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

Proof:
 DP Processor:
  DPs:
   active#(zeros()) -> cons#(0(),zeros())
   active#(zeros()) -> mark#(cons(0(),zeros()))
   active#(U11(tt(),V1)) -> isNatIListKind#(V1)
   active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
   active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1))
   active#(U12(tt(),V1)) -> isNatList#(V1)
   active#(U12(tt(),V1)) -> U13#(isNatList(V1))
   active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1)))
   active#(U13(tt())) -> mark#(tt())
   active#(U21(tt(),V1)) -> isNatKind#(V1)
   active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
   active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1))
   active#(U22(tt(),V1)) -> isNat#(V1)
   active#(U22(tt(),V1)) -> U23#(isNat(V1))
   active#(U22(tt(),V1)) -> mark#(U23(isNat(V1)))
   active#(U23(tt())) -> mark#(tt())
   active#(U31(tt(),V)) -> isNatIListKind#(V)
   active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
   active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V))
   active#(U32(tt(),V)) -> isNatList#(V)
   active#(U32(tt(),V)) -> U33#(isNatList(V))
   active#(U32(tt(),V)) -> mark#(U33(isNatList(V)))
   active#(U33(tt())) -> mark#(tt())
   active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
   active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2))
   active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
   active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2))
   active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
   active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2))
   active#(U44(tt(),V1,V2)) -> isNat#(V1)
   active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
   active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2))
   active#(U45(tt(),V2)) -> isNatIList#(V2)
   active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
   active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2)))
   active#(U46(tt())) -> mark#(tt())
   active#(U51(tt(),V2)) -> isNatIListKind#(V2)
   active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
   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)) -> isNatKind#(V1)
   active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
   active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2))
   active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
   active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2))
   active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
   active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2))
   active#(U84(tt(),V1,V2)) -> isNat#(V1)
   active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
   active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2))
   active#(U85(tt(),V2)) -> isNatList#(V2)
   active#(U85(tt(),V2)) -> U86#(isNatList(V2))
   active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2)))
   active#(U86(tt())) -> mark#(tt())
   active#(U91(tt(),L,N)) -> isNatIListKind#(L)
   active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
   active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N))
   active#(U92(tt(),L,N)) -> isNat#(N)
   active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
   active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N))
   active#(U93(tt(),L,N)) -> isNatKind#(N)
   active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
   active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L))
   active#(U94(tt(),L)) -> length#(L)
   active#(U94(tt(),L)) -> s#(length(L))
   active#(U94(tt(),L)) -> mark#(s(length(L)))
   active#(isNat(0())) -> mark#(tt())
   active#(isNat(length(V1))) -> isNatIListKind#(V1)
   active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
   active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1))
   active#(isNat(s(V1))) -> isNatKind#(V1)
   active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
   active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1))
   active#(isNatIList(V)) -> isNatIListKind#(V)
   active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
   active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V))
   active#(isNatIList(zeros())) -> mark#(tt())
   active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
   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))) -> isNatKind#(V1)
   active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
   active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2))
   active#(isNatKind(0())) -> mark#(tt())
   active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
   active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
   active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1)))
   active#(isNatKind(s(V1))) -> isNatKind#(V1)
   active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
   active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1)))
   active#(isNatList(nil())) -> mark#(tt())
   active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
   active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2))
   active#(length(nil())) -> mark#(0())
   active#(length(cons(N,L))) -> isNatList#(L)
   active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
   active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N))
   mark#(zeros()) -> active#(zeros())
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
   mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
   mark#(0()) -> active#(0())
   mark#(U11(X1,X2)) -> mark#(X1)
   mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
   mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
   mark#(tt()) -> active#(tt())
   mark#(U12(X1,X2)) -> mark#(X1)
   mark#(U12(X1,X2)) -> U12#(mark(X1),X2)
   mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
   mark#(isNatIListKind(X)) -> active#(isNatIListKind(X))
   mark#(U13(X)) -> mark#(X)
   mark#(U13(X)) -> U13#(mark(X))
   mark#(U13(X)) -> active#(U13(mark(X)))
   mark#(isNatList(X)) -> active#(isNatList(X))
   mark#(U21(X1,X2)) -> mark#(X1)
   mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
   mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
   mark#(U22(X1,X2)) -> mark#(X1)
   mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
   mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
   mark#(isNatKind(X)) -> active#(isNatKind(X))
   mark#(U23(X)) -> mark#(X)
   mark#(U23(X)) -> U23#(mark(X))
   mark#(U23(X)) -> active#(U23(mark(X)))
   mark#(isNat(X)) -> active#(isNat(X))
   mark#(U31(X1,X2)) -> mark#(X1)
   mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
   mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
   mark#(U32(X1,X2)) -> mark#(X1)
   mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
   mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
   mark#(U33(X)) -> mark#(X)
   mark#(U33(X)) -> U33#(mark(X))
   mark#(U33(X)) -> active#(U33(mark(X)))
   mark#(U41(X1,X2,X3)) -> mark#(X1)
   mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
   mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
   mark#(U42(X1,X2,X3)) -> mark#(X1)
   mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3)
   mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
   mark#(U43(X1,X2,X3)) -> mark#(X1)
   mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3)
   mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
   mark#(U44(X1,X2,X3)) -> mark#(X1)
   mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3)
   mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
   mark#(U45(X1,X2)) -> mark#(X1)
   mark#(U45(X1,X2)) -> U45#(mark(X1),X2)
   mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
   mark#(U46(X)) -> mark#(X)
   mark#(U46(X)) -> U46#(mark(X))
   mark#(U46(X)) -> active#(U46(mark(X)))
   mark#(isNatIList(X)) -> active#(isNatIList(X))
   mark#(U51(X1,X2)) -> mark#(X1)
   mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
   mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
   mark#(U52(X)) -> mark#(X)
   mark#(U52(X)) -> U52#(mark(X))
   mark#(U52(X)) -> active#(U52(mark(X)))
   mark#(U61(X)) -> mark#(X)
   mark#(U61(X)) -> U61#(mark(X))
   mark#(U61(X)) -> active#(U61(mark(X)))
   mark#(U71(X)) -> mark#(X)
   mark#(U71(X)) -> U71#(mark(X))
   mark#(U71(X)) -> active#(U71(mark(X)))
   mark#(U81(X1,X2,X3)) -> mark#(X1)
   mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3)
   mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3))
   mark#(U82(X1,X2,X3)) -> mark#(X1)
   mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3)
   mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3))
   mark#(U83(X1,X2,X3)) -> mark#(X1)
   mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3)
   mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3))
   mark#(U84(X1,X2,X3)) -> mark#(X1)
   mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3)
   mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3))
   mark#(U85(X1,X2)) -> mark#(X1)
   mark#(U85(X1,X2)) -> U85#(mark(X1),X2)
   mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2))
   mark#(U86(X)) -> mark#(X)
   mark#(U86(X)) -> U86#(mark(X))
   mark#(U86(X)) -> active#(U86(mark(X)))
   mark#(U91(X1,X2,X3)) -> mark#(X1)
   mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3)
   mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3))
   mark#(U92(X1,X2,X3)) -> mark#(X1)
   mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3)
   mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3))
   mark#(U93(X1,X2,X3)) -> mark#(X1)
   mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3)
   mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3))
   mark#(U94(X1,X2)) -> mark#(X1)
   mark#(U94(X1,X2)) -> U94#(mark(X1),X2)
   mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2))
   mark#(s(X)) -> mark#(X)
   mark#(s(X)) -> s#(mark(X))
   mark#(s(X)) -> active#(s(mark(X)))
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> length#(mark(X))
   mark#(length(X)) -> active#(length(mark(X)))
   mark#(nil()) -> active#(nil())
   cons#(mark(X1),X2) -> cons#(X1,X2)
   cons#(X1,mark(X2)) -> cons#(X1,X2)
   cons#(active(X1),X2) -> cons#(X1,X2)
   cons#(X1,active(X2)) -> cons#(X1,X2)
   U11#(mark(X1),X2) -> U11#(X1,X2)
   U11#(X1,mark(X2)) -> U11#(X1,X2)
   U11#(active(X1),X2) -> U11#(X1,X2)
   U11#(X1,active(X2)) -> U11#(X1,X2)
   U12#(mark(X1),X2) -> U12#(X1,X2)
   U12#(X1,mark(X2)) -> U12#(X1,X2)
   U12#(active(X1),X2) -> U12#(X1,X2)
   U12#(X1,active(X2)) -> U12#(X1,X2)
   isNatIListKind#(mark(X)) -> isNatIListKind#(X)
   isNatIListKind#(active(X)) -> isNatIListKind#(X)
   U13#(mark(X)) -> U13#(X)
   U13#(active(X)) -> U13#(X)
   isNatList#(mark(X)) -> isNatList#(X)
   isNatList#(active(X)) -> isNatList#(X)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U21#(X1,mark(X2)) -> U21#(X1,X2)
   U21#(active(X1),X2) -> U21#(X1,X2)
   U21#(X1,active(X2)) -> U21#(X1,X2)
   U22#(mark(X1),X2) -> U22#(X1,X2)
   U22#(X1,mark(X2)) -> U22#(X1,X2)
   U22#(active(X1),X2) -> U22#(X1,X2)
   U22#(X1,active(X2)) -> U22#(X1,X2)
   isNatKind#(mark(X)) -> isNatKind#(X)
   isNatKind#(active(X)) -> isNatKind#(X)
   U23#(mark(X)) -> U23#(X)
   U23#(active(X)) -> U23#(X)
   isNat#(mark(X)) -> isNat#(X)
   isNat#(active(X)) -> isNat#(X)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U31#(X1,mark(X2)) -> U31#(X1,X2)
   U31#(active(X1),X2) -> U31#(X1,X2)
   U31#(X1,active(X2)) -> U31#(X1,X2)
   U32#(mark(X1),X2) -> U32#(X1,X2)
   U32#(X1,mark(X2)) -> U32#(X1,X2)
   U32#(active(X1),X2) -> U32#(X1,X2)
