MAYBE

Problem:
 active(zeros()) -> mark(cons(0(),zeros()))
 active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
 active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
 active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
 active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
 active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
 active(U106(tt())) -> mark(tt())
 active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
 active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
 active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
 active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
 active(U114(tt(),L)) -> mark(s(length(L)))
 active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
 active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
 active(U122(tt())) -> mark(nil())
 active(U13(tt())) -> mark(tt())
 active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
 active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
 active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
 active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
 active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
 active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
 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(),V2)) -> mark(U62(isNatIListKind(V2)))
 active(U62(tt())) -> mark(tt())
 active(U71(tt())) -> mark(tt())
 active(U81(tt())) -> mark(tt())
 active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
 active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
 active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
 active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
 active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
 active(U96(tt())) -> mark(tt())
 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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
 active(isNatKind(0())) -> mark(tt())
 active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
 active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
 active(isNatList(nil())) -> mark(tt())
 active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
 active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
 active(length(nil())) -> mark(0())
 active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
 active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
 active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
 active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
 active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
 active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
 active(U105(X1,X2)) -> U105(active(X1),X2)
 active(U106(X)) -> U106(active(X))
 active(U11(X1,X2)) -> U11(active(X1),X2)
 active(U12(X1,X2)) -> U12(active(X1),X2)
 active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
 active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
 active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
 active(U114(X1,X2)) -> U114(active(X1),X2)
 active(s(X)) -> s(active(X))
 active(length(X)) -> length(active(X))
 active(U13(X)) -> U13(active(X))
 active(U121(X1,X2)) -> U121(active(X1),X2)
 active(U122(X)) -> U122(active(X))
 active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
 active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
 active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
 active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
 active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
 active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
 active(take(X1,X2)) -> take(active(X1),X2)
 active(take(X1,X2)) -> take(X1,active(X2))
 active(U21(X1,X2)) -> U21(active(X1),X2)
 active(U22(X1,X2)) -> U22(active(X1),X2)
 active(U23(X)) -> U23(active(X))
 active(U31(X1,X2)) -> U31(active(X1),X2)
 active(U32(X1,X2)) -> U32(active(X1),X2)
 active(U33(X)) -> U33(active(X))
 active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
 active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
 active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
 active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
 active(U45(X1,X2)) -> U45(active(X1),X2)
 active(U46(X)) -> U46(active(X))
 active(U51(X1,X2)) -> U51(active(X1),X2)
 active(U52(X)) -> U52(active(X))
 active(U61(X1,X2)) -> U61(active(X1),X2)
 active(U62(X)) -> U62(active(X))
 active(U71(X)) -> U71(active(X))
 active(U81(X)) -> U81(active(X))
 active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
 active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
 active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
 active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
 active(U95(X1,X2)) -> U95(active(X1),X2)
 active(U96(X)) -> U96(active(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
 U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
 U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
 U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
 U105(mark(X1),X2) -> mark(U105(X1,X2))
 U106(mark(X)) -> mark(U106(X))
 U11(mark(X1),X2) -> mark(U11(X1,X2))
 U12(mark(X1),X2) -> mark(U12(X1,X2))
 U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
 U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
 U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
 U114(mark(X1),X2) -> mark(U114(X1,X2))
 s(mark(X)) -> mark(s(X))
 length(mark(X)) -> mark(length(X))
 U13(mark(X)) -> mark(U13(X))
 U121(mark(X1),X2) -> mark(U121(X1,X2))
 U122(mark(X)) -> mark(U122(X))
 U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
 U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
 U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
 U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
 U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
 U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
 take(mark(X1),X2) -> mark(take(X1,X2))
 take(X1,mark(X2)) -> mark(take(X1,X2))
 U21(mark(X1),X2) -> mark(U21(X1,X2))
 U22(mark(X1),X2) -> mark(U22(X1,X2))
 U23(mark(X)) -> mark(U23(X))
 U31(mark(X1),X2) -> mark(U31(X1,X2))
 U32(mark(X1),X2) -> mark(U32(X1,X2))
 U33(mark(X)) -> mark(U33(X))
 U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
 U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
