MAYBE

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

Proof:
 DP Processor:
  DPs:
   active#(zeros()) -> cons#(0(),zeros())
   active#(U11(tt(),V1)) -> isNatIListKind#(V1)
   active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
   active#(U12(tt(),V1)) -> isNatList#(V1)
   active#(U12(tt(),V1)) -> U13#(isNatList(V1))
   active#(U21(tt(),V1)) -> isNatKind#(V1)
   active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
   active#(U22(tt(),V1)) -> isNat#(V1)
   active#(U22(tt(),V1)) -> U23#(isNat(V1))
   active#(U31(tt(),V)) -> isNatIListKind#(V)
   active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
   active#(U32(tt(),V)) -> isNatList#(V)
   active#(U32(tt(),V)) -> U33#(isNatList(V))
   active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
   active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
   active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
   active#(U44(tt(),V1,V2)) -> isNat#(V1)
   active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
   active#(U45(tt(),V2)) -> isNatIList#(V2)
   active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
   active#(U51(tt(),V2)) -> isNatIListKind#(V2)
   active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
   active#(U81(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
   active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
   active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
   active#(U84(tt(),V1,V2)) -> isNat#(V1)
   active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
   active#(U85(tt(),V2)) -> isNatList#(V2)
   active#(U85(tt(),V2)) -> U86#(isNatList(V2))
   active#(U91(tt(),L,N)) -> isNatIListKind#(L)
   active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
   active#(U92(tt(),L,N)) -> isNat#(N)
   active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
   active#(U93(tt(),L,N)) -> isNatKind#(N)
   active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
   active#(U94(tt(),L)) -> length#(L)
   active#(U94(tt(),L)) -> s#(length(L))
   active#(isNat(length(V1))) -> isNatIListKind#(V1)
   active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
   active#(isNat(s(V1))) -> isNatKind#(V1)
   active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
   active#(isNatIList(V)) -> isNatIListKind#(V)
   active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
   active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
   active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
   active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
   active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
   active#(isNatKind(s(V1))) -> isNatKind#(V1)
   active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
   active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
   active#(length(cons(N,L))) -> isNatList#(L)
   active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(U11(X1,X2)) -> active#(X1)
   active#(U11(X1,X2)) -> U11#(active(X1),X2)
   active#(U12(X1,X2)) -> active#(X1)
   active#(U12(X1,X2)) -> U12#(active(X1),X2)
   active#(U13(X)) -> active#(X)
   active#(U13(X)) -> U13#(active(X))
   active#(U21(X1,X2)) -> active#(X1)
   active#(U21(X1,X2)) -> U21#(active(X1),X2)
   active#(U22(X1,X2)) -> active#(X1)
   active#(U22(X1,X2)) -> U22#(active(X1),X2)
   active#(U23(X)) -> active#(X)
   active#(U23(X)) -> U23#(active(X))
   active#(U31(X1,X2)) -> active#(X1)
   active#(U31(X1,X2)) -> U31#(active(X1),X2)
   active#(U32(X1,X2)) -> active#(X1)
   active#(U32(X1,X2)) -> U32#(active(X1),X2)
   active#(U33(X)) -> active#(X)
   active#(U33(X)) -> U33#(active(X))
   active#(U41(X1,X2,X3)) -> active#(X1)
   active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
   active#(U42(X1,X2,X3)) -> active#(X1)
   active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
   active#(U43(X1,X2,X3)) -> active#(X1)
   active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
   active#(U44(X1,X2,X3)) -> active#(X1)
   active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
   active#(U45(X1,X2)) -> active#(X1)
   active#(U45(X1,X2)) -> U45#(active(X1),X2)
   active#(U46(X)) -> active#(X)
   active#(U46(X)) -> U46#(active(X))
   active#(U51(X1,X2)) -> active#(X1)
   active#(U51(X1,X2)) -> U51#(active(X1),X2)
   active#(U52(X)) -> active#(X)
   active#(U52(X)) -> U52#(active(X))
   active#(U61(X)) -> active#(X)
   active#(U61(X)) -> U61#(active(X))
   active#(U71(X)) -> active#(X)
   active#(U71(X)) -> U71#(active(X))
   active#(U81(X1,X2,X3)) -> active#(X1)
   active#(U81(X1,X2,X3)) -> U81#(active(X1),X2,X3)
   active#(U82(X1,X2,X3)) -> active#(X1)
   active#(U82(X1,X2,X3)) -> U82#(active(X1),X2,X3)
   active#(U83(X1,X2,X3)) -> active#(X1)
   active#(U83(X1,X2,X3)) -> U83#(active(X1),X2,X3)
   active#(U84(X1,X2,X3)) -> active#(X1)
   active#(U84(X1,X2,X3)) -> U84#(active(X1),X2,X3)
   active#(U85(X1,X2)) -> active#(X1)
   active#(U85(X1,X2)) -> U85#(active(X1),X2)
   active#(U86(X)) -> active#(X)
   active#(U86(X)) -> U86#(active(X))
   active#(U91(X1,X2,X3)) -> active#(X1)
   active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
   active#(U92(X1,X2,X3)) -> active#(X1)
   active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
   active#(U93(X1,X2,X3)) -> active#(X1)
   active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
   active#(U94(X1,X2)) -> active#(X1)
   active#(U94(X1,X2)) -> U94#(active(X1),X2)
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(length(X)) -> active#(X)
   active#(length(X)) -> length#(active(X))
   cons#(mark(X1),X2) -> cons#(X1,X2)
   U11#(mark(X1),X2) -> U11#(X1,X2)
   U12#(mark(X1),X2) -> U12#(X1,X2)
   U13#(mark(X)) -> U13#(X)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U22#(mark(X1),X2) -> U22#(X1,X2)
   U23#(mark(X)) -> U23#(X)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U32#(mark(X1),X2) -> U32#(X1,X2)
   U33#(mark(X)) -> U33#(X)
   U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
   U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
   U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
   U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
   U45#(mark(X1),X2) -> U45#(X1,X2)
   U46#(mark(X)) -> U46#(X)
   U51#(mark(X1),X2) -> U51#(X1,X2)
   U52#(mark(X)) -> U52#(X)
   U61#(mark(X)) -> U61#(X)
   U71#(mark(X)) -> U71#(X)
   U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
   U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
   U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
   U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
   U85#(mark(X1),X2) -> U85#(X1,X2)
   U86#(mark(X)) -> U86#(X)
   U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
   U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
   U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
   U94#(mark(X1),X2) -> U94#(X1,X2)
   s#(mark(X)) -> s#(X)
   length#(mark(X)) -> length#(X)
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(U11(X1,X2)) -> proper#(X2)
   proper#(U11(X1,X2)) -> proper#(X1)
   proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
   proper#(U12(X1,X2)) -> proper#(X2)
   proper#(U12(X1,X2)) -> proper#(X1)
   proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
   proper#(isNatIListKind(X)) -> proper#(X)
   proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
   proper#(U13(X)) -> proper#(X)
   proper#(U13(X)) -> U13#(proper(X))
   proper#(isNatList(X)) -> proper#(X)
   proper#(isNatList(X)) -> isNatList#(proper(X))
   proper#(U21(X1,X2)) -> proper#(X2)
   proper#(U21(X1,X2)) -> proper#(X1)
   proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
   proper#(U22(X1,X2)) -> proper#(X2)
   proper#(U22(X1,X2)) -> proper#(X1)
   proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
   proper#(isNatKind(X)) -> proper#(X)
   proper#(isNatKind(X)) -> isNatKind#(proper(X))
   proper#(U23(X)) -> proper#(X)
   proper#(U23(X)) -> U23#(proper(X))
   proper#(isNat(X)) -> proper#(X)
   proper#(isNat(X)) -> isNat#(proper(X))
   proper#(U31(X1,X2)) -> proper#(X2)
   proper#(U31(X1,X2)) -> proper#(X1)
   proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
   proper#(U32(X1,X2)) -> proper#(X2)
   proper#(U32(X1,X2)) -> proper#(X1)
   proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
   proper#(U33(X)) -> proper#(X)
   proper#(U33(X)) -> U33#(proper(X))
   proper#(U41(X1,X2,X3)) -> proper#(X3)
   proper#(U41(X1,X2,X3)) -> proper#(X2)
   proper#(U41(X1,X2,X3)) -> proper#(X1)
   proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
   proper#(U42(X1,X2,X3)) -> proper#(X3)
   proper#(U42(X1,X2,X3)) -> proper#(X2)
   proper#(U42(X1,X2,X3)) -> proper#(X1)
   proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
   proper#(U43(X1,X2,X3)) -> proper#(X3)
   proper#(U43(X1,X2,X3)) -> proper#(X2)
   proper#(U43(X1,X2,X3)) -> proper#(X1)
   proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
   proper#(U44(X1,X2,X3)) -> proper#(X3)
   proper#(U44(X1,X2,X3)) -> proper#(X2)
   proper#(U44(X1,X2,X3)) -> proper#(X1)
   proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
   proper#(U45(X1,X2)) -> proper#(X2)
   proper#(U45(X1,X2)) -> proper#(X1)
   proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
   proper#(U46(X)) -> proper#(X)
   proper#(U46(X)) -> U46#(proper(X))
   proper#(isNatIList(X)) -> proper#(X)
   proper#(isNatIList(X)) -> isNatIList#(proper(X))
   proper#(U51(X1,X2)) -> proper#(X2)
   proper#(U51(X1,X2)) -> proper#(X1)
   proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
   proper#(U52(X)) -> proper#(X)
   proper#(U52(X)) -> U52#(proper(X))
   proper#(U61(X)) -> proper#(X)
   proper#(U61(X)) -> U61#(proper(X))