   U32#(X1,active(X2)) -> U32#(X1,X2)
   U33#(mark(X)) -> U33#(X)
   U33#(active(X)) -> U33#(X)
   U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
   U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
   U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
   U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
   U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
   U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
   U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
   U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3)
   U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
   U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
   U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
   U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
   U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
   U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3)
   U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
   U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
   U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
   U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
   U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
   U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3)
   U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
   U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
   U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
   U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
   U45#(mark(X1),X2) -> U45#(X1,X2)
   U45#(X1,mark(X2)) -> U45#(X1,X2)
   U45#(active(X1),X2) -> U45#(X1,X2)
   U45#(X1,active(X2)) -> U45#(X1,X2)
   U46#(mark(X)) -> U46#(X)
   U46#(active(X)) -> U46#(X)
   isNatIList#(mark(X)) -> isNatIList#(X)
   isNatIList#(active(X)) -> isNatIList#(X)
   U51#(mark(X1),X2) -> U51#(X1,X2)
   U51#(X1,mark(X2)) -> U51#(X1,X2)
   U51#(active(X1),X2) -> U51#(X1,X2)
   U51#(X1,active(X2)) -> U51#(X1,X2)
   U52#(mark(X)) -> U52#(X)
   U52#(active(X)) -> U52#(X)
   U61#(mark(X)) -> U61#(X)
   U61#(active(X)) -> U61#(X)
   U71#(mark(X)) -> U71#(X)
   U71#(active(X)) -> U71#(X)
   U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
   U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3)
   U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3)
   U81#(active(X1),X2,X3) -> U81#(X1,X2,X3)
   U81#(X1,active(X2),X3) -> U81#(X1,X2,X3)
   U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3)
   U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
   U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3)
   U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3)
   U82#(active(X1),X2,X3) -> U82#(X1,X2,X3)
   U82#(X1,active(X2),X3) -> U82#(X1,X2,X3)
   U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3)
   U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
   U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3)
   U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3)
   U83#(active(X1),X2,X3) -> U83#(X1,X2,X3)
   U83#(X1,active(X2),X3) -> U83#(X1,X2,X3)
   U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3)
   U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
   U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3)
   U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3)
   U84#(active(X1),X2,X3) -> U84#(X1,X2,X3)
   U84#(X1,active(X2),X3) -> U84#(X1,X2,X3)
   U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3)
   U85#(mark(X1),X2) -> U85#(X1,X2)
   U85#(X1,mark(X2)) -> U85#(X1,X2)
   U85#(active(X1),X2) -> U85#(X1,X2)
   U85#(X1,active(X2)) -> U85#(X1,X2)
   U86#(mark(X)) -> U86#(X)
   U86#(active(X)) -> U86#(X)
   U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
   U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3)
   U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3)
   U91#(active(X1),X2,X3) -> U91#(X1,X2,X3)
   U91#(X1,active(X2),X3) -> U91#(X1,X2,X3)
   U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3)
   U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
   U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3)
   U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3)
   U92#(active(X1),X2,X3) -> U92#(X1,X2,X3)
   U92#(X1,active(X2),X3) -> U92#(X1,X2,X3)
   U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3)
   U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
   U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3)
   U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3)
   U93#(active(X1),X2,X3) -> U93#(X1,X2,X3)
   U93#(X1,active(X2),X3) -> U93#(X1,X2,X3)
   U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3)
   U94#(mark(X1),X2) -> U94#(X1,X2)
   U94#(X1,mark(X2)) -> U94#(X1,X2)
   U94#(active(X1),X2) -> U94#(X1,X2)
   U94#(X1,active(X2)) -> U94#(X1,X2)
   s#(mark(X)) -> s#(X)
   s#(active(X)) -> s#(X)
   length#(mark(X)) -> length#(X)
   length#(active(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))
   mark(zeros()) -> active(zeros())
   mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
   mark(0()) -> active(0())
   mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
   mark(isNatIListKind(X)) -> active(isNatIListKind(X))
   mark(U13(X)) -> active(U13(mark(X)))
   mark(isNatList(X)) -> active(isNatList(X))
   mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
   mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
   mark(isNatKind(X)) -> active(isNatKind(X))
   mark(U23(X)) -> active(U23(mark(X)))
   mark(isNat(X)) -> active(isNat(X))
   mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
   mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
   mark(U33(X)) -> active(U33(mark(X)))
   mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
   mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
   mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
   mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
   mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
   mark(U46(X)) -> active(U46(mark(X)))
   mark(isNatIList(X)) -> active(isNatIList(X))
   mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
   mark(U52(X)) -> active(U52(mark(X)))
   mark(U61(X)) -> active(U61(mark(X)))
   mark(U71(X)) -> active(U71(mark(X)))
   mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
   mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
   mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
   mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
   mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
   mark(U86(X)) -> active(U86(mark(X)))
   mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
   mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
   mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
   mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
   mark(s(X)) -> active(s(mark(X)))
   mark(length(X)) -> active(length(mark(X)))
   mark(nil()) -> active(nil())
   cons(mark(X1),X2) -> cons(X1,X2)
   cons(X1,mark(X2)) -> cons(X1,X2)
   cons(active(X1),X2) -> cons(X1,X2)
   cons(X1,active(X2)) -> cons(X1,X2)
   U11(mark(X1),X2) -> U11(X1,X2)
   U11(X1,mark(X2)) -> U11(X1,X2)
   U11(active(X1),X2) -> U11(X1,X2)
   U11(X1,active(X2)) -> U11(X1,X2)
   U12(mark(X1),X2) -> U12(X1,X2)
   U12(X1,mark(X2)) -> U12(X1,X2)
   U12(active(X1),X2) -> U12(X1,X2)
   U12(X1,active(X2)) -> U12(X1,X2)
   isNatIListKind(mark(X)) -> isNatIListKind(X)
   isNatIListKind(active(X)) -> isNatIListKind(X)
   U13(mark(X)) -> U13(X)
   U13(active(X)) -> U13(X)
   isNatList(mark(X)) -> isNatList(X)
   isNatList(active(X)) -> isNatList(X)
   U21(mark(X1),X2) -> U21(X1,X2)
   U21(X1,mark(X2)) -> U21(X1,X2)
   U21(active(X1),X2) -> U21(X1,X2)
   U21(X1,active(X2)) -> U21(X1,X2)
   U22(mark(X1),X2) -> U22(X1,X2)
   U22(X1,mark(X2)) -> U22(X1,X2)
   U22(active(X1),X2) -> U22(X1,X2)
   U22(X1,active(X2)) -> U22(X1,X2)
   isNatKind(mark(X)) -> isNatKind(X)
   isNatKind(active(X)) -> isNatKind(X)
   U23(mark(X)) -> U23(X)
   U23(active(X)) -> U23(X)
   isNat(mark(X)) -> isNat(X)
   isNat(active(X)) -> isNat(X)
   U31(mark(X1),X2) -> U31(X1,X2)
   U31(X1,mark(X2)) -> U31(X1,X2)
   U31(active(X1),X2) -> U31(X1,X2)
   U31(X1,active(X2)) -> U31(X1,X2)
   U32(mark(X1),X2) -> U32(X1,X2)
   U32(X1,mark(X2)) -> U32(X1,X2)
   U32(active(X1),X2) -> U32(X1,X2)
   U32(X1,active(X2)) -> U32(X1,X2)
   U33(mark(X)) -> U33(X)
   U33(active(X)) -> U33(X)
   U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
   U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
   U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
   U41(active(X1),X2,X3) -> U41(X1,X2,X3)
   U41(X1,active(X2),X3) -> U41(X1,X2,X3)
   U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
   U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
   U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
   U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
   U42(active(X1),X2,X3) -> U42(X1,X2,X3)
   U42(X1,active(X2),X3) -> U42(X1,X2,X3)
   U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
   U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
   U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
   U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
   U43(active(X1),X2,X3) -> U43(X1,X2,X3)
   U43(X1,active(X2),X3) -> U43(X1,X2,X3)
   U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
   U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
   U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
   U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
   U44(active(X1),X2,X3) -> U44(X1,X2,X3)
   U44(X1,active(X2),X3) -> U44(X1,X2,X3)
   U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
   U45(mark(X1),X2) -> U45(X1,X2)
   U45(X1,mark(X2)) -> U45(X1,X2)
   U45(active(X1),X2) -> U45(X1,X2)
   U45(X1,active(X2)) -> U45(X1,X2)
   U46(mark(X)) -> U46(X)
   U46(active(X)) -> U46(X)
   isNatIList(mark(X)) -> isNatIList(X)
   isNatIList(active(X)) -> isNatIList(X)
   U51(mark(X1),X2) -> U51(X1,X2)
   U51(X1,mark(X2)) -> U51(X1,X2)
   U51(active(X1),X2) -> U51(X1,X2)
   U51(X1,active(X2)) -> U51(X1,X2)
   U52(mark(X)) -> U52(X)
   U52(active(X)) -> U52(X)
   U61(mark(X)) -> U61(X)
   U61(active(X)) -> U61(X)
   U71(mark(X)) -> U71(X)
   U71(active(X)) -> U71(X)
   U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
   U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
   U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
   U81(active(X1),X2,X3) -> U81(X1,X2,X3)
   U81(X1,active(X2),X3) -> U81(X1,X2,X3)
   U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
   U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
   U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
   U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
   U82(active(X1),X2,X3) -> U82(X1,X2,X3)
   U82(X1,active(X2),X3) -> U82(X1,X2,X3)
   U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
   U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
   U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
   U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
   U83(active(X1),X2,X3) -> U83(X1,X2,X3)
   U83(X1,active(X2),X3) -> U83(X1,X2,X3)
   U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
   U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
   U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
   U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
   U84(active(X1),X2,X3) -> U84(X1,X2,X3)
   U84(X1,active(X2),X3) -> U84(X1,X2,X3)
   U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
   U85(mark(X1),X2) -> U85(X1,X2)
   U85(X1,mark(X2)) -> U85(X1,X2)
