MAYBE
0.18/0.24	MAYBE
0.18/0.24	
0.18/0.24	Problem:
0.18/0.24	 active(and(tt(),T)) -> mark(T)
0.18/0.24	 active(isNatIList(IL)) -> mark(isNatList(IL))
0.18/0.24	 active(isNat(0())) -> mark(tt())
0.18/0.24	 active(isNat(s(N))) -> mark(isNat(N))
0.18/0.24	 active(isNat(length(L))) -> mark(isNatList(L))
0.18/0.24	 active(isNatIList(zeros())) -> mark(tt())
0.18/0.24	 active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
0.18/0.24	 active(isNatList(nil())) -> mark(tt())
0.18/0.24	 active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
0.18/0.24	 active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
0.18/0.24	 active(zeros()) -> mark(cons(0(),zeros()))
0.18/0.24	 active(take(0(),IL)) -> mark(uTake1(isNatIList(IL)))
0.18/0.24	 active(uTake1(tt())) -> mark(nil())
0.18/0.24	 active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
0.18/0.24	 active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL)))
0.18/0.24	 active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
0.18/0.24	 active(uLength(tt(),L)) -> mark(s(length(L)))
0.18/0.24	 active(and(X1,X2)) -> and(active(X1),X2)
0.18/0.24	 active(and(X1,X2)) -> and(X1,active(X2))
0.18/0.24	 active(s(X)) -> s(active(X))
0.18/0.24	 active(length(X)) -> length(active(X))
0.18/0.24	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.18/0.24	 active(take(X1,X2)) -> take(active(X1),X2)
0.18/0.24	 active(take(X1,X2)) -> take(X1,active(X2))
0.18/0.24	 active(uTake1(X)) -> uTake1(active(X))
0.18/0.24	 active(uTake2(X1,X2,X3,X4)) -> uTake2(active(X1),X2,X3,X4)
0.18/0.24	 active(uLength(X1,X2)) -> uLength(active(X1),X2)
0.18/0.24	 and(mark(X1),X2) -> mark(and(X1,X2))
0.18/0.24	 and(X1,mark(X2)) -> mark(and(X1,X2))
0.18/0.24	 s(mark(X)) -> mark(s(X))
0.18/0.24	 length(mark(X)) -> mark(length(X))
0.18/0.24	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.18/0.24	 take(mark(X1),X2) -> mark(take(X1,X2))
0.18/0.24	 take(X1,mark(X2)) -> mark(take(X1,X2))
0.18/0.24	 uTake1(mark(X)) -> mark(uTake1(X))
0.18/0.24	 uTake2(mark(X1),X2,X3,X4) -> mark(uTake2(X1,X2,X3,X4))
0.18/0.24	 uLength(mark(X1),X2) -> mark(uLength(X1,X2))
0.18/0.24	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
0.18/0.24	 proper(tt()) -> ok(tt())
0.18/0.24	 proper(isNatIList(X)) -> isNatIList(proper(X))
0.18/0.24	 proper(isNatList(X)) -> isNatList(proper(X))
0.18/0.24	 proper(isNat(X)) -> isNat(proper(X))
0.18/0.24	 proper(0()) -> ok(0())
0.18/0.24	 proper(s(X)) -> s(proper(X))
0.18/0.24	 proper(length(X)) -> length(proper(X))
0.18/0.24	 proper(zeros()) -> ok(zeros())
0.18/0.24	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.18/0.24	 proper(nil()) -> ok(nil())
0.18/0.24	 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
0.18/0.24	 proper(uTake1(X)) -> uTake1(proper(X))
0.18/0.24	 proper(uTake2(X1,X2,X3,X4)) -> uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
0.18/0.24	 proper(uLength(X1,X2)) -> uLength(proper(X1),proper(X2))
0.18/0.24	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
0.18/0.24	 isNatIList(ok(X)) -> ok(isNatIList(X))
0.18/0.24	 isNatList(ok(X)) -> ok(isNatList(X))
0.18/0.24	 isNat(ok(X)) -> ok(isNat(X))
0.18/0.24	 s(ok(X)) -> ok(s(X))
0.18/0.24	 length(ok(X)) -> ok(length(X))
0.18/0.24	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.18/0.24	 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
0.18/0.24	 uTake1(ok(X)) -> ok(uTake1(X))
0.18/0.24	 uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(uTake2(X1,X2,X3,X4))
0.18/0.24	 uLength(ok(X1),ok(X2)) -> ok(uLength(X1,X2))
0.18/0.24	 top(mark(X)) -> top(proper(X))
0.18/0.24	 top(ok(X)) -> top(active(X))
0.18/0.24	
0.18/0.24	Proof:
0.18/0.24	 Open
0.18/0.25	EOF