   proper#(U71(X)) -> proper#(X)
   proper#(U71(X)) -> U71#(proper(X))
   proper#(U81(X1,X2,X3)) -> proper#(X3)
   proper#(U81(X1,X2,X3)) -> proper#(X2)
   proper#(U81(X1,X2,X3)) -> proper#(X1)
   proper#(U81(X1,X2,X3)) -> U81#(proper(X1),proper(X2),proper(X3))
   proper#(U82(X1,X2,X3)) -> proper#(X3)
   proper#(U82(X1,X2,X3)) -> proper#(X2)
   proper#(U82(X1,X2,X3)) -> proper#(X1)
   proper#(U82(X1,X2,X3)) -> U82#(proper(X1),proper(X2),proper(X3))
   proper#(U83(X1,X2,X3)) -> proper#(X3)
   proper#(U83(X1,X2,X3)) -> proper#(X2)
   proper#(U83(X1,X2,X3)) -> proper#(X1)
   proper#(U83(X1,X2,X3)) -> U83#(proper(X1),proper(X2),proper(X3))
   proper#(U84(X1,X2,X3)) -> proper#(X3)
   proper#(U84(X1,X2,X3)) -> proper#(X2)
   proper#(U84(X1,X2,X3)) -> proper#(X1)
   proper#(U84(X1,X2,X3)) -> U84#(proper(X1),proper(X2),proper(X3))
   proper#(U85(X1,X2)) -> proper#(X2)
   proper#(U85(X1,X2)) -> proper#(X1)
   proper#(U85(X1,X2)) -> U85#(proper(X1),proper(X2))
   proper#(U86(X)) -> proper#(X)
   proper#(U86(X)) -> U86#(proper(X))
   proper#(U91(X1,X2,X3)) -> proper#(X3)
   proper#(U91(X1,X2,X3)) -> proper#(X2)
   proper#(U91(X1,X2,X3)) -> proper#(X1)
   proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
   proper#(U92(X1,X2,X3)) -> proper#(X3)
   proper#(U92(X1,X2,X3)) -> proper#(X2)
   proper#(U92(X1,X2,X3)) -> proper#(X1)
   proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
   proper#(U93(X1,X2,X3)) -> proper#(X3)
   proper#(U93(X1,X2,X3)) -> proper#(X2)
   proper#(U93(X1,X2,X3)) -> proper#(X1)
   proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
   proper#(U94(X1,X2)) -> proper#(X2)
   proper#(U94(X1,X2)) -> proper#(X1)
   proper#(U94(X1,X2)) -> U94#(proper(X1),proper(X2))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(length(X)) -> proper#(X)
   proper#(length(X)) -> length#(proper(X))
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
   U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
   isNatIListKind#(ok(X)) -> isNatIListKind#(X)
   U13#(ok(X)) -> U13#(X)
   isNatList#(ok(X)) -> isNatList#(X)
   U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
   U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
   isNatKind#(ok(X)) -> isNatKind#(X)
   U23#(ok(X)) -> U23#(X)
   isNat#(ok(X)) -> isNat#(X)
   U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
   U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
   U33#(ok(X)) -> U33#(X)
   U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
   U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
   U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
   U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
   U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
   U46#(ok(X)) -> U46#(X)
   isNatIList#(ok(X)) -> isNatIList#(X)
   U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
   U52#(ok(X)) -> U52#(X)
   U61#(ok(X)) -> U61#(X)
   U71#(ok(X)) -> U71#(X)
   U81#(ok(X1),ok(X2),ok(X3)) -> U81#(X1,X2,X3)
   U82#(ok(X1),ok(X2),ok(X3)) -> U82#(X1,X2,X3)
   U83#(ok(X1),ok(X2),ok(X3)) -> U83#(X1,X2,X3)
   U84#(ok(X1),ok(X2),ok(X3)) -> U84#(X1,X2,X3)
   U85#(ok(X1),ok(X2)) -> U85#(X1,X2)
   U86#(ok(X)) -> U86#(X)
   U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
   U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
   U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
   U94#(ok(X1),ok(X2)) -> U94#(X1,X2)
   s#(ok(X)) -> s#(X)
   length#(ok(X)) -> length#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(zeros()) -> mark(cons(0(),zeros()))
   active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
   active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
   active(U13(tt())) -> mark(tt())
   active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
   active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
   active(U23(tt())) -> mark(tt())
   active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
   active(U32(tt(),V)) -> mark(U33(isNatList(V)))
   active(U33(tt())) -> mark(tt())
   active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
   active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
   active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
   active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
   active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
   active(U46(tt())) -> mark(tt())
   active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
   active(U52(tt())) -> mark(tt())
   active(U61(tt())) -> mark(tt())
   active(U71(tt())) -> mark(tt())
   active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
   active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
   active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
   active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
   active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
   active(U86(tt())) -> mark(tt())
   active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
   active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
   active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
   active(U94(tt(),L)) -> mark(s(length(L)))
   active(isNat(0())) -> mark(tt())
   active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
   active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
   active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
   active(isNatIList(zeros())) -> mark(tt())
   active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
   active(isNatIListKind(nil())) -> mark(tt())
   active(isNatIListKind(zeros())) -> mark(tt())
   active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
   active(isNatKind(0())) -> mark(tt())
   active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
   active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
   active(isNatList(nil())) -> mark(tt())
   active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
   active(length(nil())) -> mark(0())
   active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(U11(X1,X2)) -> U11(active(X1),X2)
   active(U12(X1,X2)) -> U12(active(X1),X2)
   active(U13(X)) -> U13(active(X))
   active(U21(X1,X2)) -> U21(active(X1),X2)
   active(U22(X1,X2)) -> U22(active(X1),X2)
   active(U23(X)) -> U23(active(X))
   active(U31(X1,X2)) -> U31(active(X1),X2)
   active(U32(X1,X2)) -> U32(active(X1),X2)
   active(U33(X)) -> U33(active(X))
   active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
   active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
   active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
   active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
   active(U45(X1,X2)) -> U45(active(X1),X2)
   active(U46(X)) -> U46(active(X))
   active(U51(X1,X2)) -> U51(active(X1),X2)
   active(U52(X)) -> U52(active(X))
   active(U61(X)) -> U61(active(X))
   active(U71(X)) -> U71(active(X))
   active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
   active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
   active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
   active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
   active(U85(X1,X2)) -> U85(active(X1),X2)
   active(U86(X)) -> U86(active(X))
   active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
   active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
   active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
   active(U94(X1,X2)) -> U94(active(X1),X2)
   active(s(X)) -> s(active(X))
   active(length(X)) -> length(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   U11(mark(X1),X2) -> mark(U11(X1,X2))
   U12(mark(X1),X2) -> mark(U12(X1,X2))
   U13(mark(X)) -> mark(U13(X))
   U21(mark(X1),X2) -> mark(U21(X1,X2))
   U22(mark(X1),X2) -> mark(U22(X1,X2))
   U23(mark(X)) -> mark(U23(X))
   U31(mark(X1),X2) -> mark(U31(X1,X2))
   U32(mark(X1),X2) -> mark(U32(X1,X2))
   U33(mark(X)) -> mark(U33(X))
   U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
   U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
   U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
   U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
   U45(mark(X1),X2) -> mark(U45(X1,X2))
   U46(mark(X)) -> mark(U46(X))
   U51(mark(X1),X2) -> mark(U51(X1,X2))
   U52(mark(X)) -> mark(U52(X))
   U61(mark(X)) -> mark(U61(X))
   U71(mark(X)) -> mark(U71(X))
   U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
   U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
   U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
   U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
   U85(mark(X1),X2) -> mark(U85(X1,X2))
   U86(mark(X)) -> mark(U86(X))
   U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
   U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
   U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
   U94(mark(X1),X2) -> mark(U94(X1,X2))
   s(mark(X)) -> mark(s(X))
   length(mark(X)) -> mark(length(X))
   proper(zeros()) -> ok(zeros())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
   proper(tt()) -> ok(tt())
   proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
   proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
   proper(U13(X)) -> U13(proper(X))
   proper(isNatList(X)) -> isNatList(proper(X))
   proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
   proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
   proper(isNatKind(X)) -> isNatKind(proper(X))
   proper(U23(X)) -> U23(proper(X))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
   proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
   proper(U33(X)) -> U33(proper(X))
   proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
   proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
   proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
   proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
   proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
   proper(U46(X)) -> U46(proper(X))
   proper(isNatIList(X)) -> isNatIList(proper(X))
   proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
   proper(U52(X)) -> U52(proper(X))
   proper(U61(X)) -> U61(proper(X))
   proper(U71(X)) -> U71(proper(X))
   proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
   proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
   proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
   proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
   proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
   proper(U86(X)) -> U86(proper(X))
   proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
   proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
   proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
   proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(length(X)) -> length(proper(X))
   proper(nil()) -> ok(nil())
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
   U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
   isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
   U13(ok(X)) -> ok(U13(X))
   isNatList(ok(X)) -> ok(isNatList(X))
   U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
   U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
   isNatKind(ok(X)) -> ok(isNatKind(X))
   U23(ok(X)) -> ok(U23(X))
   isNat(ok(X)) -> ok(isNat(X))
   U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
   U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
   U33(ok(X)) -> ok(U33(X))
   U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
   U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
   U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
   U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
   U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
   U46(ok(X)) -> ok(U46(X))
   isNatIList(ok(X)) -> ok(isNatIList(X))
   U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
   U52(ok(X)) -> ok(U52(X))
   U61(ok(X)) -> ok(U61(X))
   U71(ok(X)) -> ok(U71(X))
   U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
   U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
   U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
   U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
   U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
   U86(ok(X)) -> ok(U86(X))
   U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
   U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
   U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
   U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
   s(ok(X)) -> ok(s(X))
   length(ok(X)) -> ok(length(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(zeros()) -> cons#(0(),zeros())
    active#(U11(tt(),V1)) -> isNatIListKind#(V1)
    active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
    active#(U12(tt(),V1)) -> isNatList#(V1)
    active#(U12(tt(),V1)) -> U13#(isNatList(V1))
    active#(U21(tt(),V1)) -> isNatKind#(V1)
    active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
    active#(U22(tt(),V1)) -> isNat#(V1)
    active#(U22(tt(),V1)) -> U23#(isNat(V1))
    active#(U31(tt(),V)) -> isNatIListKind#(V)
    active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
    active#(U32(tt(),V)) -> isNatList#(V)
    active#(U32(tt(),V)) -> U33#(isNatList(V))
    active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
    active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
    active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
    active#(U44(tt(),V1,V2)) -> isNat#(V1)
    active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
    active#(U45(tt(),V2)) -> isNatIList#(V2)
    active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
    active#(U51(tt(),V2)) -> isNatIListKind#(V2)
    active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
    active#(U81(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
    active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
    active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
    active#(U84(tt(),V1,V2)) -> isNat#(V1)
    active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
    active#(U85(tt(),V2)) -> isNatList#(V2)
    active#(U85(tt(),V2)) -> U86#(isNatList(V2))
    active#(U91(tt(),L,N)) -> isNatIListKind#(L)
    active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
    active#(U92(tt(),L,N)) -> isNat#(N)
    active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
    active#(U93(tt(),L,N)) -> isNatKind#(N)
    active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
    active#(U94(tt(),L)) -> length#(L)
    active#(U94(tt(),L)) -> s#(length(L))
    active#(isNat(length(V1))) -> isNatIListKind#(V1)
    active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
    active#(isNat(s(V1))) -> isNatKind#(V1)
    active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
    active#(isNatIList(V)) -> isNatIListKind#(V)
    active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
    active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
    active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
    active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
    active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
    active#(isNatKind(s(V1))) -> isNatKind#(V1)
    active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
    active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
    active#(length(cons(N,L))) -> isNatList#(L)
    active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(U11(X1,X2)) -> active#(X1)
    active#(U11(X1,X2)) -> U11#(active(X1),X2)
    active#(U12(X1,X2)) -> active#(X1)
    active#(U12(X1,X2)) -> U12#(active(X1),X2)
    active#(U13(X)) -> active#(X)
    active#(U13(X)) -> U13#(active(X))
    active#(U21(X1,X2)) -> active#(X1)
    active#(U21(X1,X2)) -> U21#(active(X1),X2)
    active#(U22(X1,X2)) -> active#(X1)
    active#(U22(X1,X2)) -> U22#(active(X1),X2)
    active#(U23(X)) -> active#(X)
    active#(U23(X)) -> U23#(active(X))
    active#(U31(X1,X2)) -> active#(X1)
    active#(U31(X1,X2)) -> U31#(active(X1),X2)
    active#(U32(X1,X2)) -> active#(X1)
    active#(U32(X1,X2)) -> U32#(active(X1),X2)
    active#(U33(X)) -> active#(X)
    active#(U33(X)) -> U33#(active(X))
    active#(U41(X1,X2,X3)) -> active#(X1)
    active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
    active#(U42(X1,X2,X3)) -> active#(X1)
    active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
    active#(U43(X1,X2,X3)) -> active#(X1)
    active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
    active#(U44(X1,X2,X3)) -> active#(X1)
    active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
    active#(U45(X1,X2)) -> active#(X1)
    active#(U45(X1,X2)) -> U45#(active(X1),X2)
    active#(U46(X)) -> active#(X)
    active#(U46(X)) -> U46#(active(X))
    active#(U51(X1,X2)) -> active#(X1)
    active#(U51(X1,X2)) -> U51#(active(X1),X2)
    active#(U52(X)) -> active#(X)
    active#(U52(X)) -> U52#(active(X))
    active#(U61(X)) -> active#(X)
    active#(U61(X)) -> U61#(active(X))
    active#(U71(X)) -> active#(X)
    active#(U71(X)) -> U71#(active(X))
    active#(U81(X1,X2,X3)) -> active#(X1)
    active#(U81(X1,X2,X3)) -> U81#(active(X1),X2,X3)
    active#(U82(X1,X2,X3)) -> active#(X1)
    active#(U82(X1,X2,X3)) -> U82#(active(X1),X2,X3)
    active#(U83(X1,X2,X3)) -> active#(X1)
    active#(U83(X1,X2,X3)) -> U83#(active(X1),X2,X3)
    active#(U84(X1,X2,X3)) -> active#(X1)
    active#(U84(X1,X2,X3)) -> U84#(active(X1),X2,X3)
    active#(U85(X1,X2)) -> active#(X1)
    active#(U85(X1,X2)) -> U85#(active(X1),X2)
    active#(U86(X)) -> active#(X)
    active#(U86(X)) -> U86#(active(X))
    active#(U91(X1,X2,X3)) -> active#(X1)
    active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
    active#(U92(X1,X2,X3)) -> active#(X1)
    active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
    active#(U93(X1,X2,X3)) -> active#(X1)
    active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
    active#(U94(X1,X2)) -> active#(X1)
    active#(U94(X1,X2)) -> U94#(active(X1),X2)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(length(X)) -> active#(X)
    active#(length(X)) -> length#(active(X))
    cons#(mark(X1),X2) -> cons#(X1,X2)
    U11#(mark(X1),X2) -> U11#(X1,X2)
    U12#(mark(X1),X2) -> U12#(X1,X2)
    U13#(mark(X)) -> U13#(X)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U22#(mark(X1),X2) -> U22#(X1,X2)
    U23#(mark(X)) -> U23#(X)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U32#(mark(X1),X2) -> U32#(X1,X2)
    U33#(mark(X)) -> U33#(X)
    U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
    U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
    U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
    U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
    U45#(mark(X1),X2) -> U45#(X1,X2)
    U46#(mark(X)) -> U46#(X)
    U51#(mark(X1),X2) -> U51#(X1,X2)
    U52#(mark(X)) -> U52#(X)
    U61#(mark(X)) -> U61#(X)
    U71#(mark(X)) -> U71#(X)
    U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
    U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
    U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
    U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
    U85#(mark(X1),X2) -> U85#(X1,X2)
    U86#(mark(X)) -> U86#(X)
    U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
    U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
    U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