   U85(active(X1),X2) -> U85(X1,X2)
   U85(X1,active(X2)) -> U85(X1,X2)
   U86(mark(X)) -> U86(X)
   U86(active(X)) -> U86(X)
   U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
   U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
   U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
   U91(active(X1),X2,X3) -> U91(X1,X2,X3)
   U91(X1,active(X2),X3) -> U91(X1,X2,X3)
   U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
   U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
   U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
   U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
   U92(active(X1),X2,X3) -> U92(X1,X2,X3)
   U92(X1,active(X2),X3) -> U92(X1,X2,X3)
   U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
   U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
   U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
   U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
   U93(active(X1),X2,X3) -> U93(X1,X2,X3)
   U93(X1,active(X2),X3) -> U93(X1,X2,X3)
   U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
   U94(mark(X1),X2) -> U94(X1,X2)
   U94(X1,mark(X2)) -> U94(X1,X2)
   U94(active(X1),X2) -> U94(X1,X2)
   U94(X1,active(X2)) -> U94(X1,X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   length(mark(X)) -> length(X)
   length(active(X)) -> length(X)
  CDG Processor:
   DPs:
    active#(zeros()) -> cons#(0(),zeros())
    active#(zeros()) -> mark#(cons(0(),zeros()))
    active#(U11(tt(),V1)) -> isNatIListKind#(V1)
    active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
    active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1))
    active#(U12(tt(),V1)) -> isNatList#(V1)
    active#(U12(tt(),V1)) -> U13#(isNatList(V1))
    active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1)))
    active#(U13(tt())) -> mark#(tt())
    active#(U21(tt(),V1)) -> isNatKind#(V1)
    active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
    active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1))
    active#(U22(tt(),V1)) -> isNat#(V1)
    active#(U22(tt(),V1)) -> U23#(isNat(V1))
    active#(U22(tt(),V1)) -> mark#(U23(isNat(V1)))
    active#(U23(tt())) -> mark#(tt())
    active#(U31(tt(),V)) -> isNatIListKind#(V)
    active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
    active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V))
    active#(U32(tt(),V)) -> isNatList#(V)
    active#(U32(tt(),V)) -> U33#(isNatList(V))
    active#(U32(tt(),V)) -> mark#(U33(isNatList(V)))
    active#(U33(tt())) -> mark#(tt())
    active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
    active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2))
    active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
    active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2))
    active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
    active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2))
    active#(U44(tt(),V1,V2)) -> isNat#(V1)
    active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
    active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2))
    active#(U45(tt(),V2)) -> isNatIList#(V2)
    active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
    active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2)))
    active#(U46(tt())) -> mark#(tt())
    active#(U51(tt(),V2)) -> isNatIListKind#(V2)
    active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
    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)) -> isNatKind#(V1)
    active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
    active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2))
    active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
    active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2))
    active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
    active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2))
    active#(U84(tt(),V1,V2)) -> isNat#(V1)
    active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
    active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2))
    active#(U85(tt(),V2)) -> isNatList#(V2)
    active#(U85(tt(),V2)) -> U86#(isNatList(V2))
    active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2)))
    active#(U86(tt())) -> mark#(tt())
    active#(U91(tt(),L,N)) -> isNatIListKind#(L)
    active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
    active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N))
    active#(U92(tt(),L,N)) -> isNat#(N)
    active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
    active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N))
    active#(U93(tt(),L,N)) -> isNatKind#(N)
    active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
    active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L))
    active#(U94(tt(),L)) -> length#(L)
    active#(U94(tt(),L)) -> s#(length(L))
    active#(U94(tt(),L)) -> mark#(s(length(L)))
    active#(isNat(0())) -> mark#(tt())
    active#(isNat(length(V1))) -> isNatIListKind#(V1)
    active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
    active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1))
    active#(isNat(s(V1))) -> isNatKind#(V1)
    active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
    active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1))
    active#(isNatIList(V)) -> isNatIListKind#(V)
    active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
    active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V))
    active#(isNatIList(zeros())) -> mark#(tt())
    active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
    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))) -> isNatKind#(V1)
    active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
    active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2))
    active#(isNatKind(0())) -> mark#(tt())
    active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
    active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
    active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1)))
    active#(isNatKind(s(V1))) -> isNatKind#(V1)
    active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
    active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1)))
    active#(isNatList(nil())) -> mark#(tt())
    active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
    active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2))
    active#(length(nil())) -> mark#(0())
    active#(length(cons(N,L))) -> isNatList#(L)
    active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
    active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N))
    mark#(zeros()) -> active#(zeros())
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
    mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
    mark#(0()) -> active#(0())
    mark#(U11(X1,X2)) -> mark#(X1)
    mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
    mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
    mark#(tt()) -> active#(tt())
    mark#(U12(X1,X2)) -> mark#(X1)
    mark#(U12(X1,X2)) -> U12#(mark(X1),X2)
    mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
    mark#(isNatIListKind(X)) -> active#(isNatIListKind(X))
    mark#(U13(X)) -> mark#(X)
    mark#(U13(X)) -> U13#(mark(X))
    mark#(U13(X)) -> active#(U13(mark(X)))
    mark#(isNatList(X)) -> active#(isNatList(X))
    mark#(U21(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
    mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
    mark#(U22(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
    mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
    mark#(isNatKind(X)) -> active#(isNatKind(X))
    mark#(U23(X)) -> mark#(X)
    mark#(U23(X)) -> U23#(mark(X))
    mark#(U23(X)) -> active#(U23(mark(X)))
    mark#(isNat(X)) -> active#(isNat(X))
    mark#(U31(X1,X2)) -> mark#(X1)
    mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
    mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
    mark#(U32(X1,X2)) -> mark#(X1)
    mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
    mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
    mark#(U33(X)) -> mark#(X)
    mark#(U33(X)) -> U33#(mark(X))
    mark#(U33(X)) -> active#(U33(mark(X)))
    mark#(U41(X1,X2,X3)) -> mark#(X1)
    mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
    mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
    mark#(U42(X1,X2,X3)) -> mark#(X1)
    mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3)
    mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
    mark#(U43(X1,X2,X3)) -> mark#(X1)
    mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3)
    mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
    mark#(U44(X1,X2,X3)) -> mark#(X1)
    mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3)
    mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
    mark#(U45(X1,X2)) -> mark#(X1)
    mark#(U45(X1,X2)) -> U45#(mark(X1),X2)
    mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
    mark#(U46(X)) -> mark#(X)
    mark#(U46(X)) -> U46#(mark(X))
    mark#(U46(X)) -> active#(U46(mark(X)))
    mark#(isNatIList(X)) -> active#(isNatIList(X))
    mark#(U51(X1,X2)) -> mark#(X1)
    mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
    mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
    mark#(U52(X)) -> mark#(X)
    mark#(U52(X)) -> U52#(mark(X))
    mark#(U52(X)) -> active#(U52(mark(X)))
    mark#(U61(X)) -> mark#(X)
    mark#(U61(X)) -> U61#(mark(X))
    mark#(U61(X)) -> active#(U61(mark(X)))
    mark#(U71(X)) -> mark#(X)
    mark#(U71(X)) -> U71#(mark(X))
    mark#(U71(X)) -> active#(U71(mark(X)))
    mark#(U81(X1,X2,X3)) -> mark#(X1)
    mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3)
    mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3))
    mark#(U82(X1,X2,X3)) -> mark#(X1)
    mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3)
    mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3))
    mark#(U83(X1,X2,X3)) -> mark#(X1)
    mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3)
    mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3))
    mark#(U84(X1,X2,X3)) -> mark#(X1)
    mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3)
    mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3))
    mark#(U85(X1,X2)) -> mark#(X1)
    mark#(U85(X1,X2)) -> U85#(mark(X1),X2)
    mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2))
    mark#(U86(X)) -> mark#(X)
    mark#(U86(X)) -> U86#(mark(X))
    mark#(U86(X)) -> active#(U86(mark(X)))
    mark#(U91(X1,X2,X3)) -> mark#(X1)
    mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3)
    mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3))
    mark#(U92(X1,X2,X3)) -> mark#(X1)
    mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3)
    mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3))
    mark#(U93(X1,X2,X3)) -> mark#(X1)
    mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3)
    mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3))
    mark#(U94(X1,X2)) -> mark#(X1)
    mark#(U94(X1,X2)) -> U94#(mark(X1),X2)
    mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2))
    mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> s#(mark(X))
    mark#(s(X)) -> active#(s(mark(X)))
    mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> length#(mark(X))
    mark#(length(X)) -> active#(length(mark(X)))
    mark#(nil()) -> active#(nil())
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(X1,mark(X2)) -> cons#(X1,X2)