 U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
 U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
 U45(mark(X1),X2) -> mark(U45(X1,X2))
 U46(mark(X)) -> mark(U46(X))
 U51(mark(X1),X2) -> mark(U51(X1,X2))
 U52(mark(X)) -> mark(U52(X))
 U61(mark(X1),X2) -> mark(U61(X1,X2))
 U62(mark(X)) -> mark(U62(X))
 U71(mark(X)) -> mark(U71(X))
 U81(mark(X)) -> mark(U81(X))
 U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
 U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
 U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
 U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
 U95(mark(X1),X2) -> mark(U95(X1,X2))
 U96(mark(X)) -> mark(U96(X))
 proper(zeros()) -> ok(zeros())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
 proper(tt()) -> ok(tt())
 proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
 proper(isNatKind(X)) -> isNatKind(proper(X))
 proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
 proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
 proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
 proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
 proper(isNat(X)) -> isNat(proper(X))
 proper(U106(X)) -> U106(proper(X))
 proper(isNatIList(X)) -> isNatIList(proper(X))
 proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
 proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
 proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
 proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
 proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
 proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
 proper(s(X)) -> s(proper(X))
 proper(length(X)) -> length(proper(X))
 proper(U13(X)) -> U13(proper(X))
 proper(isNatList(X)) -> isNatList(proper(X))
 proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
 proper(U122(X)) -> U122(proper(X))
 proper(nil()) -> ok(nil())
 proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
 proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
 proper(U23(X)) -> U23(proper(X))
 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
 proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
 proper(U33(X)) -> U33(proper(X))
 proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
 proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
 proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
 proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
 proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
 proper(U46(X)) -> U46(proper(X))
 proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
 proper(U52(X)) -> U52(proper(X))
 proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
 proper(U62(X)) -> U62(proper(X))
 proper(U71(X)) -> U71(proper(X))
 proper(U81(X)) -> U81(proper(X))
 proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
 proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
 proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
 proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
 proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
 proper(U96(X)) -> U96(proper(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
 U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
 isNatKind(ok(X)) -> ok(isNatKind(X))
 U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
 isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
 U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
 U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
 isNat(ok(X)) -> ok(isNat(X))
 U106(ok(X)) -> ok(U106(X))
 isNatIList(ok(X)) -> ok(isNatIList(X))
 U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
 U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
 U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
 U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
 U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
 U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
 s(ok(X)) -> ok(s(X))
 length(ok(X)) -> ok(length(X))
 U13(ok(X)) -> ok(U13(X))
 isNatList(ok(X)) -> ok(isNatList(X))
 U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
 U122(ok(X)) -> ok(U122(X))
 U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
 U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
 U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
 U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
 U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
 U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
 U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
 U23(ok(X)) -> ok(U23(X))
 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
 U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
 U33(ok(X)) -> ok(U33(X))
 U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
 U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
 U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
 U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
 U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
 U46(ok(X)) -> ok(U46(X))
 U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
 U52(ok(X)) -> ok(U52(X))
 U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
 U62(ok(X)) -> ok(U62(X))
 U71(ok(X)) -> ok(U71(X))
 U81(ok(X)) -> ok(U81(X))
 U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
 U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
 U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
 U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
 U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
 U96(ok(X)) -> ok(U96(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(zeros()) -> cons#(0(),zeros())
   active#(U101(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2)
   active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2)
   active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2)
   active#(U104(tt(),V1,V2)) -> isNat#(V1)
   active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2)
   active#(U105(tt(),V2)) -> isNatIList#(V2)
   active#(U105(tt(),V2)) -> U106#(isNatIList(V2))
   active#(U11(tt(),V1)) -> isNatIListKind#(V1)
   active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
   active#(U111(tt(),L,N)) -> isNatIListKind#(L)
   active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N)