    U94#(mark(X1),X2) -> U94#(X1,X2)
    s#(mark(X)) -> s#(X)
    length#(mark(X)) -> length#(X)
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(U11(X1,X2)) -> proper#(X2)
    proper#(U11(X1,X2)) -> proper#(X1)
    proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
    proper#(U12(X1,X2)) -> proper#(X2)
    proper#(U12(X1,X2)) -> proper#(X1)
    proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
    proper#(isNatIListKind(X)) -> proper#(X)
    proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
    proper#(U13(X)) -> proper#(X)
    proper#(U13(X)) -> U13#(proper(X))
    proper#(isNatList(X)) -> proper#(X)
    proper#(isNatList(X)) -> isNatList#(proper(X))
    proper#(U21(X1,X2)) -> proper#(X2)
    proper#(U21(X1,X2)) -> proper#(X1)
    proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
    proper#(U22(X1,X2)) -> proper#(X2)
    proper#(U22(X1,X2)) -> proper#(X1)
    proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
    proper#(isNatKind(X)) -> proper#(X)
    proper#(isNatKind(X)) -> isNatKind#(proper(X))
    proper#(U23(X)) -> proper#(X)
    proper#(U23(X)) -> U23#(proper(X))
    proper#(isNat(X)) -> proper#(X)
    proper#(isNat(X)) -> isNat#(proper(X))
    proper#(U31(X1,X2)) -> proper#(X2)
    proper#(U31(X1,X2)) -> proper#(X1)
    proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
    proper#(U32(X1,X2)) -> proper#(X2)
    proper#(U32(X1,X2)) -> proper#(X1)
    proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
    proper#(U33(X)) -> proper#(X)
    proper#(U33(X)) -> U33#(proper(X))
    proper#(U41(X1,X2,X3)) -> proper#(X3)
    proper#(U41(X1,X2,X3)) -> proper#(X2)
    proper#(U41(X1,X2,X3)) -> proper#(X1)
    proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
    proper#(U42(X1,X2,X3)) -> proper#(X3)
    proper#(U42(X1,X2,X3)) -> proper#(X2)
    proper#(U42(X1,X2,X3)) -> proper#(X1)
    proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
    proper#(U43(X1,X2,X3)) -> proper#(X3)
    proper#(U43(X1,X2,X3)) -> proper#(X2)
    proper#(U43(X1,X2,X3)) -> proper#(X1)
    proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
    proper#(U44(X1,X2,X3)) -> proper#(X3)
    proper#(U44(X1,X2,X3)) -> proper#(X2)
    proper#(U44(X1,X2,X3)) -> proper#(X1)
    proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
    proper#(U45(X1,X2)) -> proper#(X2)
    proper#(U45(X1,X2)) -> proper#(X1)
    proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
    proper#(U46(X)) -> proper#(X)
    proper#(U46(X)) -> U46#(proper(X))
    proper#(isNatIList(X)) -> proper#(X)
    proper#(isNatIList(X)) -> isNatIList#(proper(X))
    proper#(U51(X1,X2)) -> proper#(X2)
    proper#(U51(X1,X2)) -> proper#(X1)
    proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
    proper#(U52(X)) -> proper#(X)
    proper#(U52(X)) -> U52#(proper(X))
    proper#(U61(X)) -> proper#(X)
    proper#(U61(X)) -> U61#(proper(X))
    proper#(U71(X)) -> proper#(X)
    proper#(U71(X)) -> U71#(proper(X))
    proper#(U81(X1,X2,X3)) -> proper#(X3)
    proper#(U81(X1,X2,X3)) -> proper#(X2)
    proper#(U81(X1,X2,X3)) -> proper#(X1)
    proper#(U81(X1,X2,X3)) -> U81#(proper(X1),proper(X2),proper(X3))
    proper#(U82(X1,X2,X3)) -> proper#(X3)
    proper#(U82(X1,X2,X3)) -> proper#(X2)
    proper#(U82(X1,X2,X3)) -> proper#(X1)
    proper#(U82(X1,X2,X3)) -> U82#(proper(X1),proper(X2),proper(X3))
    proper#(U83(X1,X2,X3)) -> proper#(X3)
    proper#(U83(X1,X2,X3)) -> proper#(X2)
    proper#(U83(X1,X2,X3)) -> proper#(X1)
    proper#(U83(X1,X2,X3)) -> U83#(proper(X1),proper(X2),proper(X3))
    proper#(U84(X1,X2,X3)) -> proper#(X3)
    proper#(U84(X1,X2,X3)) -> proper#(X2)
    proper#(U84(X1,X2,X3)) -> proper#(X1)
    proper#(U84(X1,X2,X3)) -> U84#(proper(X1),proper(X2),proper(X3))
    proper#(U85(X1,X2)) -> proper#(X2)
    proper#(U85(X1,X2)) -> proper#(X1)
    proper#(U85(X1,X2)) -> U85#(proper(X1),proper(X2))
    proper#(U86(X)) -> proper#(X)
    proper#(U86(X)) -> U86#(proper(X))
    proper#(U91(X1,X2,X3)) -> proper#(X3)
    proper#(U91(X1,X2,X3)) -> proper#(X2)
    proper#(U91(X1,X2,X3)) -> proper#(X1)
    proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
    proper#(U92(X1,X2,X3)) -> proper#(X3)
    proper#(U92(X1,X2,X3)) -> proper#(X2)
    proper#(U92(X1,X2,X3)) -> proper#(X1)
    proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
    proper#(U93(X1,X2,X3)) -> proper#(X3)
    proper#(U93(X1,X2,X3)) -> proper#(X2)
    proper#(U93(X1,X2,X3)) -> proper#(X1)
    proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
    proper#(U94(X1,X2)) -> proper#(X2)
    proper#(U94(X1,X2)) -> proper#(X1)
    proper#(U94(X1,X2)) -> U94#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(length(X)) -> proper#(X)
    proper#(length(X)) -> length#(proper(X))
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
    U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
    isNatIListKind#(ok(X)) -> isNatIListKind#(X)
    U13#(ok(X)) -> U13#(X)
    isNatList#(ok(X)) -> isNatList#(X)
    U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
    U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
    isNatKind#(ok(X)) -> isNatKind#(X)
    U23#(ok(X)) -> U23#(X)
    isNat#(ok(X)) -> isNat#(X)
    U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
    U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
    U33#(ok(X)) -> U33#(X)
    U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
    U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
    U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
    U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
    U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
    U46#(ok(X)) -> U46#(X)
    isNatIList#(ok(X)) -> isNatIList#(X)
    U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
    U52#(ok(X)) -> U52#(X)
    U61#(ok(X)) -> U61#(X)
    U71#(ok(X)) -> U71#(X)
    U81#(ok(X1),ok(X2),ok(X3)) -> U81#(X1,X2,X3)
    U82#(ok(X1),ok(X2),ok(X3)) -> U82#(X1,X2,X3)
    U83#(ok(X1),ok(X2),ok(X3)) -> U83#(X1,X2,X3)
    U84#(ok(X1),ok(X2),ok(X3)) -> U84#(X1,X2,X3)
    U85#(ok(X1),ok(X2)) -> U85#(X1,X2)
    U86#(ok(X)) -> U86#(X)
    U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
    U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
    U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
    U94#(ok(X1),ok(X2)) -> U94#(X1,X2)
    s#(ok(X)) -> s#(X)
    length#(ok(X)) -> length#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(zeros()) -> mark(cons(0(),zeros()))
    active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
    active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
    active(U13(tt())) -> mark(tt())
    active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
    active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
    active(U23(tt())) -> mark(tt())
    active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
    active(U32(tt(),V)) -> mark(U33(isNatList(V)))
    active(U33(tt())) -> mark(tt())
    active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
    active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
    active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
    active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
    active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
    active(U46(tt())) -> mark(tt())
    active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
    active(U52(tt())) -> mark(tt())
    active(U61(tt())) -> mark(tt())
    active(U71(tt())) -> mark(tt())
    active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
    active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
    active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
    active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
    active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
    active(U86(tt())) -> mark(tt())
    active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
    active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
    active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
    active(U94(tt(),L)) -> mark(s(length(L)))
    active(isNat(0())) -> mark(tt())
    active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
    active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
    active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
    active(isNatIList(zeros())) -> mark(tt())
    active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
    active(isNatIListKind(nil())) -> mark(tt())
    active(isNatIListKind(zeros())) -> mark(tt())
    active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
    active(isNatKind(0())) -> mark(tt())
    active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
    active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
    active(isNatList(nil())) -> mark(tt())
    active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
    active(length(nil())) -> mark(0())
    active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(U11(X1,X2)) -> U11(active(X1),X2)
    active(U12(X1,X2)) -> U12(active(X1),X2)
    active(U13(X)) -> U13(active(X))
    active(U21(X1,X2)) -> U21(active(X1),X2)
    active(U22(X1,X2)) -> U22(active(X1),X2)
    active(U23(X)) -> U23(active(X))
    active(U31(X1,X2)) -> U31(active(X1),X2)
    active(U32(X1,X2)) -> U32(active(X1),X2)
    active(U33(X)) -> U33(active(X))
    active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
    active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
    active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
    active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