    cons#(active(X1),X2) -> cons#(X1,X2)
    cons#(X1,active(X2)) -> cons#(X1,X2)
    U11#(mark(X1),X2) -> U11#(X1,X2)
    U11#(X1,mark(X2)) -> U11#(X1,X2)
    U11#(active(X1),X2) -> U11#(X1,X2)
    U11#(X1,active(X2)) -> U11#(X1,X2)
    U12#(mark(X1),X2) -> U12#(X1,X2)
    U12#(X1,mark(X2)) -> U12#(X1,X2)
    U12#(active(X1),X2) -> U12#(X1,X2)
    U12#(X1,active(X2)) -> U12#(X1,X2)
    isNatIListKind#(mark(X)) -> isNatIListKind#(X)
    isNatIListKind#(active(X)) -> isNatIListKind#(X)
    U13#(mark(X)) -> U13#(X)
    U13#(active(X)) -> U13#(X)
    isNatList#(mark(X)) -> isNatList#(X)
    isNatList#(active(X)) -> isNatList#(X)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U21#(X1,mark(X2)) -> U21#(X1,X2)
    U21#(active(X1),X2) -> U21#(X1,X2)
    U21#(X1,active(X2)) -> U21#(X1,X2)
    U22#(mark(X1),X2) -> U22#(X1,X2)
    U22#(X1,mark(X2)) -> U22#(X1,X2)
    U22#(active(X1),X2) -> U22#(X1,X2)
    U22#(X1,active(X2)) -> U22#(X1,X2)
    isNatKind#(mark(X)) -> isNatKind#(X)
    isNatKind#(active(X)) -> isNatKind#(X)
    U23#(mark(X)) -> U23#(X)
    U23#(active(X)) -> U23#(X)
    isNat#(mark(X)) -> isNat#(X)
    isNat#(active(X)) -> isNat#(X)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U31#(X1,mark(X2)) -> U31#(X1,X2)
    U31#(active(X1),X2) -> U31#(X1,X2)
    U31#(X1,active(X2)) -> U31#(X1,X2)
    U32#(mark(X1),X2) -> U32#(X1,X2)
    U32#(X1,mark(X2)) -> U32#(X1,X2)
    U32#(active(X1),X2) -> U32#(X1,X2)
    U32#(X1,active(X2)) -> U32#(X1,X2)
    U33#(mark(X)) -> U33#(X)
    U33#(active(X)) -> U33#(X)
    U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
    U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
    U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
    U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
    U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
    U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
    U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
    U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3)
    U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
    U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
    U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
    U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
    U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
    U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3)
    U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
    U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
    U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
    U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
    U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
    U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3)
    U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
    U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
    U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
    U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
    U45#(mark(X1),X2) -> U45#(X1,X2)
    U45#(X1,mark(X2)) -> U45#(X1,X2)
    U45#(active(X1),X2) -> U45#(X1,X2)
    U45#(X1,active(X2)) -> U45#(X1,X2)
    U46#(mark(X)) -> U46#(X)
    U46#(active(X)) -> U46#(X)
    isNatIList#(mark(X)) -> isNatIList#(X)
    isNatIList#(active(X)) -> isNatIList#(X)
    U51#(mark(X1),X2) -> U51#(X1,X2)
    U51#(X1,mark(X2)) -> U51#(X1,X2)
    U51#(active(X1),X2) -> U51#(X1,X2)
    U51#(X1,active(X2)) -> U51#(X1,X2)
    U52#(mark(X)) -> U52#(X)
    U52#(active(X)) -> U52#(X)
    U61#(mark(X)) -> U61#(X)
    U61#(active(X)) -> U61#(X)
    U71#(mark(X)) -> U71#(X)
    U71#(active(X)) -> U71#(X)
    U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
    U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3)
    U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3)
    U81#(active(X1),X2,X3) -> U81#(X1,X2,X3)
    U81#(X1,active(X2),X3) -> U81#(X1,X2,X3)
    U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3)
    U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
    U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3)
    U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3)
    U82#(active(X1),X2,X3) -> U82#(X1,X2,X3)
    U82#(X1,active(X2),X3) -> U82#(X1,X2,X3)
    U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3)
    U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
    U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3)
    U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3)
    U83#(active(X1),X2,X3) -> U83#(X1,X2,X3)
    U83#(X1,active(X2),X3) -> U83#(X1,X2,X3)
    U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3)
    U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
    U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3)
    U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3)
    U84#(active(X1),X2,X3) -> U84#(X1,X2,X3)
    U84#(X1,active(X2),X3) -> U84#(X1,X2,X3)
    U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3)
    U85#(mark(X1),X2) -> U85#(X1,X2)
    U85#(X1,mark(X2)) -> U85#(X1,X2)
    U85#(active(X1),X2) -> U85#(X1,X2)
    U85#(X1,active(X2)) -> U85#(X1,X2)
    U86#(mark(X)) -> U86#(X)
    U86#(active(X)) -> U86#(X)
    U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
    U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3)
    U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3)
    U91#(active(X1),X2,X3) -> U91#(X1,X2,X3)
    U91#(X1,active(X2),X3) -> U91#(X1,X2,X3)
    U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3)
    U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
    U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3)
    U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3)
    U92#(active(X1),X2,X3) -> U92#(X1,X2,X3)
    U92#(X1,active(X2),X3) -> U92#(X1,X2,X3)
    U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3)
    U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
    U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3)
    U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3)
    U93#(active(X1),X2,X3) -> U93#(X1,X2,X3)
    U93#(X1,active(X2),X3) -> U93#(X1,X2,X3)
    U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3)
    U94#(mark(X1),X2) -> U94#(X1,X2)
    U94#(X1,mark(X2)) -> U94#(X1,X2)
    U94#(active(X1),X2) -> U94#(X1,X2)
    U94#(X1,active(X2)) -> U94#(X1,X2)
    s#(mark(X)) -> s#(X)
    s#(active(X)) -> s#(X)
    length#(mark(X)) -> length#(X)
    length#(active(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))
    mark(zeros()) -> active(zeros())
    mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    mark(0()) -> active(0())
    mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
    mark(tt()) -> active(tt())
    mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
    mark(isNatIListKind(X)) -> active(isNatIListKind(X))
    mark(U13(X)) -> active(U13(mark(X)))
    mark(isNatList(X)) -> active(isNatList(X))
    mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
    mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
    mark(isNatKind(X)) -> active(isNatKind(X))
    mark(U23(X)) -> active(U23(mark(X)))
    mark(isNat(X)) -> active(isNat(X))
    mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
    mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
    mark(U33(X)) -> active(U33(mark(X)))
    mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
    mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
    mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
    mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
    mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
    mark(U46(X)) -> active(U46(mark(X)))
    mark(isNatIList(X)) -> active(isNatIList(X))
    mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
    mark(U52(X)) -> active(U52(mark(X)))
    mark(U61(X)) -> active(U61(mark(X)))
    mark(U71(X)) -> active(U71(mark(X)))
    mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
    mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
    mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
    mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
    mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
    mark(U86(X)) -> active(U86(mark(X)))
    mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
    mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
    mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
    mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
    mark(s(X)) -> active(s(mark(X)))
    mark(length(X)) -> active(length(mark(X)))
    mark(nil()) -> active(nil())
    cons(mark(X1),X2) -> cons(X1,X2)
    cons(X1,mark(X2)) -> cons(X1,X2)
    cons(active(X1),X2) -> cons(X1,X2)
    cons(X1,active(X2)) -> cons(X1,X2)
    U11(mark(X1),X2) -> U11(X1,X2)
    U11(X1,mark(X2)) -> U11(X1,X2)
    U11(active(X1),X2) -> U11(X1,X2)
    U11(X1,active(X2)) -> U11(X1,X2)
    U12(mark(X1),X2) -> U12(X1,X2)
    U12(X1,mark(X2)) -> U12(X1,X2)
    U12(active(X1),X2) -> U12(X1,X2)
    U12(X1,active(X2)) -> U12(X1,X2)
    isNatIListKind(mark(X)) -> isNatIListKind(X)
    isNatIListKind(active(X)) -> isNatIListKind(X)
    U13(mark(X)) -> U13(X)
    U13(active(X)) -> U13(X)
    isNatList(mark(X)) -> isNatList(X)
    isNatList(active(X)) -> isNatList(X)
    U21(mark(X1),X2) -> U21(X1,X2)
    U21(X1,mark(X2)) -> U21(X1,X2)
    U21(active(X1),X2) -> U21(X1,X2)
    U21(X1,active(X2)) -> U21(X1,X2)
    U22(mark(X1),X2) -> U22(X1,X2)
    U22(X1,mark(X2)) -> U22(X1,X2)
    U22(active(X1),X2) -> U22(X1,X2)
    U22(X1,active(X2)) -> U22(X1,X2)
    isNatKind(mark(X)) -> isNatKind(X)
    isNatKind(active(X)) -> isNatKind(X)
    U23(mark(X)) -> U23(X)
    U23(active(X)) -> U23(X)
    isNat(mark(X)) -> isNat(X)
    isNat(active(X)) -> isNat(X)
    U31(mark(X1),X2) -> U31(X1,X2)
    U31(X1,mark(X2)) -> U31(X1,X2)
    U31(active(X1),X2) -> U31(X1,X2)
    U31(X1,active(X2)) -> U31(X1,X2)
    U32(mark(X1),X2) -> U32(X1,X2)
    U32(X1,mark(X2)) -> U32(X1,X2)
    U32(active(X1),X2) -> U32(X1,X2)
    U32(X1,active(X2)) -> U32(X1,X2)
    U33(mark(X)) -> U33(X)
    U33(active(X)) -> U33(X)
    U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
    U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
    U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
    U41(active(X1),X2,X3) -> U41(X1,X2,X3)
    U41(X1,active(X2),X3) -> U41(X1,X2,X3)
    U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
    U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
    U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
    U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
    U42(active(X1),X2,X3) -> U42(X1,X2,X3)
    U42(X1,active(X2),X3) -> U42(X1,X2,X3)
    U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
    U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
    U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
    U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
    U43(active(X1),X2,X3) -> U43(X1,X2,X3)
    U43(X1,active(X2),X3) -> U43(X1,X2,X3)
    U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
    U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
    U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
    U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
    U44(active(X1),X2,X3) -> U44(X1,X2,X3)
    U44(X1,active(X2),X3) -> U44(X1,X2,X3)
    U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
    U45(mark(X1),X2) -> U45(X1,X2)
    U45(X1,mark(X2)) -> U45(X1,X2)
    U45(active(X1),X2) -> U45(X1,X2)
    U45(X1,active(X2)) -> U45(X1,X2)
    U46(mark(X)) -> U46(X)