   active#(U112(tt(),L,N)) -> isNat#(N)
   active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N)
   active#(U113(tt(),L,N)) -> isNatKind#(N)
   active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L)
   active#(U114(tt(),L)) -> length#(L)
   active#(U114(tt(),L)) -> s#(length(L))
   active#(U12(tt(),V1)) -> isNatList#(V1)
   active#(U12(tt(),V1)) -> U13#(isNatList(V1))
   active#(U121(tt(),IL)) -> isNatIListKind#(IL)
   active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL))
   active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL)
   active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N)
   active#(U132(tt(),IL,M,N)) -> isNat#(M)
   active#(U132(tt(),IL,M,N)) -> U133#(isNat(M),IL,M,N)
   active#(U133(tt(),IL,M,N)) -> isNatKind#(M)
   active#(U133(tt(),IL,M,N)) -> U134#(isNatKind(M),IL,M,N)
   active#(U134(tt(),IL,M,N)) -> isNat#(N)
   active#(U134(tt(),IL,M,N)) -> U135#(isNat(N),IL,M,N)
   active#(U135(tt(),IL,M,N)) -> isNatKind#(N)
   active#(U135(tt(),IL,M,N)) -> U136#(isNatKind(N),IL,M,N)
   active#(U136(tt(),IL,M,N)) -> take#(M,IL)
   active#(U136(tt(),IL,M,N)) -> cons#(N,take(M,IL))
   active#(U21(tt(),V1)) -> isNatKind#(V1)
   active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
   active#(U22(tt(),V1)) -> isNat#(V1)
   active#(U22(tt(),V1)) -> U23#(isNat(V1))
   active#(U31(tt(),V)) -> isNatIListKind#(V)
   active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
   active#(U32(tt(),V)) -> isNatList#(V)
   active#(U32(tt(),V)) -> U33#(isNatList(V))
   active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
   active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
   active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
   active#(U44(tt(),V1,V2)) -> isNat#(V1)
   active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
   active#(U45(tt(),V2)) -> isNatIList#(V2)
   active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
   active#(U51(tt(),V2)) -> isNatIListKind#(V2)
   active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
   active#(U61(tt(),V2)) -> isNatIListKind#(V2)
   active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2))
   active#(U91(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2)
   active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2)
   active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2)
   active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2)
   active#(U94(tt(),V1,V2)) -> isNat#(V1)
   active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2)
   active#(U95(tt(),V2)) -> isNatList#(V2)
   active#(U95(tt(),V2)) -> U96#(isNatList(V2))
   active#(isNat(length(V1))) -> isNatIListKind#(V1)
   active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
   active#(isNat(s(V1))) -> isNatKind#(V1)
   active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
   active#(isNatIList(V)) -> isNatIListKind#(V)
   active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
   active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
   active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
   active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1)
   active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2)
   active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
   active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1))
   active#(isNatKind(s(V1))) -> isNatKind#(V1)
   active#(isNatKind(s(V1))) -> U81#(isNatKind(V1))
   active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
   active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2)
   active#(isNatList(take(V1,V2))) -> isNatKind#(V1)
   active#(isNatList(take(V1,V2))) -> U101#(isNatKind(V1),V1,V2)
   active#(length(cons(N,L))) -> isNatList#(L)
   active#(length(cons(N,L))) -> U111#(isNatList(L),L,N)
   active#(take(0(),IL)) -> isNatIList#(IL)
   active#(take(0(),IL)) -> U121#(isNatIList(IL),IL)
   active#(take(s(M),cons(N,IL))) -> isNatIList#(IL)
   active#(take(s(M),cons(N,IL))) -> U131#(isNatIList(IL),IL,M,N)
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(U101(X1,X2,X3)) -> active#(X1)
   active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3)
   active#(U102(X1,X2,X3)) -> active#(X1)
   active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3)
   active#(U103(X1,X2,X3)) -> active#(X1)
   active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3)
   active#(U104(X1,X2,X3)) -> active#(X1)
   active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3)
   active#(U105(X1,X2)) -> active#(X1)
   active#(U105(X1,X2)) -> U105#(active(X1),X2)
   active#(U106(X)) -> active#(X)
   active#(U106(X)) -> U106#(active(X))
   active#(U11(X1,X2)) -> active#(X1)
   active#(U11(X1,X2)) -> U11#(active(X1),X2)
   active#(U12(X1,X2)) -> active#(X1)
   active#(U12(X1,X2)) -> U12#(active(X1),X2)
   active#(U111(X1,X2,X3)) -> active#(X1)
   active#(U111(X1,X2,X3)) -> U111#(active(X1),X2,X3)
   active#(U112(X1,X2,X3)) -> active#(X1)
   active#(U112(X1,X2,X3)) -> U112#(active(X1),X2,X3)
   active#(U113(X1,X2,X3)) -> active#(X1)
   active#(U113(X1,X2,X3)) -> U113#(active(X1),X2,X3)
   active#(U114(X1,X2)) -> active#(X1)
   active#(U114(X1,X2)) -> U114#(active(X1),X2)
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(length(X)) -> active#(X)
   active#(length(X)) -> length#(active(X))
   active#(U13(X)) -> active#(X)
   active#(U13(X)) -> U13#(active(X))
   active#(U121(X1,X2)) -> active#(X1)
   active#(U121(X1,X2)) -> U121#(active(X1),X2)
   active#(U122(X)) -> active#(X)
   active#(U122(X)) -> U122#(active(X))
   active#(U131(X1,X2,X3,X4)) -> active#(X1)
   active#(U131(X1,X2,X3,X4)) -> U131#(active(X1),X2,X3,X4)
   active#(U132(X1,X2,X3,X4)) -> active#(X1)
   active#(U132(X1,X2,X3,X4)) -> U132#(active(X1),X2,X3,X4)
   active#(U133(X1,X2,X3,X4)) -> active#(X1)
   active#(U133(X1,X2,X3,X4)) -> U133#(active(X1),X2,X3,X4)
   active#(U134(X1,X2,X3,X4)) -> active#(X1)
   active#(U134(X1,X2,X3,X4)) -> U134#(active(X1),X2,X3,X4)
   active#(U135(X1,X2,X3,X4)) -> active#(X1)
   active#(U135(X1,X2,X3,X4)) -> U135#(active(X1),X2,X3,X4)
   active#(U136(X1,X2,X3,X4)) -> active#(X1)
   active#(U136(X1,X2,X3,X4)) -> U136#(active(X1),X2,X3,X4)
   active#(take(X1,X2)) -> active#(X1)
