPs:
     from#(mark(X)) -> from#(X)
     from#(ok(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))
    Subterm Criterion Processor:
     simple projection:
      pi(from#) = 0
     problem:
      DPs:
       
      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))
     Qed