    U46(active(X)) -> U46(X)
    isNatIList(mark(X)) -> isNatIList(X)
    isNatIList(active(X)) -> isNatIList(X)
    U51(mark(X1),X2) -> U51(X1,X2)
    U51(X1,mark(X2)) -> U51(X1,X2)
    U51(active(X1),X2) -> U51(X1,X2)
    U51(X1,active(X2)) -> U51(X1,X2)
    U52(mark(X)) -> U52(X)
    U52(active(X)) -> U52(X)
    U61(mark(X)) -> U61(X)
    U61(active(X)) -> U61(X)
    U71(mark(X)) -> U71(X)
    U71(active(X)) -> U71(X)
    U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
    U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
    U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
    U81(active(X1),X2,X3) -> U81(X1,X2,X3)
    U81(X1,active(X2),X3) -> U81(X1,X2,X3)
    U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
    U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
    U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
    U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
    U82(active(X1),X2,X3) -> U82(X1,X2,X3)
    U82(X1,active(X2),X3) -> U82(X1,X2,X3)
    U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
    U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
    U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
    U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
    U83(active(X1),X2,X3) -> U83(X1,X2,X3)
    U83(X1,active(X2),X3) -> U83(X1,X2,X3)
    U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
    U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
    U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
    U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
    U84(active(X1),X2,X3) -> U84(X1,X2,X3)
    U84(X1,active(X2),X3) -> U84(X1,X2,X3)
    U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
    U85(mark(X1),X2) -> U85(X1,X2)
    U85(X1,mark(X2)) -> U85(X1,X2)
    U85(active(X1),X2) -> U85(X1,X2)
    U85(X1,active(X2)) -> U85(X1,X2)
    U86(mark(X)) -> U86(X)
    U86(active(X)) -> U86(X)
    U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
    U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
    U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
    U91(active(X1),X2,X3) -> U91(X1,X2,X3)
    U91(X1,active(X2),X3) -> U91(X1,X2,X3)
    U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
    U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
    U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
    U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
    U92(active(X1),X2,X3) -> U92(X1,X2,X3)
    U92(X1,active(X2),X3) -> U92(X1,X2,X3)
    U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
    U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
    U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
    U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
    U93(active(X1),X2,X3) -> U93(X1,X2,X3)
    U93(X1,active(X2),X3) -> U93(X1,X2,X3)
    U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
    U94(mark(X1),X2) -> U94(X1,X2)
    U94(X1,mark(X2)) -> U94(X1,X2)
    U94(active(X1),X2) -> U94(X1,X2)
    U94(X1,active(X2)) -> U94(X1,X2)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
    length(mark(X)) -> length(X)
    length(active(X)) -> length(X)
   graph:
    ...
   Restore Modifier:
    DPs:
     active#(zeros()) -> cons#(0(),zeros())
     active#(zeros()) -> mark#(cons(0(),zeros()))
     active#(U11(tt(),V1)) -> isNatIListKind#(V1)
     active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
     active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1))
     active#(U12(tt(),V1)) -> isNatList#(V1)
     active#(U12(tt(),V1)) -> U13#(isNatList(V1))
     active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1)))
     active#(U13(tt())) -> mark#(tt())
     active#(U21(tt(),V1)) -> isNatKind#(V1)
     active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
     active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1))
     active#(U22(tt(),V1)) -> isNat#(V1)
     active#(U22(tt(),V1)) -> U23#(isNat(V1))
     active#(U22(tt(),V1)) -> mark#(U23(isNat(V1)))
     active#(U23(tt())) -> mark#(tt())
     active#(U31(tt(),V)) -> isNatIListKind#(V)
     active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
     active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V))
     active#(U32(tt(),V)) -> isNatList#(V)
     active#(U32(tt(),V)) -> U33#(isNatList(V))
     active#(U32(tt(),V)) -> mark#(U33(isNatList(V)))
     active#(U33(tt())) -> mark#(tt())
     active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
     active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2))
     active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
     active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2))
     active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
     active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2))
     active#(U44(tt(),V1,V2)) -> isNat#(V1)
     active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
     active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2))
     active#(U45(tt(),V2)) -> isNatIList#(V2)
     active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
     active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2)))
     active#(U46(tt())) -> mark#(tt())
     active#(U51(tt(),V2)) -> isNatIListKind#(V2)
     active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
     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)) -> isNatKind#(V1)
     active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2)
     active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2))
     active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2)
     active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2))
     active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2)
     active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2))
     active#(U84(tt(),V1,V2)) -> isNat#(V1)
     active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2)
     active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2))
     active#(U85(tt(),V2)) -> isNatList#(V2)
     active#(U85(tt(),V2)) -> U86#(isNatList(V2))
     active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2)))
     active#(U86(tt())) -> mark#(tt())
     active#(U91(tt(),L,N)) -> isNatIListKind#(L)
     active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N)
     active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N))
     active#(U92(tt(),L,N)) -> isNat#(N)
     active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N)
     active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N))
     active#(U93(tt(),L,N)) -> isNatKind#(N)
     active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L)
     active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L))
     active#(U94(tt(),L)) -> length#(L)
     active#(U94(tt(),L)) -> s#(length(L))
     active#(U94(tt(),L)) -> mark#(s(length(L)))
     active#(isNat(0())) -> mark#(tt())
     active#(isNat(length(V1))) -> isNatIListKind#(V1)
     active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
     active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1))
     active#(isNat(s(V1))) -> isNatKind#(V1)
     active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
     active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1))
     active#(isNatIList(V)) -> isNatIListKind#(V)
     active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
     active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V))
     active#(isNatIList(zeros())) -> mark#(tt())
     active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
     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))) -> isNatKind#(V1)
     active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
     active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2))
     active#(isNatKind(0())) -> mark#(tt())
     active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
     active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1))
     active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1)))
     active#(isNatKind(s(V1))) -> isNatKind#(V1)
     active#(isNatKind(s(V1))) -> U71#(isNatKind(V1))
     active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1)))
     active#(isNatList(nil())) -> mark#(tt())
     active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2)
     active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2))
     active#(length(nil())) -> mark#(0())
     active#(length(cons(N,L))) -> isNatList#(L)
     active#(length(cons(N,L))) -> U91#(isNatList(L),L,N)
     active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N))
     mark#(zeros()) -> active#(zeros())
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
     mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
     mark#(0()) -> active#(0())
     mark#(U11(X1,X2)) -> mark#(X1)
     mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
     mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
     mark#(tt()) -> active#(tt())
     mark#(U12(X1,X2)) -> mark#(X1)
     mark#(U12(X1,X2)) -> U12#(mark(X1),X2)
     mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
     mark#(isNatIListKind(X)) -> active#(isNatIListKind(X))
     mark#(U13(X)) -> mark#(X)
     mark#(U13(X)) -> U13#(mark(X))
     mark#(U13(X)) -> active#(U13(mark(X)))
     mark#(isNatList(X)) -> active#(isNatList(X))
     mark#(U21(X1,X2)) -> mark#(X1)
     mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
     mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
     mark#(U22(X1,X2)) -> mark#(X1)
     mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
     mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
     mark#(isNatKind(X)) -> active#(isNatKind(X))
     mark#(U23(X)) -> mark#(X)
     mark#(U23(X)) -> U23#(mark(X))
     mark#(U23(X)) -> active#(U23(mark(X)))
     mark#(isNat(X)) -> active#(isNat(X))
     mark#(U31(X1,X2)) -> mark#(X1)
     mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
     mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
     mark#(U32(X1,X2)) -> mark#(X1)
     mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
     mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
     mark#(U33(X)) -> mark#(X)
     mark#(U33(X)) -> U33#(mark(X))
     mark#(U33(X)) -> active#(U33(mark(X)))
     mark#(U41(X1,X2,X3)) -> mark#(X1)
     mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
     mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
     mark#(U42(X1,X2,X3)) -> mark#(X1)
     mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3)
     mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
     mark#(U43(X1,X2,X3)) -> mark#(X1)
     mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3)
     mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
     mark#(U44(X1,X2,X3)) -> mark#(X1)
     mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3)
     mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
     mark#(U45(X1,X2)) -> mark#(X1)
     mark#(U45(X1,X2)) -> U45#(mark(X1),X2)
     mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
     mark#(U46(X)) -> mark#(X)
     mark#(U46(X)) -> U46#(mark(X))
     mark#(U46(X)) -> active#(U46(mark(X)))
     mark#(isNatIList(X)) -> active#(isNatIList(X))
     mark#(U51(X1,X2)) -> mark#(X1)
     mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
     mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
     mark#(U52(X)) -> mark#(X)
     mark#(U52(X)) -> U52#(mark(X))
     mark#(U52(X)) -> active#(U52(mark(X)))