   active#(take(X1,X2)) -> take#(active(X1),X2)
   active#(take(X1,X2)) -> active#(X2)
   active#(take(X1,X2)) -> take#(X1,active(X2))
   active#(U21(X1,X2)) -> active#(X1)
   active#(U21(X1,X2)) -> U21#(active(X1),X2)
   active#(U22(X1,X2)) -> active#(X1)
   active#(U22(X1,X2)) -> U22#(active(X1),X2)
   active#(U23(X)) -> active#(X)
   active#(U23(X)) -> U23#(active(X))
   active#(U31(X1,X2)) -> active#(X1)
   active#(U31(X1,X2)) -> U31#(active(X1),X2)
   active#(U32(X1,X2)) -> active#(X1)
   active#(U32(X1,X2)) -> U32#(active(X1),X2)
   active#(U33(X)) -> active#(X)
   active#(U33(X)) -> U33#(active(X))
   active#(U41(X1,X2,X3)) -> active#(X1)
   active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
   active#(U42(X1,X2,X3)) -> active#(X1)
   active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
   active#(U43(X1,X2,X3)) -> active#(X1)
   active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
   active#(U44(X1,X2,X3)) -> active#(X1)
   active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
   active#(U45(X1,X2)) -> active#(X1)
   active#(U45(X1,X2)) -> U45#(active(X1),X2)
   active#(U46(X)) -> active#(X)
   active#(U46(X)) -> U46#(active(X))
   active#(U51(X1,X2)) -> active#(X1)
   active#(U51(X1,X2)) -> U51#(active(X1),X2)
   active#(U52(X)) -> active#(X)
   active#(U52(X)) -> U52#(active(X))
   active#(U61(X1,X2)) -> active#(X1)
   active#(U61(X1,X2)) -> U61#(active(X1),X2)
   active#(U62(X)) -> active#(X)
   active#(U62(X)) -> U62#(active(X))
   active#(U71(X)) -> active#(X)
   active#(U71(X)) -> U71#(active(X))
   active#(U81(X)) -> active#(X)
   active#(U81(X)) -> U81#(active(X))
   active#(U91(X1,X2,X3)) -> active#(X1)
   active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
   active#(U92(X1,X2,X3)) -> active#(X1)
   active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
   active#(U93(X1,X2,X3)) -> active#(X1)
   active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
   active#(U94(X1,X2,X3)) -> active#(X1)
   active#(U94(X1,X2,X3)) -> U94#(active(X1),X2,X3)
   active#(U95(X1,X2)) -> active#(X1)
   active#(U95(X1,X2)) -> U95#(active(X1),X2)
   active#(U96(X)) -> active#(X)
   active#(U96(X)) -> U96#(active(X))
   cons#(mark(X1),X2) -> cons#(X1,X2)
   U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
   U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3)
   U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3)
   U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3)
   U105#(mark(X1),X2) -> U105#(X1,X2)
   U106#(mark(X)) -> U106#(X)
   U11#(mark(X1),X2) -> U11#(X1,X2)
   U12#(mark(X1),X2) -> U12#(X1,X2)
   U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3)
   U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3)
   U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3)
   U114#(mark(X1),X2) -> U114#(X1,X2)
   s#(mark(X)) -> s#(X)
   length#(mark(X)) -> length#(X)
   U13#(mark(X)) -> U13#(X)
   U121#(mark(X1),X2) -> U121#(X1,X2)
   U122#(mark(X)) -> U122#(X)
   U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4)
   U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4)
   U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4)
   U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4)
   U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4)
   U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4)
   take#(mark(X1),X2) -> take#(X1,X2)
   take#(X1,mark(X2)) -> take#(X1,X2)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U22#(mark(X1),X2) -> U22#(X1,X2)
   U23#(mark(X)) -> U23#(X)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U32#(mark(X1),X2) -> U32#(X1,X2)
   U33#(mark(X)) -> U33#(X)
   U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
   U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
   U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
   U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
   U45#(mark(X1),X2) -> U45#(X1,X2)
   U46#(mark(X)) -> U46#(X)
   U51#(mark(X1),X2) -> U51#(X1,X2)
   U52#(mark(X)) -> U52#(X)
   U61#(mark(X1),X2) -> U61#(X1,X2)
   U62#(mark(X)) -> U62#(X)
   U71#(mark(X)) -> U71#(X)
   U81#(mark(X)) -> U81#(X)
   U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
   U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
   U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
   U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3)
   U95#(mark(X1),X2) -> U95#(X1,X2)
   U96#(mark(X)) -> U96#(X)
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(U101(X1,X2,X3)) -> proper#(X3)
   proper#(U101(X1,X2,X3)) -> proper#(X2)
   proper#(U101(X1,X2,X3)) -> proper#(X1)
   proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3))
   proper#(U102(X1,X2,X3)) -> proper#(X3)
   proper#(U102(X1,X2,X3)) -> proper#(X2)
   proper#(U102(X1,X2,X3)) -> proper#(X1)
   proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3))
   proper#(isNatKind(X)) -> proper#(X)
   proper#(isNatKind(X)) -> isNatKind#(proper(X))
   proper#(U103(X1,X2,X3)) -> proper#(X3)
   proper#(U103(X1,X2,X3)) -> proper#(X2)
   proper#(U103(X1,X2,X3)) -> proper#(X1)
   proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3))
   proper#(isNatIListKind(X)) -> proper#(X)
   proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
   proper#(U104(X1,X2,X3)) -> proper#(X3)
   proper#(U104(X1,X2,X3)) -> proper#(X2)
   proper#(U104(X1,X2,X3)) -> proper#(X1)
   proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3))
   proper#(U105(X1,X2)) -> proper#(X2)
   proper#(U105(X1,X2)) -> proper#(X1)
   proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2))
   proper#(isNat(X)) -> proper#(X)
   proper#(isNat(X)) -> isNat#(proper(X))
   proper#(U106(X)) -> proper#(X)
   proper#(U106(X)) -> U106#(proper(X))
   proper#(isNatIList(X)) -> proper#(X)
   proper#(isNatIList(X)) -> isNatIList#(proper(X))
   proper#(U11(X1,X2)) -> proper#(X2)
   proper#(U11(X1,X2)) -> proper#(X1)
   proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
   proper#(U12(X1,X2)) -> proper#(X2)
   proper#(U12(X1,X2)) -> proper#(X1)
   proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
   proper#(U111(X1,X2,X3)) -> proper#(X3)
   proper#(U111(X1,X2,X3)) -> proper#(X2)