    active(U45(X1,X2)) -> U45(active(X1),X2)
    active(U46(X)) -> U46(active(X))
    active(U51(X1,X2)) -> U51(active(X1),X2)
    active(U52(X)) -> U52(active(X))
    active(U61(X)) -> U61(active(X))
    active(U71(X)) -> U71(active(X))
    active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
    active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
    active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
    active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
    active(U85(X1,X2)) -> U85(active(X1),X2)
    active(U86(X)) -> U86(active(X))
    active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
    active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
    active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
    active(U94(X1,X2)) -> U94(active(X1),X2)
    active(s(X)) -> s(active(X))
    active(length(X)) -> length(active(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    U11(mark(X1),X2) -> mark(U11(X1,X2))
    U12(mark(X1),X2) -> mark(U12(X1,X2))
    U13(mark(X)) -> mark(U13(X))
    U21(mark(X1),X2) -> mark(U21(X1,X2))
    U22(mark(X1),X2) -> mark(U22(X1,X2))
    U23(mark(X)) -> mark(U23(X))
    U31(mark(X1),X2) -> mark(U31(X1,X2))
    U32(mark(X1),X2) -> mark(U32(X1,X2))
    U33(mark(X)) -> mark(U33(X))
    U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
    U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
    U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
    U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
    U45(mark(X1),X2) -> mark(U45(X1,X2))
    U46(mark(X)) -> mark(U46(X))
    U51(mark(X1),X2) -> mark(U51(X1,X2))
    U52(mark(X)) -> mark(U52(X))
    U61(mark(X)) -> mark(U61(X))
    U71(mark(X)) -> mark(U71(X))
    U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
    U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
    U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
    U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
    U85(mark(X1),X2) -> mark(U85(X1,X2))
    U86(mark(X)) -> mark(U86(X))
    U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
    U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
    U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
    U94(mark(X1),X2) -> mark(U94(X1,X2))
    s(mark(X)) -> mark(s(X))
    length(mark(X)) -> mark(length(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
    proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
    proper(U13(X)) -> U13(proper(X))
    proper(isNatList(X)) -> isNatList(proper(X))
    proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
    proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
    proper(isNatKind(X)) -> isNatKind(proper(X))
    proper(U23(X)) -> U23(proper(X))
    proper(isNat(X)) -> isNat(proper(X))
    proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
    proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
    proper(U33(X)) -> U33(proper(X))
    proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
    proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
    proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
    proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
    proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
    proper(U46(X)) -> U46(proper(X))
    proper(isNatIList(X)) -> isNatIList(proper(X))
    proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
    proper(U52(X)) -> U52(proper(X))
    proper(U61(X)) -> U61(proper(X))
    proper(U71(X)) -> U71(proper(X))
    proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
    proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
    proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
    proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
    proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
    proper(U86(X)) -> U86(proper(X))
    proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
    proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
    proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
    proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
    proper(s(X)) -> s(proper(X))
    proper(length(X)) -> length(proper(X))
    proper(nil()) -> ok(nil())
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
    U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
    isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
    U13(ok(X)) -> ok(U13(X))
    isNatList(ok(X)) -> ok(isNatList(X))
    U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
    U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
    isNatKind(ok(X)) -> ok(isNatKind(X))
    U23(ok(X)) -> ok(U23(X))
    isNat(ok(X)) -> ok(isNat(X))
    U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
    U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
    U33(ok(X)) -> ok(U33(X))
    U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
    U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
    U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
    U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
    U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
    U46(ok(X)) -> ok(U46(X))
    isNatIList(ok(X)) -> ok(isNatIList(X))
    U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
    U52(ok(X)) -> ok(U52(X))
    U61(ok(X)) -> ok(U61(X))
    U71(ok(X)) -> ok(U71(X))
    U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
    U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
    U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
    U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
    U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
    U86(ok(X)) -> ok(U86(X))
    U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
    U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
    U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
    U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
    s(ok(X)) -> ok(s(X))
    length(ok(X)) -> ok(length(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    ...
   EDG Processor:
    DPs:
     active#(zeros()) -> cons#(0(),zeros())
     active#(U11(tt(),V1)) -> isNatIListKind#(V1)
     active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
     active#(U12(tt(),V1)) -> isNatList#(V1)
     active#(U12(tt(),V1)) -> U13#(isNatList(V1))
     active#(U21(tt(),V1)) -> isNatKind#(V1)
     active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
     active#(U22(tt(),V1)) -> isNat#(V1)
     active#(U22(tt(),V1)) -> U23#(isNat(V1))
     active#(U31(tt(),V)) -> isNatIListKind#(V)
     active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
     active#(U32(tt(),V)) -> isNatList#(V)
     active#(U32(tt(),V)) -> U33#(isNatList(V))
     active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
     active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
     active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
     active#(U44(tt(),V1,V2)) -> isNat#(V1)
     active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
     active#(U45(tt(),V2)) -> isNatIList#(V2)
     active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
     active#(U51(tt(),V2)) -> isNatIListKind#(V2)
     active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
     active#(U81(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
     active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
     active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
     active#(U84(tt(),V1,V2)) -> isNat#(V1)
     active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
     active#(U85(tt(),V2)) -> isNatList#(V2)
     active#(U85(tt(),V2)) -> U86#(isNatList(V2))
     active#(U91(tt(),L,N)) -> isNatIListKind#(L)
     active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
     active#(U92(tt(),L,N)) -> isNat#(N)
     active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
     active#(U93(tt(),L,N)) -> isNatKind#(N)
     active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
     active#(U94(tt(),L)) -> length#(L)
     active#(U94(tt(),L)) -> s#(length(L))
     active#(isNat(length(V1))) -> isNatIListKind#(V1)
     active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
     active#(isNat(s(V1))) -> isNatKind#(V1)
     active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
     active#(isNatIList(V)) -> isNatIListKind#(V)
     active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
     active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
     active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
     active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
     active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
     active#(isNatKind(s(V1))) -> isNatKind#(V1)
     active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
     active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
     active#(length(cons(N,L))) -> isNatList#(L)
     active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(U11(X1,X2)) -> active#(X1)
     active#(U11(X1,X2)) -> U11#(active(X1),X2)
     active#(U12(X1,X2)) -> active#(X1)
     active#(U12(X1,X2)) -> U12#(active(X1),X2)
     active#(U13(X)) -> active#(X)
     active#(U13(X)) -> U13#(active(X))
     active#(U21(X1,X2)) -> active#(X1)
     active#(U21(X1,X2)) -> U21#(active(X1),X2)
     active#(U22(X1,X2)) -> active#(X1)
     active#(U22(X1,X2)) -> U22#(active(X1),X2)
     active#(U23(X)) -> active#(X)
     active#(U23(X)) -> U23#(active(X))
     active#(U31(X1,X2)) -> active#(X1)
     active#(U31(X1,X2)) -> U31#(active(X1),X2)
     active#(U32(X1,X2)) -> active#(X1)
     active#(U32(X1,X2)) -> U32#(active(X1),X2)
     active#(U33(X)) -> active#(X)