     mark#(U61(X)) -> mark#(X)
     mark#(U61(X)) -> U61#(mark(X))
     mark#(U61(X)) -> active#(U61(mark(X)))
     mark#(U71(X)) -> mark#(X)
     mark#(U71(X)) -> U71#(mark(X))
     mark#(U71(X)) -> active#(U71(mark(X)))
     mark#(U81(X1,X2,X3)) -> mark#(X1)
     mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3)
     mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3))
     mark#(U82(X1,X2,X3)) -> mark#(X1)
     mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3)
     mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3))
     mark#(U83(X1,X2,X3)) -> mark#(X1)
     mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3)
     mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3))
     mark#(U84(X1,X2,X3)) -> mark#(X1)
     mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3)
     mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3))
     mark#(U85(X1,X2)) -> mark#(X1)
     mark#(U85(X1,X2)) -> U85#(mark(X1),X2)
     mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2))
     mark#(U86(X)) -> mark#(X)
     mark#(U86(X)) -> U86#(mark(X))
     mark#(U86(X)) -> active#(U86(mark(X)))
     mark#(U91(X1,X2,X3)) -> mark#(X1)
     mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3)
     mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3))
     mark#(U92(X1,X2,X3)) -> mark#(X1)
     mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3)
     mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3))
     mark#(U93(X1,X2,X3)) -> mark#(X1)
     mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3)
     mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3))
     mark#(U94(X1,X2)) -> mark#(X1)
     mark#(U94(X1,X2)) -> U94#(mark(X1),X2)
     mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2))
     mark#(s(X)) -> mark#(X)
     mark#(s(X)) -> s#(mark(X))
     mark#(s(X)) -> active#(s(mark(X)))
     mark#(length(X)) -> mark#(X)
     mark#(length(X)) -> length#(mark(X))
     mark#(length(X)) -> active#(length(mark(X)))
     mark#(nil()) -> active#(nil())
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(X1,mark(X2)) -> cons#(X1,X2)
     cons#(active(X1),X2) -> cons#(X1,X2)
     cons#(X1,active(X2)) -> cons#(X1,X2)
     U11#(mark(X1),X2) -> U11#(X1,X2)
     U11#(X1,mark(X2)) -> U11#(X1,X2)
     U11#(active(X1),X2) -> U11#(X1,X2)
     U11#(X1,active(X2)) -> U11#(X1,X2)
     U12#(mark(X1),X2) -> U12#(X1,X2)
     U12#(X1,mark(X2)) -> U12#(X1,X2)
     U12#(active(X1),X2) -> U12#(X1,X2)
     U12#(X1,active(X2)) -> U12#(X1,X2)
     isNatIListKind#(mark(X)) -> isNatIListKind#(X)
     isNatIListKind#(active(X)) -> isNatIListKind#(X)
     U13#(mark(X)) -> U13#(X)
     U13#(active(X)) -> U13#(X)
     isNatList#(mark(X)) -> isNatList#(X)
     isNatList#(active(X)) -> isNatList#(X)
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U21#(X1,mark(X2)) -> U21#(X1,X2)
     U21#(active(X1),X2) -> U21#(X1,X2)
     U21#(X1,active(X2)) -> U21#(X1,X2)
     U22#(mark(X1),X2) -> U22#(X1,X2)
     U22#(X1,mark(X2)) -> U22#(X1,X2)
     U22#(active(X1),X2) -> U22#(X1,X2)
     U22#(X1,active(X2)) -> U22#(X1,X2)
     isNatKind#(mark(X)) -> isNatKind#(X)
     isNatKind#(active(X)) -> isNatKind#(X)
     U23#(mark(X)) -> U23#(X)
     U23#(active(X)) -> U23#(X)
     isNat#(mark(X)) -> isNat#(X)
     isNat#(active(X)) -> isNat#(X)
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U31#(X1,mark(X2)) -> U31#(X1,X2)
     U31#(active(X1),X2) -> U31#(X1,X2)
     U31#(X1,active(X2)) -> U31#(X1,X2)
     U32#(mark(X1),X2) -> U32#(X1,X2)
     U32#(X1,mark(X2)) -> U32#(X1,X2)
     U32#(active(X1),X2) -> U32#(X1,X2)
     U32#(X1,active(X2)) -> U32#(X1,X2)
     U33#(mark(X)) -> U33#(X)
     U33#(active(X)) -> U33#(X)
     U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
     U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
     U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
     U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
     U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
     U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
     U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
     U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3)
     U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
     U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
     U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
     U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
     U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
     U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3)
     U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
     U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
     U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
     U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
     U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
     U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3)
     U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
     U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
     U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
     U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
     U45#(mark(X1),X2) -> U45#(X1,X2)
     U45#(X1,mark(X2)) -> U45#(X1,X2)
     U45#(active(X1),X2) -> U45#(X1,X2)
     U45#(X1,active(X2)) -> U45#(X1,X2)
     U46#(mark(X)) -> U46#(X)
     U46#(active(X)) -> U46#(X)
     isNatIList#(mark(X)) -> isNatIList#(X)
     isNatIList#(active(X)) -> isNatIList#(X)
     U51#(mark(X1),X2) -> U51#(X1,X2)
     U51#(X1,mark(X2)) -> U51#(X1,X2)
     U51#(active(X1),X2) -> U51#(X1,X2)
     U51#(X1,active(X2)) -> U51#(X1,X2)
     U52#(mark(X)) -> U52#(X)
     U52#(active(X)) -> U52#(X)
     U61#(mark(X)) -> U61#(X)
     U61#(active(X)) -> U61#(X)
     U71#(mark(X)) -> U71#(X)
     U71#(active(X)) -> U71#(X)
     U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
     U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3)
     U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3)
     U81#(active(X1),X2,X3) -> U81#(X1,X2,X3)
     U81#(X1,active(X2),X3) -> U81#(X1,X2,X3)
     U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3)
     U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
     U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3)
     U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3)
     U82#(active(X1),X2,X3) -> U82#(X1,X2,X3)
     U82#(X1,active(X2),X3) -> U82#(X1,X2,X3)
     U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3)
     U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
     U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3)
     U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3)
     U83#(active(X1),X2,X3) -> U83#(X1,X2,X3)
     U83#(X1,active(X2),X3) -> U83#(X1,X2,X3)
     U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3)
     U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
     U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3)
     U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3)
     U84#(active(X1),X2,X3) -> U84#(X1,X2,X3)
     U84#(X1,active(X2),X3) -> U84#(X1,X2,X3)
     U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3)
     U85#(mark(X1),X2) -> U85#(X1,X2)
     U85#(X1,mark(X2)) -> U85#(X1,X2)
     U85#(active(X1),X2) -> U85#(X1,X2)
     U85#(X1,active(X2)) -> U85#(X1,X2)
     U86#(mark(X)) -> U86#(X)
     U86#(active(X)) -> U86#(X)
     U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
     U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3)
     U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3)
     U91#(active(X1),X2,X3) -> U91#(X1,X2,X3)
     U91#(X1,active(X2),X3) -> U91#(X1,X2,X3)
     U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3)
     U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
     U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3)
     U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3)
     U92#(active(X1),X2,X3) -> U92#(X1,X2,X3)
     U92#(X1,active(X2),X3) -> U92#(X1,X2,X3)
     U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3)
     U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
     U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3)
     U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3)
     U93#(active(X1),X2,X3) -> U93#(X1,X2,X3)
     U93#(X1,active(X2),X3) -> U93#(X1,X2,X3)
     U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3)
     U94#(mark(X1),X2) -> U94#(X1,X2)
     U94#(X1,mark(X2)) -> U94#(X1,X2)
     U94#(active(X1),X2) -> U94#(X1,X2)
     U94#(X1,active(X2)) -> U94#(X1,X2)
     s#(mark(X)) -> s#(X)
     s#(active(X)) -> s#(X)
     length#(mark(X)) -> length#(X)
     length#(active(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))
     mark(zeros()) -> active(zeros())
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(0()) -> active(0())
     mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
     mark(tt()) -> active(tt())
     mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
     mark(isNatIListKind(X)) -> active(isNatIListKind(X))
     mark(U13(X)) -> active(U13(mark(X)))
     mark(isNatList(X)) -> active(isNatList(X))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
     mark(isNatKind(X)) -> active(isNatKind(X))
     mark(U23(X)) -> active(U23(mark(X)))
     mark(isNat(X)) -> active(isNat(X))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
     mark(U33(X)) -> active(U33(mark(X)))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
     mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
     mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
     mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
     mark(U46(X)) -> active(U46(mark(X)))
     mark(isNatIList(X)) -> active(isNatIList(X))
     mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
     mark(U52(X)) -> active(U52(mark(X)))
     mark(U61(X)) -> active(U61(mark(X)))
     mark(U71(X)) -> active(U71(mark(X)))
     mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
     mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
     mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
     mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
     mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
     mark(U86(X)) -> active(U86(mark(X)))
     mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
     mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
     mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
     mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
     mark(s(X)) -> active(s(mark(X)))
     mark(length(X)) -> active(length(mark(X)))
     mark(nil()) -> active(nil())
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     U11(mark(X1),X2) -> U11(X1,X2)
     U11(X1,mark(X2)) -> U11(X1,X2)
     U11(active(X1),X2) -> U11(X1,X2)
     U11(X1,active(X2)) -> U11(X1,X2)
     U12(mark(X1),X2) -> U12(X1,X2)
     U12(X1,mark(X2)) -> U12(X1,X2)
     U12(active(X1),X2) -> U12(X1,X2)
     U12(X1,active(X2)) -> U12(X1,X2)
     isNatIListKind(mark(X)) -> isNatIListKind(X)
     isNatIListKind(active(X)) -> isNatIListKind(X)
     U13(mark(X)) -> U13(X)
     U13(active(X)) -> U13(X)
     isNatList(mark(X)) -> isNatList(X)
     isNatList(active(X)) -> isNatList(X)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U22(mark(X1),X2) -> U22(X1,X2)
     U22(X1,mark(X2)) -> U22(X1,X2)
     U22(active(X1),X2) -> U22(X1,X2)
     U22(X1,active(X2)) -> U22(X1,X2)
     isNatKind(mark(X)) -> isNatKind(X)
     isNatKind(active(X)) -> isNatKind(X)
     U23(mark(X)) -> U23(X)