   proper#(U111(X1,X2,X3)) -> proper#(X1)
   proper#(U111(X1,X2,X3)) -> U111#(proper(X1),proper(X2),proper(X3))
   proper#(U112(X1,X2,X3)) -> proper#(X3)
   proper#(U112(X1,X2,X3)) -> proper#(X2)
   proper#(U112(X1,X2,X3)) -> proper#(X1)
   proper#(U112(X1,X2,X3)) -> U112#(proper(X1),proper(X2),proper(X3))
   proper#(U113(X1,X2,X3)) -> proper#(X3)
   proper#(U113(X1,X2,X3)) -> proper#(X2)
   proper#(U113(X1,X2,X3)) -> proper#(X1)
   proper#(U113(X1,X2,X3)) -> U113#(proper(X1),proper(X2),proper(X3))
   proper#(U114(X1,X2)) -> proper#(X2)
   proper#(U114(X1,X2)) -> proper#(X1)
   proper#(U114(X1,X2)) -> U114#(proper(X1),proper(X2))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(length(X)) -> proper#(X)
   proper#(length(X)) -> length#(proper(X))
   proper#(U13(X)) -> proper#(X)
   proper#(U13(X)) -> U13#(proper(X))
   proper#(isNatList(X)) -> proper#(X)
   proper#(isNatList(X)) -> isNatList#(proper(X))
   proper#(U121(X1,X2)) -> proper#(X2)
   proper#(U121(X1,X2)) -> proper#(X1)
   proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2))
   proper#(U122(X)) -> proper#(X)
   proper#(U122(X)) -> U122#(proper(X))
   proper#(U131(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U131(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U131(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U131(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U131(X1,X2,X3,X4)) -> U131#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(U132(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U132(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U132(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U132(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U132(X1,X2,X3,X4)) -> U132#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(U133(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U133(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U133(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U133(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U133(X1,X2,X3,X4)) -> U133#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(U134(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U134(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U134(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U134(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U134(X1,X2,X3,X4)) -> U134#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(U135(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U135(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U135(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U135(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U135(X1,X2,X3,X4)) -> U135#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(U136(X1,X2,X3,X4)) -> proper#(X4)
   proper#(U136(X1,X2,X3,X4)) -> proper#(X3)
   proper#(U136(X1,X2,X3,X4)) -> proper#(X2)
   proper#(U136(X1,X2,X3,X4)) -> proper#(X1)
   proper#(U136(X1,X2,X3,X4)) -> U136#(proper(X1),proper(X2),proper(X3),proper(X4))
   proper#(take(X1,X2)) -> proper#(X2)
   proper#(take(X1,X2)) -> proper#(X1)
   proper#(take(X1,X2)) -> take#(proper(X1),proper(X2))
   proper#(U21(X1,X2)) -> proper#(X2)
   proper#(U21(X1,X2)) -> proper#(X1)
   proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
   proper#(U22(X1,X2)) -> proper#(X2)
   proper#(U22(X1,X2)) -> proper#(X1)
   proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
   proper#(U23(X)) -> proper#(X)
   proper#(U23(X)) -> U23#(proper(X))
   proper#(U31(X1,X2)) -> proper#(X2)
   proper#(U31(X1,X2)) -> proper#(X1)
   proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
   proper#(U32(X1,X2)) -> proper#(X2)
   proper#(U32(X1,X2)) -> proper#(X1)
   proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
   proper#(U33(X)) -> proper#(X)
   proper#(U33(X)) -> U33#(proper(X))
   proper#(U41(X1,X2,X3)) -> proper#(X3)
   proper#(U41(X1,X2,X3)) -> proper#(X2)
   proper#(U41(X1,X2,X3)) -> proper#(X1)
   proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
   proper#(U42(X1,X2,X3)) -> proper#(X3)
   proper#(U42(X1,X2,X3)) -> proper#(X2)
   proper#(U42(X1,X2,X3)) -> proper#(X1)
   proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
   proper#(U43(X1,X2,X3)) -> proper#(X3)
   proper#(U43(X1,X2,X3)) -> proper#(X2)
   proper#(U43(X1,X2,X3)) -> proper#(X1)
   proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
   proper#(U44(X1,X2,X3)) -> proper#(X3)
   proper#(U44(X1,X2,X3)) -> proper#(X2)
   proper#(U44(X1,X2,X3)) -> proper#(X1)
   proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
   proper#(U45(X1,X2)) -> proper#(X2)
   proper#(U45(X1,X2)) -> proper#(X1)
   proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
   proper#(U46(X)) -> proper#(X)
   proper#(U46(X)) -> U46#(proper(X))
   proper#(U51(X1,X2)) -> proper#(X2)
   proper#(U51(X1,X2)) -> proper#(X1)
   proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
   proper#(U52(X)) -> proper#(X)
   proper#(U52(X)) -> U52#(proper(X))
   proper#(U61(X1,X2)) -> proper#(X2)
   proper#(U61(X1,X2)) -> proper#(X1)
   proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2))
   proper#(U62(X)) -> proper#(X)
   proper#(U62(X)) -> U62#(proper(X))
   proper#(U71(X)) -> proper#(X)
   proper#(U71(X)) -> U71#(proper(X))
   proper#(U81(X)) -> proper#(X)
   proper#(U81(X)) -> U81#(proper(X))
   proper#(U91(X1,X2,X3)) -> proper#(X3)
   proper#(U91(X1,X2,X3)) -> proper#(X2)
   proper#(U91(X1,X2,X3)) -> proper#(X1)
   proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
   proper#(U92(X1,X2,X3)) -> proper#(X3)
   proper#(U92(X1,X2,X3)) -> proper#(X2)
   proper#(U92(X1,X2,X3)) -> proper#(X1)
   proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
   proper#(U93(X1,X2,X3)) -> proper#(X3)
   proper#(U93(X1,X2,X3)) -> proper#(X2)
   proper#(U93(X1,X2,X3)) -> proper#(X1)
   proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
   proper#(U94(X1,X2,X3)) -> proper#(X3)
   proper#(U94(X1,X2,X3)) -> proper#(X2)
   proper#(U94(X1,X2,X3)) -> proper#(X1)
   proper#(U94(X1,X2,X3)) -> U94#(proper(X1),proper(X2),proper(X3))
   proper#(U95(X1,X2)) -> proper#(X2)
   proper#(U95(X1,X2)) -> proper#(X1)
   proper#(U95(X1,X2)) -> U95#(proper(X1),proper(X2))
   proper#(U96(X)) -> proper#(X)
