MAYBE

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

Proof:
 DP Processor:
  DPs:
   active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
   active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(first(X1,X2)) -> active#(X1)
   active#(first(X1,X2)) -> first#(active(X1),X2)
   active#(first(X1,X2)) -> active#(X2)
   active#(first(X1,X2)) -> first#(X1,active(X2))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(from(X)) -> active#(X)
   active#(from(X)) -> from#(active(X))
   first#(mark(X1),X2) -> first#(X1,X2)
   first#(X1,mark(X2)) -> first#(X1,X2)
   s#(mark(X)) -> s#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   from#(mark(X)) -> from#(X)
   proper#(first(X1,X2)) -> proper#(X2)
   proper#(first(X1,X2)) -> proper#(X1)
   proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   first#(ok(X1),ok(X2)) -> first#(X1,X2)
   s#(ok(X)) -> s#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   from#(ok(X)) -> from#(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(first(0(),X)) -> mark(nil())
   active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(first(X1,X2)) -> first(active(X1),X2)
   active(first(X1,X2)) -> first(X1,active(X2))
   active(s(X)) -> s(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(from(X)) -> from(active(X))
   first(mark(X1),X2) -> mark(first(X1,X2))
   first(X1,mark(X2)) -> mark(first(X1,X2))
   s(mark(X)) -> mark(s(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   proper(first(X1,X2)) -> first(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(nil()) -> ok(nil())
   proper(s(X)) -> s(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   first(ok(X1),ok(X2)) -> ok(first(X1,X2))
   s(ok(X)) -> ok(s(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   from(ok(X)) -> ok(from(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Usable Rule Processor:
   DPs:
    active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
    active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(first(X1,X2)) -> active#(X1)
    active#(first(X1,X2)) -> first#(active(X1),X2)
    active#(first(X1,X2)) -> active#(X2)
    active#(first(X1,X2)) -> first#(X1,active(X2))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(from(X)) -> active#(X)
    active#(from(X)) -> from#(active(X))
    first#(mark(X1),X2) -> first#(X1,X2)
    first#(X1,mark(X2)) -> first#(X1,X2)
    s#(mark(X)) -> s#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    from#(mark(X)) -> from#(X)
    proper#(first(X1,X2)) -> proper#(X2)
    proper#(first(X1,X2)) -> proper#(X1)
    proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    first#(ok(X1),ok(X2)) -> first#(X1,X2)
    s#(ok(X)) -> s#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    from#(ok(X)) -> from#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    f18(x,y) -> x
    f18(x,y) -> y
    first(mark(X1),X2) -> mark(first(X1,X2))
    first(X1,mark(X2)) -> mark(first(X1,X2))
    first(ok(X1),ok(X2)) -> ok(first(X1,X2))
    s(mark(X)) -> mark(s(X))
    s(ok(X)) -> ok(s(X))
    from(mark(X)) -> mark(from(X))
    from(ok(X)) -> ok(from(X))
    active(first(0(),X)) -> mark(nil())
    active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(first(X1,X2)) -> first(active(X1),X2)
    active(first(X1,X2)) -> first(X1,active(X2))
    active(s(X)) -> s(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(from(X)) -> from(active(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    proper(first(X1,X2)) -> first(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(nil()) -> ok(nil())
    proper(s(X)) -> s(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
   ADG Processor:
    DPs:
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     active#(from(X)) -> s#(X)
     active#(from(X)) -> from#(s(X))
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(first(X1,X2)) -> active#(X1)
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(first(X1,X2)) -> active#(X2)
     active#(first(X1,X2)) -> first#(X1,active(X2))
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(from(X)) -> active#(X)
     active#(from(X)) -> from#(active(X))
     first#(mark(X1),X2) -> first#(X1,X2)
     first#(X1,mark(X2)) -> first#(X1,X2)
     s#(mark(X)) -> s#(X)
     cons#(mark(X1),X2) -> cons#(X1,X2)
     from#(mark(X)) -> from#(X)
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(from(X)) -> proper#(X)
     proper#(from(X)) -> from#(proper(X))
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     s#(ok(X)) -> s#(X)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     from#(ok(X)) -> from#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     f18(x,y) -> x
     f18(x,y) -> y
     first(mark(X1),X2) -> mark(first(X1,X2))
     first(X1,mark(X2)) -> mark(first(X1,X2))
     first(ok(X1),ok(X2)) -> ok(first(X1,X2))
     s(mark(X)) -> mark(s(X))
     s(ok(X)) -> ok(s(X))
     from(mark(X)) -> mark(from(X))
     from(ok(X)) -> ok(from(X))
     active(first(0(),X)) -> mark(nil())
     active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(first(X1,X2)) -> first(active(X1),X2)
     active(first(X1,X2)) -> first(X1,active(X2))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     proper(first(X1,X2)) -> first(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(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#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     top#(ok(X)) -> active#(X) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     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#(first(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(first(X1,X2)) -> active#(X2)
     top#(ok(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(X1,active(X2))
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(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#(from(X)) -> active#(X)
     top#(ok(X)) -> active#(X) ->
