MAYBE

Problem:
 active(zeros()) -> mark(cons(0(),zeros()))
 active(and(tt(),X)) -> mark(X)
 active(length(nil())) -> mark(0())
 active(length(cons(N,L))) -> mark(s(length(L)))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(and(X1,X2)) -> and(active(X1),X2)
 active(length(X)) -> length(active(X))
 active(s(X)) -> s(active(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 and(mark(X1),X2) -> mark(and(X1,X2))
 length(mark(X)) -> mark(length(X))
 s(mark(X)) -> mark(s(X))
 proper(zeros()) -> ok(zeros())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
 proper(tt()) -> ok(tt())
 proper(length(X)) -> length(proper(X))
 proper(nil()) -> ok(nil())
 proper(s(X)) -> s(proper(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
 length(ok(X)) -> ok(length(X))
 s(ok(X)) -> ok(s(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(zeros()) -> cons#(0(),zeros())
   active#(length(cons(N,L))) -> length#(L)
   active#(length(cons(N,L))) -> s#(length(L))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(and(X1,X2)) -> active#(X1)
   active#(and(X1,X2)) -> and#(active(X1),X2)
   active#(length(X)) -> active#(X)
   active#(length(X)) -> length#(active(X))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   cons#(mark(X1),X2) -> cons#(X1,X2)
   and#(mark(X1),X2) -> and#(X1,X2)
   length#(mark(X)) -> length#(X)
   s#(mark(X)) -> s#(X)
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(and(X1,X2)) -> proper#(X2)
   proper#(and(X1,X2)) -> proper#(X1)
   proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
   proper#(length(X)) -> proper#(X)
   proper#(length(X)) -> length#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   and#(ok(X1),ok(X2)) -> and#(X1,X2)
   length#(ok(X)) -> length#(X)
   s#(ok(X)) -> s#(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(zeros()) -> mark(cons(0(),zeros()))
   active(and(tt(),X)) -> mark(X)
   active(length(nil())) -> mark(0())
   active(length(cons(N,L))) -> mark(s(length(L)))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(and(X1,X2)) -> and(active(X1),X2)
   active(length(X)) -> length(active(X))
   active(s(X)) -> s(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   and(mark(X1),X2) -> mark(and(X1,X2))
   length(mark(X)) -> mark(length(X))
   s(mark(X)) -> mark(s(X))
   proper(zeros()) -> ok(zeros())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(and(X1,X2)) -> and(proper(X1),proper(X2))
   proper(tt()) -> ok(tt())
   proper(length(X)) -> length(proper(X))
   proper(nil()) -> ok(nil())
   proper(s(X)) -> s(proper(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   and(ok(X1),ok(X2)) -> ok(and(X1,X2))
   length(ok(X)) -> ok(length(X))
   s(ok(X)) -> ok(s(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(zeros()) -> cons#(0(),zeros())
    active#(length(cons(N,L))) -> length#(L)
    active#(length(cons(N,L))) -> s#(length(L))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(and(X1,X2)) -> active#(X1)
    active#(and(X1,X2)) -> and#(active(X1),X2)
    active#(length(X)) -> active#(X)
    active#(length(X)) -> length#(active(X))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    cons#(mark(X1),X2) -> cons#(X1,X2)
    and#(mark(X1),X2) -> and#(X1,X2)
    length#(mark(X)) -> length#(X)
    s#(mark(X)) -> s#(X)
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(and(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(length(X)) -> proper#(X)
    proper#(length(X)) -> length#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    length#(ok(X)) -> length#(X)
    s#(ok(X)) -> s#(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(zeros()) -> mark(cons(0(),zeros()))
    active(and(tt(),X)) -> mark(X)
    active(length(nil())) -> mark(0())
    active(length(cons(N,L))) -> mark(s(length(L)))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(and(X1,X2)) -> and(active(X1),X2)
    active(length(X)) -> length(active(X))
    active(s(X)) -> s(active(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    and(mark(X1),X2) -> mark(and(X1,X2))
    length(mark(X)) -> mark(length(X))
    s(mark(X)) -> mark(s(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(length(X)) -> length(proper(X))
    proper(nil()) -> ok(nil())
    proper(s(X)) -> s(proper(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    length(ok(X)) -> ok(length(X))
    s(ok(X)) -> ok(s(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#(length(X)) -> length#(active(X))
    top#(ok(X)) -> active#(X) -> active#(length(X)) -> active#(X)
    top#(ok(X)) -> active#(X) ->
    active#(and(X1,X2)) -> and#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1)
    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#(length(cons(N,L))) -> s#(length(L))
    top#(ok(X)) -> active#(X) -> active#(length(cons(N,L))) -> length#(L)
    top#(ok(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    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#(s(X)) -> s#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(s(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#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2)
    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)