     active#(U33(X)) -> U33#(active(X))
     active#(U41(X1,X2,X3)) -> active#(X1)
     active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
     active#(U42(X1,X2,X3)) -> active#(X1)
     active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
     active#(U43(X1,X2,X3)) -> active#(X1)
     active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
     active#(U44(X1,X2,X3)) -> active#(X1)
     active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
     active#(U45(X1,X2)) -> active#(X1)
     active#(U45(X1,X2)) -> U45#(active(X1),X2)
     active#(U46(X)) -> active#(X)
     active#(U46(X)) -> U46#(active(X))
     active#(U51(X1,X2)) -> active#(X1)
     active#(U51(X1,X2)) -> U51#(active(X1),X2)
     active#(U52(X)) -> active#(X)
     active#(U52(X)) -> U52#(active(X))
     active#(U61(X)) -> active#(X)
     active#(U61(X)) -> U61#(active(X))
     active#(U71(X)) -> active#(X)
     active#(U71(X)) -> U71#(active(X))
     active#(U81(X1,X2,X3)) -> active#(X1)
     active#(U81(X1,X2,X3)) -> U81#(active(X1),X2,X3)
     active#(U82(X1,X2,X3)) -> active#(X1)
     active#(U82(X1,X2,X3)) -> U82#(active(X1),X2,X3)
     active#(U83(X1,X2,X3)) -> active#(X1)
     active#(U83(X1,X2,X3)) -> U83#(active(X1),X2,X3)
     active#(U84(X1,X2,X3)) -> active#(X1)
     active#(U84(X1,X2,X3)) -> U84#(active(X1),X2,X3)
     active#(U85(X1,X2)) -> active#(X1)
     active#(U85(X1,X2)) -> U85#(active(X1),X2)
     active#(U86(X)) -> active#(X)
     active#(U86(X)) -> U86#(active(X))
     active#(U91(X1,X2,X3)) -> active#(X1)
     active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
     active#(U92(X1,X2,X3)) -> active#(X1)
     active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
     active#(U93(X1,X2,X3)) -> active#(X1)
     active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
     active#(U94(X1,X2)) -> active#(X1)
     active#(U94(X1,X2)) -> U94#(active(X1),X2)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(length(X)) -> active#(X)
     active#(length(X)) -> length#(active(X))
     cons#(mark(X1),X2) -> cons#(X1,X2)
     U11#(mark(X1),X2) -> U11#(X1,X2)
     U12#(mark(X1),X2) -> U12#(X1,X2)
     U13#(mark(X)) -> U13#(X)
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U22#(mark(X1),X2) -> U22#(X1,X2)
     U23#(mark(X)) -> U23#(X)
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U32#(mark(X1),X2) -> U32#(X1,X2)
     U33#(mark(X)) -> U33#(X)
     U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
     U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
     U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
     U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
     U45#(mark(X1),X2) -> U45#(X1,X2)
     U46#(mark(X)) -> U46#(X)
     U51#(mark(X1),X2) -> U51#(X1,X2)
     U52#(mark(X)) -> U52#(X)
     U61#(mark(X)) -> U61#(X)
     U71#(mark(X)) -> U71#(X)
     U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
     U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
     U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
     U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
     U85#(mark(X1),X2) -> U85#(X1,X2)
     U86#(mark(X)) -> U86#(X)
     U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
     U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
     U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
     U94#(mark(X1),X2) -> U94#(X1,X2)
     s#(mark(X)) -> s#(X)
     length#(mark(X)) -> length#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(U11(X1,X2)) -> proper#(X2)
     proper#(U11(X1,X2)) -> proper#(X1)
     proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
     proper#(U12(X1,X2)) -> proper#(X2)
     proper#(U12(X1,X2)) -> proper#(X1)
     proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
     proper#(isNatIListKind(X)) -> proper#(X)
     proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
     proper#(U13(X)) -> proper#(X)
     proper#(U13(X)) -> U13#(proper(X))
     proper#(isNatList(X)) -> proper#(X)
     proper#(isNatList(X)) -> isNatList#(proper(X))
     proper#(U21(X1,X2)) -> proper#(X2)
     proper#(U21(X1,X2)) -> proper#(X1)
     proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
     proper#(U22(X1,X2)) -> proper#(X2)
     proper#(U22(X1,X2)) -> proper#(X1)
     proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
     proper#(isNatKind(X)) -> proper#(X)
     proper#(isNatKind(X)) -> isNatKind#(proper(X))
     proper#(U23(X)) -> proper#(X)
     proper#(U23(X)) -> U23#(proper(X))
     proper#(isNat(X)) -> proper#(X)
     proper#(isNat(X)) -> isNat#(proper(X))
     proper#(U31(X1,X2)) -> proper#(X2)
     proper#(U31(X1,X2)) -> proper#(X1)
     proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
     proper#(U32(X1,X2)) -> proper#(X2)
     proper#(U32(X1,X2)) -> proper#(X1)
     proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
     proper#(U33(X)) -> proper#(X)
     proper#(U33(X)) -> U33#(proper(X))
     proper#(U41(X1,X2,X3)) -> proper#(X3)
     proper#(U41(X1,X2,X3)) -> proper#(X2)
     proper#(U41(X1,X2,X3)) -> proper#(X1)
     proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
     proper#(U42(X1,X2,X3)) -> proper#(X3)
     proper#(U42(X1,X2,X3)) -> proper#(X2)
     proper#(U42(X1,X2,X3)) -> proper#(X1)
     proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
     proper#(U43(X1,X2,X3)) -> proper#(X3)
     proper#(U43(X1,X2,X3)) -> proper#(X2)
     proper#(U43(X1,X2,X3)) -> proper#(X1)
     proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
     proper#(U44(X1,X2,X3)) -> proper#(X3)
     proper#(U44(X1,X2,X3)) -> proper#(X2)
     proper#(U44(X1,X2,X3)) -> proper#(X1)
     proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
     proper#(U45(X1,X2)) -> proper#(X2)
     proper#(U45(X1,X2)) -> proper#(X1)
     proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
     proper#(U46(X)) -> proper#(X)
     proper#(U46(X)) -> U46#(proper(X))
     proper#(isNatIList(X)) -> proper#(X)
     proper#(isNatIList(X)) -> isNatIList#(proper(X))
     proper#(U51(X1,X2)) -> proper#(X2)
     proper#(U51(X1,X2)) -> proper#(X1)
     proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
     proper#(U52(X)) -> proper#(X)
     proper#(U52(X)) -> U52#(proper(X))
     proper#(U61(X)) -> proper#(X)
     proper#(U61(X)) -> U61#(proper(X))
     proper#(U71(X)) -> proper#(X)
     proper#(U71(X)) -> U71#(proper(X))
     proper#(U81(X1,X2,X3)) -> proper#(X3)
     proper#(U81(X1,X2,X3)) -> proper#(X2)
     proper#(U81(X1,X2,X3)) -> proper#(X1)
     proper#(U81(X1,X2,X3)) -> U81#(proper(X1),proper(X2),proper(X3))
     proper#(U82(X1,X2,X3)) -> proper#(X3)
     proper#(U82(X1,X2,X3)) -> proper#(X2)
     proper#(U82(X1,X2,X3)) -> proper#(X1)
     proper#(U82(X1,X2,X3)) -> U82#(proper(X1),proper(X2),proper(X3))
     proper#(U83(X1,X2,X3)) -> proper#(X3)
     proper#(U83(X1,X2,X3)) -> proper#(X2)
     proper#(U83(X1,X2,X3)) -> proper#(X1)
     proper#(U83(X1,X2,X3)) -> U83#(proper(X1),proper(X2),proper(X3))
     proper#(U84(X1,X2,X3)) -> proper#(X3)
     proper#(U84(X1,X2,X3)) -> proper#(X2)
     proper#(U84(X1,X2,X3)) -> proper#(X1)
     proper#(U84(X1,X2,X3)) -> U84#(proper(X1),proper(X2),proper(X3))
     proper#(U85(X1,X2)) -> proper#(X2)
     proper#(U85(X1,X2)) -> proper#(X1)
     proper#(U85(X1,X2)) -> U85#(proper(X1),proper(X2))
     proper#(U86(X)) -> proper#(X)
     proper#(U86(X)) -> U86#(proper(X))
     proper#(U91(X1,X2,X3)) -> proper#(X3)
     proper#(U91(X1,X2,X3)) -> proper#(X2)
     proper#(U91(X1,X2,X3)) -> proper#(X1)
     proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
     proper#(U92(X1,X2,X3)) -> proper#(X3)
     proper#(U92(X1,X2,X3)) -> proper#(X2)
     proper#(U92(X1,X2,X3)) -> proper#(X1)
     proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
     proper#(U93(X1,X2,X3)) -> proper#(X3)
     proper#(U93(X1,X2,X3)) -> proper#(X2)
     proper#(U93(X1,X2,X3)) -> proper#(X1)
     proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
     proper#(U94(X1,X2)) -> proper#(X2)
     proper#(U94(X1,X2)) -> proper#(X1)
     proper#(U94(X1,X2)) -> U94#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(length(X)) -> proper#(X)
     proper#(length(X)) -> length#(proper(X))
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
     U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
     isNatIListKind#(ok(X)) -> isNatIListKind#(X)
     U13#(ok(X)) -> U13#(X)
     isNatList#(ok(X)) -> isNatList#(X)
     U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
     U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
     isNatKind#(ok(X)) -> isNatKind#(X)
     U23#(ok(X)) -> U23#(X)
     isNat#(ok(X)) -> isNat#(X)
     U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
     U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
     U33#(ok(X)) -> U33#(X)
     U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
     U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
     U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
     U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
     U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
     U46#(ok(X)) -> U46#(X)
     isNatIList#(ok(X)) -> isNatIList#(X)
     U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
     U52#(ok(X)) -> U52#(X)
     U61#(ok(X)) -> U61#(X)
     U71#(ok(X)) -> U71#(X)
     U81#(ok(X1),ok(X2),ok(X3)) -> U81#(X1,X2,X3)
     U82#(ok(X1),ok(X2),ok(X3)) -> U82#(X1,X2,X3)
     U83#(ok(X1),ok(X2),ok(X3)) -> U83#(X1,X2,X3)
     U84#(ok(X1),ok(X2),ok(X3)) -> U84#(X1,X2,X3)
     U85#(ok(X1),ok(X2)) -> U85#(X1,X2)
     U86#(ok(X)) -> U86#(X)