     active#(from(X)) -> from#(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#(first(X1,X2)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) -> proper#(first(X1,X2)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) ->
     proper#(first(X1,X2)) -> first#(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#(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#(from(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(from(X)) -> proper#(X) ->
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(from(X)) -> proper#(X) ->
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(from(X)) -> proper#(X) ->
     proper#(first(X1,X2)) -> first#(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#(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#(from(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(from(X)) -> from#(proper(X)) ->
     from#(mark(X)) -> from#(X)
     proper#(from(X)) -> from#(proper(X)) ->
     from#(ok(X)) -> from#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> first#(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#(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#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> first#(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#(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#(from(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> from#(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#(first(X1,X2)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) -> proper#(first(X1,X2)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) ->
     proper#(first(X1,X2)) -> first#(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#(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#(from(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(from(X)) -> from#(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#(first(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> proper#(X)
     proper#(first(X1,X2)) -> proper#(X2) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> proper#(X2)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> proper#(X1)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> proper#(X)
     proper#(first(X1,X2)) -> proper#(X1) ->
     proper#(from(X)) -> from#(proper(X))
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2)) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2)) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     proper#(first(X1,X2)) -> first#(proper(X1),proper(X2)) ->
     first#(ok(X1),ok(X2)) -> first#(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)
     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)
     first#(ok(X1),ok(X2)) -> first#(X1,X2) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     first#(ok(X1),ok(X2)) -> first#(X1,X2) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     first#(ok(X1),ok(X2)) -> first#(X1,X2) ->
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     first#(mark(X1),X2) -> first#(X1,X2) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     first#(mark(X1),X2) -> first#(X1,X2) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     first#(mark(X1),X2) -> first#(X1,X2) ->
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     first#(X1,mark(X2)) -> first#(X1,X2) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     first#(X1,mark(X2)) -> first#(X1,X2) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     first#(X1,mark(X2)) -> first#(X1,X2) ->
     first#(ok(X1),ok(X2)) -> first#(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)) -> 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)) -> active#(X) ->
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(from(X)) -> active#(X) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     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#(first(X1,X2)) -> active#(X1)
     active#(from(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(from(X)) -> active#(X) ->
     active#(first(X1,X2)) -> active#(X2)
     active#(from(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(X1,active(X2))
     active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(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#(from(X)) -> active#(X)
     active#(from(X)) -> active#(X) ->
     active#(from(X)) -> from#(active(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#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     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#(first(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> active#(X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> first#(X1,active(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#(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#(from(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> from#(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#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(s(X)) -> active#(X) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     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#(first(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(s(X)) -> active#(X) -> active#(first(X1,X2)) -> active#(X2)
     active#(s(X)) -> active#(X) ->
     active#(first(X1,X2)) -> first#(X1,active(X2))
     active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(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#(from(X)) -> active#(X)
     active#(s(X)) -> active#(X) ->
     active#(from(X)) -> from#(active(X))
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z) ->
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(active(X1),X2) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(active(X1),X2) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(active(X1),X2) ->
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(X1,active(X2)) ->
     first#(mark(X1),X2) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(X1,active(X2)) ->
     first#(X1,mark(X2)) -> first#(X1,X2)
     active#(first(X1,X2)) -> first#(X1,active(X2)) ->
     first#(ok(X1),ok(X2)) -> first#(X1,X2)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     active#(first(X1,X2)) -> active#(X2) ->