     U23(active(X)) -> U23(X)
     isNat(mark(X)) -> isNat(X)
     isNat(active(X)) -> isNat(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U32(mark(X1),X2) -> U32(X1,X2)
     U32(X1,mark(X2)) -> U32(X1,X2)
     U32(active(X1),X2) -> U32(X1,X2)
     U32(X1,active(X2)) -> U32(X1,X2)
     U33(mark(X)) -> U33(X)
     U33(active(X)) -> U33(X)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
     U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
     U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
     U42(active(X1),X2,X3) -> U42(X1,X2,X3)
     U42(X1,active(X2),X3) -> U42(X1,X2,X3)
     U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
     U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
     U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
     U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
     U43(active(X1),X2,X3) -> U43(X1,X2,X3)
     U43(X1,active(X2),X3) -> U43(X1,X2,X3)
     U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
     U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
     U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
     U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
     U44(active(X1),X2,X3) -> U44(X1,X2,X3)
     U44(X1,active(X2),X3) -> U44(X1,X2,X3)
     U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
     U45(mark(X1),X2) -> U45(X1,X2)
     U45(X1,mark(X2)) -> U45(X1,X2)
     U45(active(X1),X2) -> U45(X1,X2)
     U45(X1,active(X2)) -> U45(X1,X2)
     U46(mark(X)) -> U46(X)
     U46(active(X)) -> U46(X)
     isNatIList(mark(X)) -> isNatIList(X)
     isNatIList(active(X)) -> isNatIList(X)
     U51(mark(X1),X2) -> U51(X1,X2)
     U51(X1,mark(X2)) -> U51(X1,X2)
     U51(active(X1),X2) -> U51(X1,X2)
     U51(X1,active(X2)) -> U51(X1,X2)
     U52(mark(X)) -> U52(X)
     U52(active(X)) -> U52(X)
     U61(mark(X)) -> U61(X)
     U61(active(X)) -> U61(X)
     U71(mark(X)) -> U71(X)
     U71(active(X)) -> U71(X)
     U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
     U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
     U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
     U81(active(X1),X2,X3) -> U81(X1,X2,X3)
     U81(X1,active(X2),X3) -> U81(X1,X2,X3)
     U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
     U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
     U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
     U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
     U82(active(X1),X2,X3) -> U82(X1,X2,X3)
     U82(X1,active(X2),X3) -> U82(X1,X2,X3)
     U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
     U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
     U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
     U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
     U83(active(X1),X2,X3) -> U83(X1,X2,X3)
     U83(X1,active(X2),X3) -> U83(X1,X2,X3)
     U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
     U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
     U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
     U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
     U84(active(X1),X2,X3) -> U84(X1,X2,X3)
     U84(X1,active(X2),X3) -> U84(X1,X2,X3)
     U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
     U85(mark(X1),X2) -> U85(X1,X2)
     U85(X1,mark(X2)) -> U85(X1,X2)
     U85(active(X1),X2) -> U85(X1,X2)
     U85(X1,active(X2)) -> U85(X1,X2)
     U86(mark(X)) -> U86(X)
     U86(active(X)) -> U86(X)
     U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
     U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
     U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
     U91(active(X1),X2,X3) -> U91(X1,X2,X3)
     U91(X1,active(X2),X3) -> U91(X1,X2,X3)
     U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
     U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
     U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
     U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
     U92(active(X1),X2,X3) -> U92(X1,X2,X3)
     U92(X1,active(X2),X3) -> U92(X1,X2,X3)
     U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
     U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
     U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
     U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
     U93(active(X1),X2,X3) -> U93(X1,X2,X3)
     U93(X1,active(X2),X3) -> U93(X1,X2,X3)
     U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
     U94(mark(X1),X2) -> U94(X1,X2)
     U94(X1,mark(X2)) -> U94(X1,X2)
     U94(active(X1),X2) -> U94(X1,X2)
     U94(X1,active(X2)) -> U94(X1,X2)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     length(mark(X)) -> length(X)
     length(active(X)) -> length(X)
    SCC Processor:
     #sccs: 38
     #rules: 231
     #arcs: 4461/123904
     DPs:
      mark#(s(X)) -> mark#(X)
      mark#(length(X)) -> active#(length(mark(X)))
      active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N))
      mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3))
      active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N))
      mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3))
      active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N))
      mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3))
      active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L))
      mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2))
      active#(U94(tt(),L)) -> mark#(s(length(L)))
      mark#(U94(X1,X2)) -> mark#(X1)
      mark#(length(X)) -> mark#(X)
      mark#(U93(X1,X2,X3)) -> mark#(X1)
      mark#(U92(X1,X2,X3)) -> mark#(X1)
      mark#(U91(X1,X2,X3)) -> mark#(X1)
      mark#(U86(X)) -> mark#(X)
      mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2))
      active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2)))
      mark#(U85(X1,X2)) -> mark#(X1)
      mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3))
      active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2))
      mark#(U84(X1,X2,X3)) -> mark#(X1)
      mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3))
      active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2))
      mark#(U83(X1,X2,X3)) -> mark#(X1)
      mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3))
      active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2))
      mark#(U82(X1,X2,X3)) -> mark#(X1)
      mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3))
      active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2))
      mark#(U81(X1,X2,X3)) -> mark#(X1)
      mark#(U71(X)) -> mark#(X)
      mark#(U61(X)) -> mark#(X)
      mark#(U52(X)) -> mark#(X)
      mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
      active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2)))
      mark#(U51(X1,X2)) -> mark#(X1)
      mark#(isNatIList(X)) -> active#(isNatIList(X))
      active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2))
      mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
      active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2))
      mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
      active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2))
      mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
      active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2))
      mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
      active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2))
      mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
      active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2)))
      mark#(U46(X)) -> mark#(X)
      mark#(U45(X1,X2)) -> mark#(X1)
      mark#(U44(X1,X2,X3)) -> mark#(X1)
      mark#(U43(X1,X2,X3)) -> mark#(X1)
      mark#(U42(X1,X2,X3)) -> mark#(X1)
      mark#(U41(X1,X2,X3)) -> mark#(X1)
      mark#(U33(X)) -> mark#(X)
      mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
      active#(U32(tt(),V)) -> mark#(U33(isNatList(V)))
      mark#(U32(X1,X2)) -> mark#(X1)
      mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
      active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V))
      mark#(U31(X1,X2)) -> mark#(X1)
      mark#(isNat(X)) -> active#(isNat(X))
      active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1))
      mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
      active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1))
      mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
      active#(U22(tt(),V1)) -> mark#(U23(isNat(V1)))
      mark#(U23(X)) -> mark#(X)
      mark#(isNatKind(X)) -> active#(isNatKind(X))
      active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1)))
      active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1)))
      mark#(U22(X1,X2)) -> mark#(X1)
      mark#(U21(X1,X2)) -> mark#(X1)
      mark#(isNatList(X)) -> active#(isNatList(X))
      active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2))
      mark#(U13(X)) -> mark#(X)
      mark#(isNatIListKind(X)) -> active#(isNatIListKind(X))
      active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2))
      mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
      active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1)))
      mark#(U12(X1,X2)) -> mark#(X1)
      mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
      active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1))
      mark#(U11(X1,X2)) -> mark#(X1)
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(zeros()) -> active#(zeros())
      active#(zeros()) -> mark#(cons(0(),zeros()))
      active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1))
      active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V))
     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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      cons#(X1,active(X2)) -> cons#(X1,X2)
      cons#(active(X1),X2) -> cons#(X1,X2)
      cons#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      isNatIListKind#(mark(X)) -> isNatIListKind#(X)
      isNatIListKind#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U12#(mark(X1),X2) -> U12#(X1,X2)
      U12#(X1,active(X2)) -> U12#(X1,X2)
      U12#(active(X1),X2) -> U12#(X1,X2)
      U12#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      isNatList#(mark(X)) -> isNatList#(X)
      isNatList#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U13#(mark(X)) -> U13#(X)
      U13#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      isNatKind#(mark(X)) -> isNatKind#(X)
      isNatKind#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U22#(mark(X1),X2) -> U22#(X1,X2)
      U22#(X1,active(X2)) -> U22#(X1,X2)
      U22#(active(X1),X2) -> U22#(X1,X2)
      U22#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      isNat#(mark(X)) -> isNat#(X)
      isNat#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U23#(mark(X)) -> U23#(X)
      U23#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U32#(mark(X1),X2) -> U32#(X1,X2)
      U32#(X1,active(X2)) -> U32#(X1,X2)
      U32#(active(X1),X2) -> U32#(X1,X2)
      U32#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U33#(mark(X)) -> U33#(X)
      U33#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
      U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
      U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
      U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
      U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
      U42#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
      U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
      U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
      U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
      U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
      U43#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
      U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
      U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
      U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
      U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
      U44#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U45#(mark(X1),X2) -> U45#(X1,X2)
      U45#(X1,active(X2)) -> U45#(X1,X2)
      U45#(active(X1),X2) -> U45#(X1,X2)
      U45#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      isNatIList#(mark(X)) -> isNatIList#(X)
      isNatIList#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U46#(mark(X)) -> U46#(X)
      U46#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U52#(mark(X)) -> U52#(X)
      U52#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3)
      U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3)
      U82#(X1,active(X2),X3) -> U82#(X1,X2,X3)
      U82#(active(X1),X2,X3) -> U82#(X1,X2,X3)
      U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3)
      U82#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3)
      U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3)
      U83#(X1,active(X2),X3) -> U83#(X1,X2,X3)
      U83#(active(X1),X2,X3) -> U83#(X1,X2,X3)
      U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3)
      U83#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3)
      U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3)
      U84#(X1,active(X2),X3) -> U84#(X1,X2,X3)
      U84#(active(X1),X2,X3) -> U84#(X1,X2,X3)
      U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3)
      U84#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U85#(mark(X1),X2) -> U85#(X1,X2)
      U85#(X1,active(X2)) -> U85#(X1,X2)
      U85#(active(X1),X2) -> U85#(X1,X2)
      U85#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U86#(mark(X)) -> U86#(X)
      U86#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
      U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3)
      U92#(X1,active(X2),X3) -> U92#(X1,X2,X3)
      U92#(active(X1),X2,X3) -> U92#(X1,X2,X3)
      U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3)
      U92#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
      U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3)
      U93#(X1,active(X2),X3) -> U93#(X1,X2,X3)
      U93#(active(X1),X2,X3) -> U93#(X1,X2,X3)
      U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3)
      U93#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U94#(mark(X1),X2) -> U94#(X1,X2)
      U94#(X1,active(X2)) -> U94#(X1,X2)
      U94#(active(X1),X2) -> U94#(X1,X2)
      U94#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      length#(mark(X)) -> length#(X)
      length#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      s#(mark(X)) -> s#(X)
      s#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U11#(mark(X1),X2) -> U11#(X1,X2)
      U11#(X1,active(X2)) -> U11#(X1,X2)
      U11#(active(X1),X2) -> U11#(X1,X2)
      U11#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U21#(mark(X1),X2) -> U21#(X1,X2)
      U21#(X1,active(X2)) -> U21#(X1,X2)
      U21#(active(X1),X2) -> U21#(X1,X2)
      U21#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U31#(mark(X1),X2) -> U31#(X1,X2)
      U31#(X1,active(X2)) -> U31#(X1,X2)
      U31#(active(X1),X2) -> U31#(X1,X2)
      U31#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
      U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
      U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
      U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
      U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
      U41#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U51#(mark(X1),X2) -> U51#(X1,X2)
      U51#(X1,active(X2)) -> U51#(X1,X2)
      U51#(active(X1),X2) -> U51#(X1,X2)
      U51#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U61#(mark(X)) -> U61#(X)
      U61#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U71#(mark(X)) -> U71#(X)
      U71#(active(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3)
      U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3)
      U81#(X1,active(X2),X3) -> U81#(X1,X2,X3)
      U81#(active(X1),X2,X3) -> U81#(X1,X2,X3)
      U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3)
      U81#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open
     
     DPs:
      U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
      U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3)
      U91#(X1,active(X2),X3) -> U91#(X1,X2,X3)
      U91#(active(X1),X2,X3) -> U91#(X1,X2,X3)
      U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3)
      U91#(X1,mark(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))
      mark(zeros()) -> active(zeros())
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
      mark(0()) -> active(0())
      mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
      mark(isNatIListKind(X)) -> active(isNatIListKind(X))
      mark(U13(X)) -> active(U13(mark(X)))
      mark(isNatList(X)) -> active(isNatList(X))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(isNatKind(X)) -> active(isNatKind(X))
      mark(U23(X)) -> active(U23(mark(X)))
      mark(isNat(X)) -> active(isNat(X))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U33(X)) -> active(U33(mark(X)))
      mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
      mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
      mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
      mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
      mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
      mark(U46(X)) -> active(U46(mark(X)))
      mark(isNatIList(X)) -> active(isNatIList(X))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3))
      mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3))
      mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3))
      mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3))
      mark(U85(X1,X2)) -> active(U85(mark(X1),X2))
      mark(U86(X)) -> active(U86(mark(X)))
      mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3))
      mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3))
      mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3))
      mark(U94(X1,X2)) -> active(U94(mark(X1),X2))
      mark(s(X)) -> active(s(mark(X)))
      mark(length(X)) -> active(length(mark(X)))
      mark(nil()) -> active(nil())
      cons(mark(X1),X2) -> cons(X1,X2)
      cons(X1,mark(X2)) -> cons(X1,X2)
      cons(active(X1),X2) -> cons(X1,X2)
      cons(X1,active(X2)) -> cons(X1,X2)
      U11(mark(X1),X2) -> U11(X1,X2)
      U11(X1,mark(X2)) -> U11(X1,X2)
      U11(active(X1),X2) -> U11(X1,X2)
      U11(X1,active(X2)) -> U11(X1,X2)
      U12(mark(X1),X2) -> U12(X1,X2)
      U12(X1,mark(X2)) -> U12(X1,X2)
      U12(active(X1),X2) -> U12(X1,X2)
      U12(X1,active(X2)) -> U12(X1,X2)
      isNatIListKind(mark(X)) -> isNatIListKind(X)
      isNatIListKind(active(X)) -> isNatIListKind(X)
      U13(mark(X)) -> U13(X)
      U13(active(X)) -> U13(X)
      isNatList(mark(X)) -> isNatList(X)
      isNatList(active(X)) -> isNatList(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(X1,X2)
      isNatKind(mark(X)) -> isNatKind(X)
      isNatKind(active(X)) -> isNatKind(X)
      U23(mark(X)) -> U23(X)
      U23(active(X)) -> U23(X)
      isNat(mark(X)) -> isNat(X)
      isNat(active(X)) -> isNat(X)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U33(mark(X)) -> U33(X)
      U33(active(X)) -> U33(X)
      U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
      U41(active(X1),X2,X3) -> U41(X1,X2,X3)
      U41(X1,active(X2),X3) -> U41(X1,X2,X3)
      U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
      U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
      U42(active(X1),X2,X3) -> U42(X1,X2,X3)
      U42(X1,active(X2),X3) -> U42(X1,X2,X3)
      U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
      U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
      U43(active(X1),X2,X3) -> U43(X1,X2,X3)
      U43(X1,active(X2),X3) -> U43(X1,X2,X3)
      U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
      U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
      U44(active(X1),X2,X3) -> U44(X1,X2,X3)
      U44(X1,active(X2),X3) -> U44(X1,X2,X3)
      U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
      U45(mark(X1),X2) -> U45(X1,X2)
      U45(X1,mark(X2)) -> U45(X1,X2)
      U45(active(X1),X2) -> U45(X1,X2)
      U45(X1,active(X2)) -> U45(X1,X2)
      U46(mark(X)) -> U46(X)
      U46(active(X)) -> U46(X)
      isNatIList(mark(X)) -> isNatIList(X)
      isNatIList(active(X)) -> isNatIList(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,mark(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,mark(X3)) -> U81(X1,X2,X3)
      U81(active(X1),X2,X3) -> U81(X1,X2,X3)
      U81(X1,active(X2),X3) -> U81(X1,X2,X3)
      U81(X1,X2,active(X3)) -> U81(X1,X2,X3)
      U82(mark(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,mark(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,mark(X3)) -> U82(X1,X2,X3)
      U82(active(X1),X2,X3) -> U82(X1,X2,X3)
      U82(X1,active(X2),X3) -> U82(X1,X2,X3)
      U82(X1,X2,active(X3)) -> U82(X1,X2,X3)
      U83(mark(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,mark(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,mark(X3)) -> U83(X1,X2,X3)
      U83(active(X1),X2,X3) -> U83(X1,X2,X3)
      U83(X1,active(X2),X3) -> U83(X1,X2,X3)
      U83(X1,X2,active(X3)) -> U83(X1,X2,X3)
      U84(mark(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,mark(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,mark(X3)) -> U84(X1,X2,X3)
      U84(active(X1),X2,X3) -> U84(X1,X2,X3)
      U84(X1,active(X2),X3) -> U84(X1,X2,X3)
      U84(X1,X2,active(X3)) -> U84(X1,X2,X3)
      U85(mark(X1),X2) -> U85(X1,X2)
      U85(X1,mark(X2)) -> U85(X1,X2)
      U85(active(X1),X2) -> U85(X1,X2)
      U85(X1,active(X2)) -> U85(X1,X2)
      U86(mark(X)) -> U86(X)
      U86(active(X)) -> U86(X)
      U91(mark(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,mark(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,mark(X3)) -> U91(X1,X2,X3)
      U91(active(X1),X2,X3) -> U91(X1,X2,X3)
      U91(X1,active(X2),X3) -> U91(X1,X2,X3)
      U91(X1,X2,active(X3)) -> U91(X1,X2,X3)
      U92(mark(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,mark(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,mark(X3)) -> U92(X1,X2,X3)
      U92(active(X1),X2,X3) -> U92(X1,X2,X3)
      U92(X1,active(X2),X3) -> U92(X1,X2,X3)
      U92(X1,X2,active(X3)) -> U92(X1,X2,X3)
      U93(mark(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,mark(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,mark(X3)) -> U93(X1,X2,X3)
      U93(active(X1),X2,X3) -> U93(X1,X2,X3)
      U93(X1,active(X2),X3) -> U93(X1,X2,X3)
      U93(X1,X2,active(X3)) -> U93(X1,X2,X3)
      U94(mark(X1),X2) -> U94(X1,X2)
      U94(X1,mark(X2)) -> U94(X1,X2)
      U94(active(X1),X2) -> U94(X1,X2)
      U94(X1,active(X2)) -> U94(X1,X2)
      s(mark(X)) -> s(X)
      s(active(X)) -> s(X)
      length(mark(X)) -> length(X)
      length(active(X)) -> length(X)
     Open