MAYBE
0.18/0.20	MAYBE
0.18/0.20	
0.18/0.20	Problem:
0.18/0.20	 a__and(tt(),T) -> mark(T)
0.18/0.20	 a__isNatIList(IL) -> a__isNatList(IL)
0.18/0.20	 a__isNat(0()) -> tt()
0.18/0.20	 a__isNat(s(N)) -> a__isNat(N)
0.18/0.20	 a__isNat(length(L)) -> a__isNatList(L)
0.18/0.20	 a__isNatIList(zeros()) -> tt()
0.18/0.20	 a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
0.18/0.20	 a__isNatList(nil()) -> tt()
0.18/0.20	 a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
0.18/0.20	 a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
0.18/0.20	 a__zeros() -> cons(0(),zeros())
0.18/0.20	 a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
0.18/0.20	 a__uTake1(tt()) -> nil()
0.18/0.20	 a__take(s(M),cons(N,IL)) ->
0.18/0.20	 a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
0.18/0.20	 a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
0.18/0.20	 a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
0.18/0.20	 a__uLength(tt(),L) -> s(a__length(mark(L)))
0.18/0.20	 mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
0.18/0.20	 mark(isNatIList(X)) -> a__isNatIList(X)
0.18/0.20	 mark(isNatList(X)) -> a__isNatList(X)
0.18/0.20	 mark(isNat(X)) -> a__isNat(X)
0.18/0.20	 mark(length(X)) -> a__length(mark(X))
0.18/0.20	 mark(zeros()) -> a__zeros()
0.18/0.20	 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
0.18/0.20	 mark(uTake1(X)) -> a__uTake1(mark(X))
0.18/0.20	 mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
0.18/0.20	 mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
0.18/0.20	 mark(tt()) -> tt()
0.18/0.20	 mark(0()) -> 0()
0.18/0.20	 mark(s(X)) -> s(mark(X))
0.18/0.20	 mark(cons(X1,X2)) -> cons(mark(X1),X2)
0.18/0.20	 mark(nil()) -> nil()
0.18/0.20	 a__and(X1,X2) -> and(X1,X2)
0.18/0.20	 a__isNatIList(X) -> isNatIList(X)
0.18/0.20	 a__isNatList(X) -> isNatList(X)
0.18/0.20	 a__isNat(X) -> isNat(X)
0.18/0.20	 a__length(X) -> length(X)
0.18/0.20	 a__zeros() -> zeros()
0.18/0.20	 a__take(X1,X2) -> take(X1,X2)
0.18/0.20	 a__uTake1(X) -> uTake1(X)
0.18/0.20	 a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
0.18/0.20	 a__uLength(X1,X2) -> uLength(X1,X2)
0.18/0.20	
0.18/0.20	Proof:
0.18/0.20	 Open
0.18/0.21	EOF