MAYBE
0.18/0.22	MAYBE
0.18/0.22	
0.18/0.22	Problem:
0.18/0.22	 zeros() -> cons(0(),n__zeros())
0.18/0.22	 U11(tt(),V1) -> U12(isNatList(activate(V1)))
0.18/0.22	 U12(tt()) -> tt()
0.18/0.22	 U21(tt(),V1) -> U22(isNat(activate(V1)))
0.18/0.22	 U22(tt()) -> tt()
0.18/0.22	 U31(tt(),V) -> U32(isNatList(activate(V)))
0.18/0.22	 U32(tt()) -> tt()
0.18/0.22	 U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
0.18/0.22	 U42(tt(),V2) -> U43(isNatIList(activate(V2)))
0.18/0.22	 U43(tt()) -> tt()
0.18/0.22	 U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
0.18/0.22	 U52(tt(),V2) -> U53(isNatList(activate(V2)))
0.18/0.22	 U53(tt()) -> tt()
0.18/0.22	 U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
0.18/0.22	 U62(tt(),V2) -> U63(isNatIList(activate(V2)))
0.18/0.22	 U63(tt()) -> tt()
0.18/0.22	 U71(tt(),L) -> s(length(activate(L)))
0.18/0.22	 U81(tt()) -> nil()
0.18/0.22	 U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
0.18/0.22	 and(tt(),X) -> activate(X)
0.18/0.22	 isNat(n__0()) -> tt()
0.18/0.22	 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
0.18/0.22	 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
0.18/0.22	 isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
0.18/0.22	 isNatIList(n__zeros()) -> tt()
0.18/0.22	 isNatIList(n__cons(V1,V2)) ->
0.18/0.22	 U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
0.18/0.22	 isNatIListKind(n__nil()) -> tt()
0.18/0.22	 isNatIListKind(n__zeros()) -> tt()
0.18/0.22	 isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
0.18/0.22	 isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
0.18/0.22	 isNatKind(n__0()) -> tt()
0.18/0.22	 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
0.18/0.22	 isNatKind(n__s(V1)) -> isNatKind(activate(V1))
0.18/0.22	 isNatList(n__nil()) -> tt()
0.18/0.22	 isNatList(n__cons(V1,V2)) ->
0.18/0.22	 U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
0.18/0.22	 isNatList(n__take(V1,V2)) ->
0.18/0.22	 U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
0.18/0.22	 length(nil()) -> 0()
0.18/0.22	 length(cons(N,L)) ->
0.18/0.22	 U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and
0.18/0.22	                                                                    (
0.18/0.22	                                                                    isNat(N),n__isNatKind(N))),
0.18/0.22	     activate(L))
0.18/0.22	 take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
0.18/0.22	 take(s(M),cons(N,IL)) ->
0.18/0.22	 U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),
0.18/0.22	         n__and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N)))),
0.18/0.22	     activate(IL),M,N)
0.18/0.22	 zeros() -> n__zeros()
0.18/0.22	 take(X1,X2) -> n__take(X1,X2)
0.18/0.22	 0() -> n__0()
0.18/0.22	 length(X) -> n__length(X)
0.18/0.22	 s(X) -> n__s(X)
0.18/0.22	 cons(X1,X2) -> n__cons(X1,X2)
0.18/0.22	 isNatIListKind(X) -> n__isNatIListKind(X)
0.18/0.22	 nil() -> n__nil()
0.18/0.22	 and(X1,X2) -> n__and(X1,X2)
0.18/0.22	 isNatKind(X) -> n__isNatKind(X)
0.18/0.22	 activate(n__zeros()) -> zeros()
0.18/0.22	 activate(n__take(X1,X2)) -> take(X1,X2)
0.18/0.22	 activate(n__0()) -> 0()
0.18/0.22	 activate(n__length(X)) -> length(X)
0.18/0.22	 activate(n__s(X)) -> s(X)
0.18/0.22	 activate(n__cons(X1,X2)) -> cons(X1,X2)
0.18/0.22	 activate(n__isNatIListKind(X)) -> isNatIListKind(X)
0.18/0.22	 activate(n__nil()) -> nil()
0.18/0.22	 activate(n__and(X1,X2)) -> and(X1,X2)
0.18/0.22	 activate(n__isNatKind(X)) -> isNatKind(X)
0.18/0.22	 activate(X) -> X
0.18/0.22	
0.18/0.22	Proof:
0.18/0.22	 Open
0.18/0.22	EOF