     U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
     U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
     U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
     U94#(ok(X1),ok(X2)) -> U94#(X1,X2)
     s#(ok(X)) -> s#(X)
     length#(ok(X)) -> length#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(zeros()) -> mark(cons(0(),zeros()))
     active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
     active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
     active(U13(tt())) -> mark(tt())
     active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
     active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
     active(U23(tt())) -> mark(tt())
     active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
     active(U32(tt(),V)) -> mark(U33(isNatList(V)))
     active(U33(tt())) -> mark(tt())
     active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
     active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
     active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
     active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
     active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
     active(U46(tt())) -> mark(tt())
     active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
     active(U52(tt())) -> mark(tt())
     active(U61(tt())) -> mark(tt())
     active(U71(tt())) -> mark(tt())
     active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
     active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
     active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
     active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
     active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
     active(U86(tt())) -> mark(tt())
     active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
     active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
     active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
     active(U94(tt(),L)) -> mark(s(length(L)))
     active(isNat(0())) -> mark(tt())
     active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
     active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
     active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
     active(isNatIList(zeros())) -> mark(tt())
     active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
     active(isNatIListKind(nil())) -> mark(tt())
     active(isNatIListKind(zeros())) -> mark(tt())
     active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
     active(isNatKind(0())) -> mark(tt())
     active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
     active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
     active(isNatList(nil())) -> mark(tt())
     active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(U11(X1,X2)) -> U11(active(X1),X2)
     active(U12(X1,X2)) -> U12(active(X1),X2)
     active(U13(X)) -> U13(active(X))
     active(U21(X1,X2)) -> U21(active(X1),X2)
     active(U22(X1,X2)) -> U22(active(X1),X2)
     active(U23(X)) -> U23(active(X))
     active(U31(X1,X2)) -> U31(active(X1),X2)
     active(U32(X1,X2)) -> U32(active(X1),X2)
     active(U33(X)) -> U33(active(X))
     active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
     active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
     active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
     active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
     active(U45(X1,X2)) -> U45(active(X1),X2)
     active(U46(X)) -> U46(active(X))
     active(U51(X1,X2)) -> U51(active(X1),X2)
     active(U52(X)) -> U52(active(X))
     active(U61(X)) -> U61(active(X))
     active(U71(X)) -> U71(active(X))
     active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
     active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
     active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
     active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
     active(U85(X1,X2)) -> U85(active(X1),X2)
     active(U86(X)) -> U86(active(X))
     active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
     active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
     active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
     active(U94(X1,X2)) -> U94(active(X1),X2)
     active(s(X)) -> s(active(X))
     active(length(X)) -> length(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     U11(mark(X1),X2) -> mark(U11(X1,X2))
     U12(mark(X1),X2) -> mark(U12(X1,X2))
     U13(mark(X)) -> mark(U13(X))
     U21(mark(X1),X2) -> mark(U21(X1,X2))
     U22(mark(X1),X2) -> mark(U22(X1,X2))
     U23(mark(X)) -> mark(U23(X))
     U31(mark(X1),X2) -> mark(U31(X1,X2))
     U32(mark(X1),X2) -> mark(U32(X1,X2))
     U33(mark(X)) -> mark(U33(X))
     U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
     U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
     U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
     U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
     U45(mark(X1),X2) -> mark(U45(X1,X2))
     U46(mark(X)) -> mark(U46(X))
     U51(mark(X1),X2) -> mark(U51(X1,X2))
     U52(mark(X)) -> mark(U52(X))
     U61(mark(X)) -> mark(U61(X))
     U71(mark(X)) -> mark(U71(X))
     U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
     U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
     U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
     U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
     U85(mark(X1),X2) -> mark(U85(X1,X2))
     U86(mark(X)) -> mark(U86(X))
     U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
     U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
     U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
     U94(mark(X1),X2) -> mark(U94(X1,X2))
     s(mark(X)) -> mark(s(X))
     length(mark(X)) -> mark(length(X))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
     proper(tt()) -> ok(tt())
     proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
     proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
     proper(U13(X)) -> U13(proper(X))
     proper(isNatList(X)) -> isNatList(proper(X))
     proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
     proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
     proper(isNatKind(X)) -> isNatKind(proper(X))
     proper(U23(X)) -> U23(proper(X))
     proper(isNat(X)) -> isNat(proper(X))
     proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
     proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
     proper(U33(X)) -> U33(proper(X))
     proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
     proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
     proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
     proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
     proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
     proper(U46(X)) -> U46(proper(X))
     proper(isNatIList(X)) -> isNatIList(proper(X))
     proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
     proper(U52(X)) -> U52(proper(X))
     proper(U61(X)) -> U61(proper(X))
     proper(U71(X)) -> U71(proper(X))
     proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
     proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
     proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
     proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
     proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
     proper(U86(X)) -> U86(proper(X))
     proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
     proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
     proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
     proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
     proper(s(X)) -> s(proper(X))
     proper(length(X)) -> length(proper(X))
     proper(nil()) -> ok(nil())
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
     U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
     isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
     U13(ok(X)) -> ok(U13(X))
     isNatList(ok(X)) -> ok(isNatList(X))
     U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
     U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
     isNatKind(ok(X)) -> ok(isNatKind(X))
     U23(ok(X)) -> ok(U23(X))
     isNat(ok(X)) -> ok(isNat(X))
     U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
     U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
     U33(ok(X)) -> ok(U33(X))
     U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
     U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
     U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
     U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
     U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
     U46(ok(X)) -> ok(U46(X))
     isNatIList(ok(X)) -> ok(isNatIList(X))
     U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
     U52(ok(X)) -> ok(U52(X))
     U61(ok(X)) -> ok(U61(X))
     U71(ok(X)) -> ok(U71(X))
     U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
     U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
     U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
     U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
     U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
     U86(ok(X)) -> ok(U86(X))
     U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
     U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
     U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
     U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
     s(ok(X)) -> ok(s(X))
     length(ok(X)) -> ok(length(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    graph:
     ...
    SCC Processor:
     #sccs: 40
     #rules: 173
     #arcs: 12087/93025
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      proper#(length(X)) -> proper#(X)
      proper#(s(X)) -> proper#(X)
      proper#(U94(X1,X2)) -> proper#(X1)
      proper#(U94(X1,X2)) -> proper#(X2)
      proper#(U93(X1,X2,X3)) -> proper#(X1)
      proper#(U93(X1,X2,X3)) -> proper#(X2)
      proper#(U93(X1,X2,X3)) -> proper#(X3)
      proper#(U92(X1,X2,X3)) -> proper#(X1)
      proper#(U92(X1,X2,X3)) -> proper#(X2)
      proper#(U92(X1,X2,X3)) -> proper#(X3)
      proper#(U91(X1,X2,X3)) -> proper#(X1)
      proper#(U91(X1,X2,X3)) -> proper#(X2)
      proper#(U91(X1,X2,X3)) -> proper#(X3)
      proper#(U86(X)) -> proper#(X)
      proper#(U85(X1,X2)) -> proper#(X1)
      proper#(U85(X1,X2)) -> proper#(X2)
      proper#(U84(X1,X2,X3)) -> proper#(X1)
      proper#(U84(X1,X2,X3)) -> proper#(X2)
      proper#(U84(X1,X2,X3)) -> proper#(X3)
      proper#(U83(X1,X2,X3)) -> proper#(X1)
      proper#(U83(X1,X2,X3)) -> proper#(X2)
      proper#(U83(X1,X2,X3)) -> proper#(X3)
      proper#(U82(X1,X2,X3)) -> proper#(X1)
      proper#(U82(X1,X2,X3)) -> proper#(X2)
      proper#(U82(X1,X2,X3)) -> proper#(X3)
      proper#(U81(X1,X2,X3)) -> proper#(X1)
      proper#(U81(X1,X2,X3)) -> proper#(X2)
      proper#(U81(X1,X2,X3)) -> proper#(X3)
      proper#(U71(X)) -> proper#(X)
      proper#(U61(X)) -> proper#(X)
      proper#(U52(X)) -> proper#(X)
      proper#(U51(X1,X2)) -> proper#(X1)
      proper#(U51(X1,X2)) -> proper#(X2)
      proper#(isNatIList(X)) -> proper#(X)
      proper#(U46(X)) -> proper#(X)
      proper#(U45(X1,X2)) -> proper#(X1)
      proper#(U45(X1,X2)) -> proper#(X2)
      proper#(U44(X1,X2,X3)) -> proper#(X1)
      proper#(U44(X1,X2,X3)) -> proper#(X2)
      proper#(U44(X1,X2,X3)) -> proper#(X3)
      proper#(U43(X1,X2,X3)) -> proper#(X1)
      proper#(U43(X1,X2,X3)) -> proper#(X2)
      proper#(U43(X1,X2,X3)) -> proper#(X3)
      proper#(U42(X1,X2,X3)) -> proper#(X1)
      proper#(U42(X1,X2,X3)) -> proper#(X2)
      proper#(U42(X1,X2,X3)) -> proper#(X3)
      proper#(U41(X1,X2,X3)) -> proper#(X1)
      proper#(U41(X1,X2,X3)) -> proper#(X2)
      proper#(U41(X1,X2,X3)) -> proper#(X3)
      proper#(U33(X)) -> proper#(X)
      proper#(U32(X1,X2)) -> proper#(X1)
      proper#(U32(X1,X2)) -> proper#(X2)
      proper#(U31(X1,X2)) -> proper#(X1)
      proper#(U31(X1,X2)) -> proper#(X2)
      proper#(isNat(X)) -> proper#(X)
      proper#(U23(X)) -> proper#(X)
      proper#(isNatKind(X)) -> proper#(X)
      proper#(U22(X1,X2)) -> proper#(X1)
      proper#(U22(X1,X2)) -> proper#(X2)
      proper#(U21(X1,X2)) -> proper#(X1)
      proper#(U21(X1,X2)) -> proper#(X2)
      proper#(isNatList(X)) -> proper#(X)
      proper#(U13(X)) -> proper#(X)
      proper#(isNatIListKind(X)) -> proper#(X)
      proper#(U12(X1,X2)) -> proper#(X1)
      proper#(U12(X1,X2)) -> proper#(X2)
      proper#(U11(X1,X2)) -> proper#(X1)
      proper#(U11(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> proper#(X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      active#(length(X)) -> active#(X)
      active#(s(X)) -> active#(X)
      active#(U94(X1,X2)) -> active#(X1)
      active#(U93(X1,X2,X3)) -> active#(X1)
      active#(U92(X1,X2,X3)) -> active#(X1)
      active#(U91(X1,X2,X3)) -> active#(X1)
      active#(U86(X)) -> active#(X)
      active#(U85(X1,X2)) -> active#(X1)
      active#(U84(X1,X2,X3)) -> active#(X1)
      active#(U83(X1,X2,X3)) -> active#(X1)
      active#(U82(X1,X2,X3)) -> active#(X1)
      active#(U81(X1,X2,X3)) -> active#(X1)
      active#(U71(X)) -> active#(X)
      active#(U61(X)) -> active#(X)
      active#(U52(X)) -> active#(X)
      active#(U51(X1,X2)) -> active#(X1)
      active#(U46(X)) -> active#(X)
      active#(U45(X1,X2)) -> active#(X1)
      active#(U44(X1,X2,X3)) -> active#(X1)
      active#(U43(X1,X2,X3)) -> active#(X1)
      active#(U42(X1,X2,X3)) -> active#(X1)
      active#(U41(X1,X2,X3)) -> active#(X1)
      active#(U33(X)) -> active#(X)
      active#(U32(X1,X2)) -> active#(X1)
      active#(U31(X1,X2)) -> active#(X1)
      active#(U23(X)) -> active#(X)
      active#(U22(X1,X2)) -> active#(X1)
      active#(U21(X1,X2)) -> active#(X1)
      active#(U13(X)) -> active#(X)
      active#(U12(X1,X2)) -> active#(X1)
      active#(U11(X1,X2)) -> active#(X1)
      active#(cons(X1,X2)) -> active#(X1)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      isNatIList#(ok(X)) -> isNatIList#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      isNat#(ok(X)) -> isNat#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      isNatIListKind#(ok(X)) -> isNatIListKind#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      isNatKind#(ok(X)) -> isNatKind#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      isNatList#(ok(X)) -> isNatList#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
      cons#(mark(X1),X2) -> cons#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
      U11#(mark(X1),X2) -> U11#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
      U12#(mark(X1),X2) -> U12#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U13#(ok(X)) -> U13#(X)
      U13#(mark(X)) -> U13#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
      U21#(mark(X1),X2) -> U21#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
      U22#(mark(X1),X2) -> U22#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U23#(ok(X)) -> U23#(X)
      U23#(mark(X)) -> U23#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
      U31#(mark(X1),X2) -> U31#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
      U32#(mark(X1),X2) -> U32#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U33#(ok(X)) -> U33#(X)
      U33#(mark(X)) -> U33#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
      U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
      U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
      U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
      U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
      U45#(mark(X1),X2) -> U45#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U46#(ok(X)) -> U46#(X)
      U46#(mark(X)) -> U46#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
      U51#(mark(X1),X2) -> U51#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U52#(ok(X)) -> U52#(X)
      U52#(mark(X)) -> U52#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U61#(ok(X)) -> U61#(X)
      U61#(mark(X)) -> U61#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U71#(ok(X)) -> U71#(X)
      U71#(mark(X)) -> U71#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U81#(ok(X1),ok(X2),ok(X3)) -> U81#(X1,X2,X3)
      U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U82#(ok(X1),ok(X2),ok(X3)) -> U82#(X1,X2,X3)
      U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U83#(ok(X1),ok(X2),ok(X3)) -> U83#(X1,X2,X3)
      U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U84#(ok(X1),ok(X2),ok(X3)) -> U84#(X1,X2,X3)
      U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U85#(ok(X1),ok(X2)) -> U85#(X1,X2)
      U85#(mark(X1),X2) -> U85#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U86#(ok(X)) -> U86#(X)
      U86#(mark(X)) -> U86#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
      U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
      U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
      U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      U94#(ok(X1),ok(X2)) -> U94#(X1,X2)
      U94#(mark(X1),X2) -> U94#(X1,X2)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      s#(ok(X)) -> s#(X)
      s#(mark(X)) -> s#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open
     
     DPs:
      length#(ok(X)) -> length#(X)
      length#(mark(X)) -> length#(X)
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U13(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V))
      active(U32(tt(),V)) -> mark(U33(isNatList(V)))
      active(U33(tt())) -> mark(tt())
      active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
      active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
      active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
      active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2))
      active(U45(tt(),V2)) -> mark(U46(isNatIList(V2)))
      active(U46(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
      active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
      active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
      active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2))
      active(U85(tt(),V2)) -> mark(U86(isNatList(V2)))
      active(U86(tt())) -> mark(tt())
      active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N))
      active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N))
      active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L))
      active(U94(tt(),L)) -> mark(s(length(L)))
      active(isNat(0())) -> mark(tt())
      active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
      active(isNatIList(zeros())) -> mark(tt())
      active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2))
      active(isNatIListKind(nil())) -> mark(tt())
      active(isNatIListKind(zeros())) -> mark(tt())
      active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U13(X)) -> U13(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X)) -> U61(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
      active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
      active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
      active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
      active(U85(X1,X2)) -> U85(active(X1),X2)
      active(U86(X)) -> U86(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2)) -> U94(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U13(mark(X)) -> mark(U13(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X)) -> mark(U61(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
      U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
      U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
      U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
      U85(mark(X1),X2) -> mark(U85(X1,X2))
      U86(mark(X)) -> mark(U86(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2) -> mark(U94(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U23(X)) -> U23(proper(X))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X)) -> U61(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
      proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
      proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
      proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
      proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
      proper(U86(X)) -> U86(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2)) -> U94(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(nil()) -> ok(nil())
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U23(ok(X)) -> ok(U23(X))
      isNat(ok(X)) -> ok(isNat(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X)) -> ok(U61(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
      U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
      U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
      U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
      U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
      U86(ok(X)) -> ok(U86(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2)) -> ok(U94(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Open