    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#(length(X)) -> length#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(length(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2)
    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)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(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#(length(X)) -> length#(proper(X))
    proper#(length(X)) -> proper#(X) ->
    proper#(length(X)) -> proper#(X)
    proper#(length(X)) -> proper#(X) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(length(X)) -> proper#(X) ->
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(length(X)) -> proper#(X) ->
    proper#(and(X1,X2)) -> proper#(X2)
    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)) -> length#(proper(X)) ->
    length#(ok(X)) -> length#(X)
    proper#(length(X)) -> length#(proper(X)) ->
    length#(mark(X)) -> length#(X)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(length(X)) -> length#(proper(X))
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(length(X)) -> proper#(X)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(length(X)) -> length#(proper(X))
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(length(X)) -> proper#(X)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(and(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) ->
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) ->
    and#(mark(X1),X2) -> and#(X1,X2)
    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#(length(X)) -> length#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(length(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(and(X1,X2)) -> proper#(X2)
    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#(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#(length(X)) -> length#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(length(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(and(X1,X2)) -> proper#(X2)
    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)) -> 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)
    and#(ok(X1),ok(X2)) -> and#(X1,X2) ->
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    and#(ok(X1),ok(X2)) -> and#(X1,X2) ->
    and#(mark(X1),X2) -> and#(X1,X2)
    and#(mark(X1),X2) -> and#(X1,X2) ->
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2)
    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)
    length#(ok(X)) -> length#(X) -> length#(ok(X)) -> length#(X)
    length#(ok(X)) -> length#(X) -> length#(mark(X)) -> length#(X)
    length#(mark(X)) -> length#(X) -> length#(ok(X)) -> length#(X)
    length#(mark(X)) -> length#(X) ->
    length#(mark(X)) -> length#(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)
    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#(length(X)) -> length#(active(X))
    active#(s(X)) -> active#(X) -> active#(length(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(and(X1,X2)) -> and#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1)
    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#(length(cons(N,L))) -> s#(length(L))
    active#(s(X)) -> active#(X) ->
    active#(length(cons(N,L))) -> length#(L)
    active#(s(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(length(cons(N,L))) -> s#(length(L)) ->
    s#(ok(X)) -> s#(X)
    active#(length(cons(N,L))) -> s#(length(L)) ->
    s#(mark(X)) -> s#(X)
    active#(length(cons(N,L))) -> length#(L) ->
    length#(ok(X)) -> length#(X)
    active#(length(cons(N,L))) -> length#(L) ->
    length#(mark(X)) -> length#(X)
    active#(length(X)) -> length#(active(X)) ->
    length#(ok(X)) -> length#(X)
    active#(length(X)) -> length#(active(X)) ->
    length#(mark(X)) -> length#(X)
    active#(length(X)) -> active#(X) ->
    active#(s(X)) -> s#(active(X))
    active#(length(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(length(X)) -> active#(X) ->
    active#(length(X)) -> length#(active(X))
    active#(length(X)) -> active#(X) ->
    active#(length(X)) -> active#(X)
    active#(length(X)) -> active#(X) ->
    active#(and(X1,X2)) -> and#(active(X1),X2)
    active#(length(X)) -> active#(X) ->
    active#(and(X1,X2)) -> active#(X1)
    active#(length(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(length(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(length(X)) -> active#(X) ->
    active#(length(cons(N,L))) -> s#(length(L))
    active#(length(X)) -> active#(X) ->
    active#(length(cons(N,L))) -> length#(L)
    active#(length(X)) -> active#(X) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(and(X1,X2)) -> and#(active(X1),X2) ->
    and#(ok(X1),ok(X2)) -> and#(X1,X2)
    active#(and(X1,X2)) -> and#(active(X1),X2) ->
    and#(mark(X1),X2) -> and#(X1,X2)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(and(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(length(X)) -> length#(active(X))
    active#(and(X1,X2)) -> active#(X1) ->
    active#(length(X)) -> active#(X)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(and(X1,X2)) -> and#(active(X1),X2)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(and(X1,X2)) -> active#(X1)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(length(cons(N,L))) -> s#(length(L))