     active#(from(X)) -> s#(X)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(from(X)) -> from#(s(X))
     active#(first(X1,X2)) -> active#(X2) ->
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(X1,X2)) -> active#(X1)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(X1,X2)) -> active#(X2)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(first(X1,X2)) -> first#(X1,active(X2))
     active#(first(X1,X2)) -> active#(X2) ->
     active#(s(X)) -> active#(X)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(s(X)) -> s#(active(X))
     active#(first(X1,X2)) -> active#(X2) ->
     active#(cons(X1,X2)) -> active#(X1)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(from(X)) -> active#(X)
     active#(first(X1,X2)) -> active#(X2) ->
     active#(from(X)) -> from#(active(X))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> s#(X)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> from#(s(X))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> cons#(X,from(s(X)))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> active#(X1)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> first#(active(X1),X2)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> active#(X2)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(first(X1,X2)) -> first#(X1,active(X2))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(first(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> active#(X1)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(first(X1,X2)) -> active#(X1) ->
     active#(from(X)) -> active#(X)
     active#(first(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X))
    Restore Modifier:
     DPs:
      active#(first(s(X),cons(Y,Z))) -> first#(X,Z)
      active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z))
      active#(from(X)) -> s#(X)
      active#(from(X)) -> from#(s(X))
      active#(from(X)) -> cons#(X,from(s(X)))
      active#(first(X1,X2)) -> active#(X1)
      active#(first(X1,X2)) -> first#(active(X1),X2)
      active#(first(X1,X2)) -> active#(X2)
      active#(first(X1,X2)) -> first#(X1,active(X2))
      active#(s(X)) -> active#(X)
      active#(s(X)) -> s#(active(X))
      active#(cons(X1,X2)) -> active#(X1)
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(from(X)) -> active#(X)
      active#(from(X)) -> from#(active(X))
      first#(mark(X1),X2) -> first#(X1,X2)
      first#(X1,mark(X2)) -> first#(X1,X2)
      s#(mark(X)) -> s#(X)
      cons#(mark(X1),X2) -> cons#(X1,X2)
      from#(mark(X)) -> from#(X)
      proper#(first(X1,X2)) -> proper#(X2)
      proper#(first(X1,X2)) -> proper#(X1)
      proper#(first(X1,X2)) -> first#(proper(X1),proper(X2))
      proper#(s(X)) -> proper#(X)
      proper#(s(X)) -> s#(proper(X))
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(from(X)) -> proper#(X)
      proper#(from(X)) -> from#(proper(X))
      first#(ok(X1),ok(X2)) -> first#(X1,X2)
      s#(ok(X)) -> s#(X)
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
      from#(ok(X)) -> from#(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(first(0(),X)) -> mark(nil())
      active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(first(X1,X2)) -> first(active(X1),X2)
      active(first(X1,X2)) -> first(X1,active(X2))
      active(s(X)) -> s(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(from(X)) -> from(active(X))
      first(mark(X1),X2) -> mark(first(X1,X2))
      first(X1,mark(X2)) -> mark(first(X1,X2))
      s(mark(X)) -> mark(s(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      from(mark(X)) -> mark(from(X))
      proper(first(X1,X2)) -> first(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(nil()) -> ok(nil())
      proper(s(X)) -> s(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(from(X)) -> from(proper(X))
      first(ok(X1),ok(X2)) -> ok(first(X1,X2))
      s(ok(X)) -> ok(s(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      from(ok(X)) -> ok(from(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     SCC Processor:
      #sccs: 7
      #rules: 22
      #arcs: 221/1444
      DPs:
       top#(ok(X)) -> top#(active(X))
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       proper#(from(X)) -> proper#(X)
       proper#(cons(X1,X2)) -> proper#(X1)
       proper#(cons(X1,X2)) -> proper#(X2)
       proper#(s(X)) -> proper#(X)
       proper#(first(X1,X2)) -> proper#(X1)
       proper#(first(X1,X2)) -> proper#(X2)
      TRS:
       active(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       active#(from(X)) -> active#(X)
       active#(cons(X1,X2)) -> active#(X1)
       active#(s(X)) -> active#(X)
       active#(first(X1,X2)) -> active#(X2)
       active#(first(X1,X2)) -> active#(X1)
      TRS:
       active(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       first#(ok(X1),ok(X2)) -> first#(X1,X2)
       first#(X1,mark(X2)) -> first#(X1,X2)
       first#(mark(X1),X2) -> first#(X1,X2)
      TRS:
       active(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(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(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(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(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(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(first(0(),X)) -> mark(nil())
       active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(first(X1,X2)) -> first(active(X1),X2)
       active(first(X1,X2)) -> first(X1,active(X2))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(from(X)) -> from(active(X))
       first(mark(X1),X2) -> mark(first(X1,X2))
       first(X1,mark(X2)) -> mark(first(X1,X2))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       proper(first(X1,X2)) -> first(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       first(ok(X1),ok(X2)) -> ok(first(X1,X2))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       from(ok(X)) -> ok(from(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open