MAYBE
0.28/0.36	MAYBE
0.28/0.36	
0.28/0.36	Problem:
0.28/0.36	 active(zeros()) -> mark(cons(0(),zeros()))
0.28/0.36	 active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
0.28/0.36	 active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
0.28/0.36	 active(U13(tt())) -> mark(tt())
0.28/0.36	 active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
0.28/0.36	 active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
0.28/0.36	 active(U23(tt())) -> mark(tt())
0.28/0.36	 active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
0.28/0.36	 active(U32(tt(),V)) -> mark(U33(isNatList(V)))
0.28/0.36	 active(U33(tt())) -> mark(tt())
0.28/0.36	 active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
0.28/0.36	 active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
0.28/0.36	 active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
0.28/0.36	 active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
0.28/0.36	 active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
0.28/0.36	 active(U46(tt())) -> mark(tt())
0.28/0.36	 active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
0.28/0.36	 active(U52(tt())) -> mark(tt())
0.28/0.36	 active(U61(tt())) -> mark(tt())
0.28/0.36	 active(U71(tt())) -> mark(tt())
0.28/0.36	 active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
0.28/0.36	 active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
0.28/0.36	 active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
0.28/0.36	 active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
0.28/0.36	 active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
0.28/0.36	 active(U86(tt())) -> mark(tt())
0.28/0.36	 active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
0.28/0.36	 active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
0.28/0.36	 active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
0.28/0.36	 active(U94(tt(),L)) -> mark(s(length(L)))
0.28/0.36	 active(isNat(0())) -> mark(tt())
0.28/0.36	 active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
0.28/0.36	 active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
0.28/0.36	 active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
0.28/0.36	 active(isNatIList(zeros())) -> mark(tt())
0.28/0.36	 active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
0.28/0.36	 active(isNatIListKind(nil())) -> mark(tt())
0.28/0.36	 active(isNatIListKind(zeros())) -> mark(tt())
0.28/0.36	 active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
0.28/0.36	 active(isNatKind(0())) -> mark(tt())
0.28/0.36	 active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
0.28/0.36	 active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
0.28/0.36	 active(isNatList(nil())) -> mark(tt())
0.28/0.36	 active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
0.28/0.36	 active(length(nil())) -> mark(0())
0.28/0.36	 active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
0.28/0.36	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.28/0.36	 active(U11(X1,X2)) -> U11(active(X1),X2)
0.28/0.36	 active(U12(X1,X2)) -> U12(active(X1),X2)
0.28/0.36	 active(U13(X)) -> U13(active(X))
0.28/0.36	 active(U21(X1,X2)) -> U21(active(X1),X2)
0.28/0.36	 active(U22(X1,X2)) -> U22(active(X1),X2)
0.28/0.36	 active(U23(X)) -> U23(active(X))
0.28/0.36	 active(U31(X1,X2)) -> U31(active(X1),X2)
0.28/0.36	 active(U32(X1,X2)) -> U32(active(X1),X2)
0.28/0.36	 active(U33(X)) -> U33(active(X))
0.28/0.36	 active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
0.28/0.36	 active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
0.28/0.36	 active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
0.28/0.36	 active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
0.28/0.36	 active(U45(X1,X2)) -> U45(active(X1),X2)
0.28/0.36	 active(U46(X)) -> U46(active(X))
0.28/0.36	 active(U51(X1,X2)) -> U51(active(X1),X2)
0.28/0.36	 active(U52(X)) -> U52(active(X))
0.28/0.36	 active(U61(X)) -> U61(active(X))
0.28/0.36	 active(U71(X)) -> U71(active(X))
0.28/0.36	 active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
0.28/0.36	 active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
0.28/0.36	 active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
0.28/0.36	 active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
0.28/0.36	 active(U85(X1,X2)) -> U85(active(X1),X2)
0.28/0.36	 active(U86(X)) -> U86(active(X))
0.28/0.36	 active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
0.28/0.36	 active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
0.28/0.36	 active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
0.28/0.36	 active(U94(X1,X2)) -> U94(active(X1),X2)
0.28/0.36	 active(s(X)) -> s(active(X))
0.28/0.36	 active(length(X)) -> length(active(X))
0.28/0.36	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.28/0.36	 U11(mark(X1),X2) -> mark(U11(X1,X2))
0.28/0.36	 U12(mark(X1),X2) -> mark(U12(X1,X2))
0.28/0.36	 U13(mark(X)) -> mark(U13(X))
0.28/0.36	 U21(mark(X1),X2) -> mark(U21(X1,X2))
0.28/0.36	 U22(mark(X1),X2) -> mark(U22(X1,X2))
0.28/0.36	 U23(mark(X)) -> mark(U23(X))
0.28/0.36	 U31(mark(X1),X2) -> mark(U31(X1,X2))
0.28/0.36	 U32(mark(X1),X2) -> mark(U32(X1,X2))