    active#(and(X1,X2)) -> active#(X1) ->
    active#(length(cons(N,L))) -> length#(L)
    active#(and(X1,X2)) -> active#(X1) ->
    active#(zeros()) -> cons#(0(),zeros())
    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#(length(X)) -> length#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(length(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(and(X1,X2)) -> and#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(and(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#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(length(cons(N,L))) -> s#(length(L))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(length(cons(N,L))) -> length#(L)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(zeros()) -> cons#(0(),zeros())
    active#(zeros()) -> cons#(0(),zeros()) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(zeros()) -> cons#(0(),zeros()) -> cons#(mark(X1),X2) -> cons#(X1,X2)
   SCC Processor:
    #sccs: 7
    #rules: 20
    #arcs: 171/1089
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(cons(X1,X2)) -> active#(X1)
     active#(and(X1,X2)) -> active#(X1)
     active#(length(X)) -> active#(X)
     active#(s(X)) -> active#(X)
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(and(X1,X2)) -> proper#(X2)
     proper#(and(X1,X2)) -> proper#(X1)
     proper#(length(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X)
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     length#(mark(X)) -> length#(X)
     length#(ok(X)) -> length#(X)
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     and#(mark(X1),X2) -> and#(X1,X2)
     and#(ok(X1),ok(X2)) -> and#(X1,X2)
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(and#) = 1
     problem:
      DPs:
       and#(mark(X1),X2) -> and#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(and#) = 0
      problem:
       DPs:
        
       TRS:
        active(zeros()) -> mark(cons(0(),zeros()))
        active(and(tt(),X)) -> mark(X)
        active(length(nil())) -> mark(0())
        active(length(cons(N,L))) -> mark(s(length(L)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(and(X1,X2)) -> and(active(X1),X2)
        active(length(X)) -> length(active(X))
        active(s(X)) -> s(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        and(mark(X1),X2) -> mark(and(X1,X2))
        length(mark(X)) -> mark(length(X))
        s(mark(X)) -> mark(s(X))
        proper(zeros()) -> ok(zeros())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(s(X)) -> s(proper(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        length(ok(X)) -> ok(length(X))
        s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
     active(and(tt(),X)) -> mark(X)
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(s(length(L)))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(and(X1,X2)) -> and(active(X1),X2)
     active(length(X)) -> length(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     and(mark(X1),X2) -> mark(and(X1,X2))
     length(mark(X)) -> mark(length(X))
     s(mark(X)) -> mark(s(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(and(X1,X2)) -> and(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     proper(s(X)) -> s(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     and(ok(X1),ok(X2)) -> ok(and(X1,X2))
     length(ok(X)) -> ok(length(X))
     s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
       active(and(tt(),X)) -> mark(X)
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(s(length(L)))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(and(X1,X2)) -> and(active(X1),X2)
       active(length(X)) -> length(active(X))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       and(mark(X1),X2) -> mark(and(X1,X2))
       length(mark(X)) -> mark(length(X))
       s(mark(X)) -> mark(s(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(and(X1,X2)) -> and(proper(X1),proper(X2))
       proper(tt()) -> ok(tt())
       proper(length(X)) -> length(proper(X))
       proper(nil()) -> ok(nil())
       proper(s(X)) -> s(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       and(ok(X1),ok(X2)) -> ok(and(X1,X2))
       length(ok(X)) -> ok(length(X))
       s(ok(X)) -> ok(s(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(zeros()) -> mark(cons(0(),zeros()))
        active(and(tt(),X)) -> mark(X)
        active(length(nil())) -> mark(0())
        active(length(cons(N,L))) -> mark(s(length(L)))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(and(X1,X2)) -> and(active(X1),X2)
        active(length(X)) -> length(active(X))
        active(s(X)) -> s(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        and(mark(X1),X2) -> mark(and(X1,X2))
        length(mark(X)) -> mark(length(X))
        s(mark(X)) -> mark(s(X))
        proper(zeros()) -> ok(zeros())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(0()) -> ok(0())
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(s(X)) -> s(proper(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        length(ok(X)) -> ok(length(X))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed