MAYBE
0.18/0.24	MAYBE
0.18/0.24	
0.18/0.24	Problem:
0.18/0.24	 active(zeros()) -> mark(cons(0(),zeros()))
0.18/0.24	 active(U11(tt(),L)) -> mark(s(length(L)))
0.18/0.24	 active(U21(tt())) -> mark(nil())
0.18/0.24	 active(U31(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
0.18/0.24	 active(and(tt(),X)) -> mark(X)
0.18/0.24	 active(isNat(0())) -> mark(tt())
0.18/0.24	 active(isNat(length(V1))) -> mark(isNatList(V1))
0.18/0.24	 active(isNat(s(V1))) -> mark(isNat(V1))
0.18/0.24	 active(isNatIList(V)) -> mark(isNatList(V))
0.18/0.24	 active(isNatIList(zeros())) -> mark(tt())
0.18/0.24	 active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
0.18/0.24	 active(isNatList(nil())) -> mark(tt())
0.18/0.24	 active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2)))
0.18/0.24	 active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
0.18/0.24	 active(length(nil())) -> mark(0())
0.18/0.24	 active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L))
0.18/0.24	 active(take(0(),IL)) -> mark(U21(isNatIList(IL)))
0.18/0.24	 active(take(s(M),cons(N,IL))) -> mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N))
0.18/0.24	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.18/0.24	 active(U11(X1,X2)) -> U11(active(X1),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(U21(X)) -> U21(active(X))
0.18/0.24	 active(U31(X1,X2,X3,X4)) -> U31(active(X1),X2,X3,X4)
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(and(X1,X2)) -> and(active(X1),X2)
0.18/0.24	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.18/0.24	 U11(mark(X1),X2) -> mark(U11(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	 U21(mark(X)) -> mark(U21(X))
0.18/0.24	 U31(mark(X1),X2,X3,X4) -> mark(U31(X1,X2,X3,X4))
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	 and(mark(X1),X2) -> mark(and(X1,X2))
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(0()) -> ok(0())
0.18/0.24	 proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
0.18/0.24	 proper(tt()) -> ok(tt())
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(U21(X)) -> U21(proper(X))
0.18/0.24	 proper(nil()) -> ok(nil())
0.18/0.24	 proper(U31(X1,X2,X3,X4)) -> U31(proper(X1),proper(X2),proper(X3),proper(X4))
0.18/0.24	 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
0.18/0.24	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
0.18/0.24	 proper(isNat(X)) -> isNat(proper(X))
0.18/0.24	 proper(isNatList(X)) -> isNatList(proper(X))
0.18/0.24	 proper(isNatIList(X)) -> isNatIList(proper(X))
0.18/0.24	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.18/0.24	 U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
0.18/0.24	 s(ok(X)) -> ok(s(X))
0.18/0.24	 length(ok(X)) -> ok(length(X))
0.18/0.24	 U21(ok(X)) -> ok(U21(X))
0.18/0.24	 U31(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U31(X1,X2,X3,X4))
0.18/0.24	 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
0.18/0.24	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
0.18/0.24	 isNat(ok(X)) -> ok(isNat(X))
0.18/0.24	 isNatList(ok(X)) -> ok(isNatList(X))
0.18/0.24	 isNatIList(ok(X)) -> ok(isNatIList(X))
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
0.18/0.24	EOF