0.28/0.36	 U33(mark(X)) -> mark(U33(X))
0.28/0.36	 U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
0.28/0.36	 U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
0.28/0.36	 U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
0.28/0.37	 U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
0.28/0.37	 U45(mark(X1),X2) -> mark(U45(X1,X2))
0.28/0.37	 U46(mark(X)) -> mark(U46(X))
0.28/0.37	 U51(mark(X1),X2) -> mark(U51(X1,X2))
0.28/0.37	 U52(mark(X)) -> mark(U52(X))
0.28/0.37	 U61(mark(X)) -> mark(U61(X))
0.28/0.37	 U71(mark(X)) -> mark(U71(X))
0.28/0.37	 U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
0.28/0.37	 U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
0.28/0.37	 U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
0.28/0.37	 U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
0.28/0.37	 U85(mark(X1),X2) -> mark(U85(X1,X2))
0.28/0.37	 U86(mark(X)) -> mark(U86(X))
0.28/0.37	 U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
0.28/0.37	 U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
0.28/0.37	 U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
0.28/0.37	 U94(mark(X1),X2) -> mark(U94(X1,X2))
0.28/0.37	 s(mark(X)) -> mark(s(X))
0.28/0.37	 length(mark(X)) -> mark(length(X))
0.28/0.37	 proper(zeros()) -> ok(zeros())
0.28/0.37	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.28/0.37	 proper(0()) -> ok(0())
0.28/0.37	 proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
0.28/0.37	 proper(tt()) -> ok(tt())
0.28/0.37	 proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
0.28/0.37	 proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
0.28/0.37	 proper(U13(X)) -> U13(proper(X))
0.28/0.37	 proper(isNatList(X)) -> isNatList(proper(X))
0.28/0.37	 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
0.28/0.37	 proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
0.28/0.37	 proper(isNatKind(X)) -> isNatKind(proper(X))
0.28/0.37	 proper(U23(X)) -> U23(proper(X))
0.28/0.37	 proper(isNat(X)) -> isNat(proper(X))
0.28/0.37	 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
0.28/0.37	 proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
0.28/0.37	 proper(U33(X)) -> U33(proper(X))
0.28/0.37	 proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
0.28/0.37	 proper(U46(X)) -> U46(proper(X))
0.28/0.37	 proper(isNatIList(X)) -> isNatIList(proper(X))
0.28/0.37	 proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
0.28/0.37	 proper(U52(X)) -> U52(proper(X))
0.28/0.37	 proper(U61(X)) -> U61(proper(X))
0.28/0.37	 proper(U71(X)) -> U71(proper(X))
0.28/0.37	 proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
0.28/0.37	 proper(U86(X)) -> U86(proper(X))
0.28/0.37	 proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
0.28/0.37	 proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
0.28/0.37	 proper(s(X)) -> s(proper(X))
0.28/0.37	 proper(length(X)) -> length(proper(X))
0.28/0.37	 proper(nil()) -> ok(nil())
0.28/0.37	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.28/0.37	 U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
0.28/0.37	 U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
0.28/0.37	 isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
0.28/0.37	 U13(ok(X)) -> ok(U13(X))
0.28/0.37	 isNatList(ok(X)) -> ok(isNatList(X))
0.28/0.37	 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
0.28/0.37	 U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
0.28/0.37	 isNatKind(ok(X)) -> ok(isNatKind(X))
0.28/0.37	 U23(ok(X)) -> ok(U23(X))
0.28/0.37	 isNat(ok(X)) -> ok(isNat(X))
0.28/0.37	 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
0.28/0.37	 U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
0.28/0.37	 U33(ok(X)) -> ok(U33(X))
0.28/0.37	 U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
0.28/0.37	 U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
0.28/0.37	 U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
0.28/0.37	 U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
0.28/0.37	 U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
0.28/0.37	 U46(ok(X)) -> ok(U46(X))
0.28/0.37	 isNatIList(ok(X)) -> ok(isNatIList(X))
0.28/0.37	 U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
0.28/0.37	 U52(ok(X)) -> ok(U52(X))
0.28/0.37	 U61(ok(X)) -> ok(U61(X))
0.28/0.37	 U71(ok(X)) -> ok(U71(X))
0.28/0.37	 U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
0.28/0.37	 U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
0.28/0.37	 U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
0.28/0.37	 U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
0.28/0.37	 U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
0.28/0.37	 U86(ok(X)) -> ok(U86(X))
0.28/0.37	 U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
0.28/0.37	 U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
0.28/0.37	 U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
0.28/0.37	 U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
0.28/0.37	 s(ok(X)) -> ok(s(X))
0.28/0.37	 length(ok(X)) -> ok(length(X))
0.28/0.37	 top(mark(X)) -> top(proper(X))
0.28/0.37	 top(ok(X)) -> top(active(X))
0.28/0.37	
0.28/0.37	Proof:
0.28/0.37	 Open
0.28/0.37	EOF