   proper#(U96(X)) -> U96#(proper(X))
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3)
   U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3)
   isNatKind#(ok(X)) -> isNatKind#(X)
   U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3)
   isNatIListKind#(ok(X)) -> isNatIListKind#(X)
   U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3)
   U105#(ok(X1),ok(X2)) -> U105#(X1,X2)
   isNat#(ok(X)) -> isNat#(X)
   U106#(ok(X)) -> U106#(X)
   isNatIList#(ok(X)) -> isNatIList#(X)
   U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
   U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
   U111#(ok(X1),ok(X2),ok(X3)) -> U111#(X1,X2,X3)
   U112#(ok(X1),ok(X2),ok(X3)) -> U112#(X1,X2,X3)
   U113#(ok(X1),ok(X2),ok(X3)) -> U113#(X1,X2,X3)
   U114#(ok(X1),ok(X2)) -> U114#(X1,X2)
   s#(ok(X)) -> s#(X)
   length#(ok(X)) -> length#(X)
   U13#(ok(X)) -> U13#(X)
   isNatList#(ok(X)) -> isNatList#(X)
   U121#(ok(X1),ok(X2)) -> U121#(X1,X2)
   U122#(ok(X)) -> U122#(X)
   U131#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U131#(X1,X2,X3,X4)
   U132#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U132#(X1,X2,X3,X4)
   U133#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U133#(X1,X2,X3,X4)
   U134#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U134#(X1,X2,X3,X4)
   U135#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U135#(X1,X2,X3,X4)
   U136#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U136#(X1,X2,X3,X4)
   take#(ok(X1),ok(X2)) -> take#(X1,X2)
   U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
   U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
   U23#(ok(X)) -> U23#(X)
   U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
   U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
   U33#(ok(X)) -> U33#(X)
   U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
   U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
   U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
   U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
   U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
   U46#(ok(X)) -> U46#(X)
   U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
   U52#(ok(X)) -> U52#(X)
   U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
   U62#(ok(X)) -> U62#(X)
   U71#(ok(X)) -> U71#(X)
   U81#(ok(X)) -> U81#(X)
   U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
   U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
   U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
   U94#(ok(X1),ok(X2),ok(X3)) -> U94#(X1,X2,X3)
   U95#(ok(X1),ok(X2)) -> U95#(X1,X2)
   U96#(ok(X)) -> U96#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(zeros()) -> mark(cons(0(),zeros()))
   active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
   active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
   active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
   active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
   active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
   active(U106(tt())) -> mark(tt())
   active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
   active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
   active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
   active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
   active(U114(tt(),L)) -> mark(s(length(L)))
   active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
   active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
   active(U122(tt())) -> mark(nil())
   active(U13(tt())) -> mark(tt())
   active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
   active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
   active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
   active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
   active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
   active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
   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(),V2)) -> mark(U62(isNatIListKind(V2)))
   active(U62(tt())) -> mark(tt())
   active(U71(tt())) -> mark(tt())
   active(U81(tt())) -> mark(tt())
   active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
   active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
   active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
   active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
   active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
   active(U96(tt())) -> mark(tt())
   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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
   active(isNatKind(0())) -> mark(tt())
   active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
   active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
   active(isNatList(nil())) -> mark(tt())
   active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
   active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
   active(length(nil())) -> mark(0())
   active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
   active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
   active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
   active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
   active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
   active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
   active(U105(X1,X2)) -> U105(active(X1),X2)
   active(U106(X)) -> U106(active(X))
   active(U11(X1,X2)) -> U11(active(X1),X2)
   active(U12(X1,X2)) -> U12(active(X1),X2)
   active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
   active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
   active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
   active(U114(X1,X2)) -> U114(active(X1),X2)
   active(s(X)) -> s(active(X))
   active(length(X)) -> length(active(X))
   active(U13(X)) -> U13(active(X))
   active(U121(X1,X2)) -> U121(active(X1),X2)
   active(U122(X)) -> U122(active(X))
   active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
   active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
   active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
   active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
