MAYBE

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

Proof:
 Open