   active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
   active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
   active(take(X1,X2)) -> take(active(X1),X2)
   active(take(X1,X2)) -> take(X1,active(X2))
   active(U21(X1,X2)) -> U21(active(X1),X2)
   active(U22(X1,X2)) -> U22(active(X1),X2)
   active(U23(X)) -> U23(active(X))
   active(U31(X1,X2)) -> U31(active(X1),X2)
   active(U32(X1,X2)) -> U32(active(X1),X2)
   active(U33(X)) -> U33(active(X))
   active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
   active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
   active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
   active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
   active(U45(X1,X2)) -> U45(active(X1),X2)
   active(U46(X)) -> U46(active(X))
   active(U51(X1,X2)) -> U51(active(X1),X2)
   active(U52(X)) -> U52(active(X))
   active(U61(X1,X2)) -> U61(active(X1),X2)
   active(U62(X)) -> U62(active(X))
   active(U71(X)) -> U71(active(X))
   active(U81(X)) -> U81(active(X))
   active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
   active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
   active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
   active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
   active(U95(X1,X2)) -> U95(active(X1),X2)
   active(U96(X)) -> U96(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
   U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
   U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
   U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
   U105(mark(X1),X2) -> mark(U105(X1,X2))
   U106(mark(X)) -> mark(U106(X))
   U11(mark(X1),X2) -> mark(U11(X1,X2))
   U12(mark(X1),X2) -> mark(U12(X1,X2))
   U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
   U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
   U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
   U114(mark(X1),X2) -> mark(U114(X1,X2))
   s(mark(X)) -> mark(s(X))
   length(mark(X)) -> mark(length(X))
   U13(mark(X)) -> mark(U13(X))
   U121(mark(X1),X2) -> mark(U121(X1,X2))
   U122(mark(X)) -> mark(U122(X))
   U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
   U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
   U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
   U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
   U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
   U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
   take(mark(X1),X2) -> mark(take(X1,X2))
   take(X1,mark(X2)) -> mark(take(X1,X2))
   U21(mark(X1),X2) -> mark(U21(X1,X2))
   U22(mark(X1),X2) -> mark(U22(X1,X2))
   U23(mark(X)) -> mark(U23(X))
   U31(mark(X1),X2) -> mark(U31(X1,X2))
   U32(mark(X1),X2) -> mark(U32(X1,X2))
   U33(mark(X)) -> mark(U33(X))
   U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
   U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
   U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
   U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
   U45(mark(X1),X2) -> mark(U45(X1,X2))
   U46(mark(X)) -> mark(U46(X))
   U51(mark(X1),X2) -> mark(U51(X1,X2))
   U52(mark(X)) -> mark(U52(X))
   U61(mark(X1),X2) -> mark(U61(X1,X2))
   U62(mark(X)) -> mark(U62(X))
   U71(mark(X)) -> mark(U71(X))
   U81(mark(X)) -> mark(U81(X))
   U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
   U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
   U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
   U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
   U95(mark(X1),X2) -> mark(U95(X1,X2))
   U96(mark(X)) -> mark(U96(X))
   proper(zeros()) -> ok(zeros())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
   proper(tt()) -> ok(tt())
   proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
   proper(isNatKind(X)) -> isNatKind(proper(X))
   proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
   proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
   proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
   proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U106(X)) -> U106(proper(X))
   proper(isNatIList(X)) -> isNatIList(proper(X))
   proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
   proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
   proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
   proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
   proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
   proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(length(X)) -> length(proper(X))
   proper(U13(X)) -> U13(proper(X))
   proper(isNatList(X)) -> isNatList(proper(X))
   proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
   proper(U122(X)) -> U122(proper(X))
   proper(nil()) -> ok(nil())
   proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
   proper(take(X1,X2)) -> take(proper(X1),proper(X2))
   proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
   proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
   proper(U23(X)) -> U23(proper(X))
   proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
   proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
   proper(U33(X)) -> U33(proper(X))
   proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
   proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
   proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
   proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
   proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
   proper(U46(X)) -> U46(proper(X))
   proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
   proper(U52(X)) -> U52(proper(X))
   proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
   proper(U62(X)) -> U62(proper(X))
   proper(U71(X)) -> U71(proper(X))
   proper(U81(X)) -> U81(proper(X))
   proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
   proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
   proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
   proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
   proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
   proper(U96(X)) -> U96(proper(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
   U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
   isNatKind(ok(X)) -> ok(isNatKind(X))
   U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
   isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
   U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
   U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
   isNat(ok(X)) -> ok(isNat(X))
   U106(ok(X)) -> ok(U106(X))
   isNatIList(ok(X)) -> ok(isNatIList(X))
   U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
   U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
   U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
   U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
   U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
   U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
   s(ok(X)) -> ok(s(X))
   length(ok(X)) -> ok(length(X))
   U13(ok(X)) -> ok(U13(X))
   isNatList(ok(X)) -> ok(isNatList(X))
   U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
   U122(ok(X)) -> ok(U122(X))
   U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
   U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
   U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
   U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
   U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
   U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
   take(ok(X1),ok(X2)) -> ok(take(X1,X2))
   U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
   U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
   U23(ok(X)) -> ok(U23(X))
   U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
   U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
   U33(ok(X)) -> ok(U33(X))
   U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
   U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
   U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
   U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
   U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
   U46(ok(X)) -> ok(U46(X))
   U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
   U52(ok(X)) -> ok(U52(X))
   U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
   U62(ok(X)) -> ok(U62(X))
   U71(ok(X)) -> ok(U71(X))
   U81(ok(X)) -> ok(U81(X))
   U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
   U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
   U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
   U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
   U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
   U96(ok(X)) -> ok(U96(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Usable Rule Processor:
   DPs:
    active#(zeros()) -> cons#(0(),zeros())
    active#(U101(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2)
    active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2)
    active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2)
    active#(U104(tt(),V1,V2)) -> isNat#(V1)
    active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2)
    active#(U105(tt(),V2)) -> isNatIList#(V2)
    active#(U105(tt(),V2)) -> U106#(isNatIList(V2))
    active#(U11(tt(),V1)) -> isNatIListKind#(V1)
    active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
    active#(U111(tt(),L,N)) -> isNatIListKind#(L)
    active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N)
    active#(U112(tt(),L,N)) -> isNat#(N)
    active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N)
    active#(U113(tt(),L,N)) -> isNatKind#(N)
    active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L)
    active#(U114(tt(),L)) -> length#(L)
    active#(U114(tt(),L)) -> s#(length(L))
    active#(U12(tt(),V1)) -> isNatList#(V1)
    active#(U12(tt(),V1)) -> U13#(isNatList(V1))
    active#(U121(tt(),IL)) -> isNatIListKind#(IL)
    active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL))
    active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL)
    active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N)
    active#(U132(tt(),IL,M,N)) -> isNat#(M)
    active#(U132(tt(),IL,M,N)) -> U133#(isNat(M),IL,M,N)
    active#(U133(tt(),IL,M,N)) -> isNatKind#(M)
    active#(U133(tt(),IL,M,N)) -> U134#(isNatKind(M),IL,M,N)
    active#(U134(tt(),IL,M,N)) -> isNat#(N)
    active#(U134(tt(),IL,M,N)) -> U135#(isNat(N),IL,M,N)
    active#(U135(tt(),IL,M,N)) -> isNatKind#(N)
    active#(U135(tt(),IL,M,N)) -> U136#(isNatKind(N),IL,M,N)
    active#(U136(tt(),IL,M,N)) -> take#(M,IL)
    active#(U136(tt(),IL,M,N)) -> cons#(N,take(M,IL))
    active#(U21(tt(),V1)) -> isNatKind#(V1)
    active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
    active#(U22(tt(),V1)) -> isNat#(V1)
    active#(U22(tt(),V1)) -> U23#(isNat(V1))
    active#(U31(tt(),V)) -> isNatIListKind#(V)
    active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
    active#(U32(tt(),V)) -> isNatList#(V)
    active#(U32(tt(),V)) -> U33#(isNatList(V))
    active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
    active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
    active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
    active#(U44(tt(),V1,V2)) -> isNat#(V1)
    active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
    active#(U45(tt(),V2)) -> isNatIList#(V2)
    active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
    active#(U51(tt(),V2)) -> isNatIListKind#(V2)
    active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
    active#(U61(tt(),V2)) -> isNatIListKind#(V2)
    active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2))
    active#(U91(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2)
    active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2)
    active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2)
    active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2)
    active#(U94(tt(),V1,V2)) -> isNat#(V1)
    active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2)
    active#(U95(tt(),V2)) -> isNatList#(V2)
    active#(U95(tt(),V2)) -> U96#(isNatList(V2))
    active#(isNat(length(V1))) -> isNatIListKind#(V1)
    active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
    active#(isNat(s(V1))) -> isNatKind#(V1)
    active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
    active#(isNatIList(V)) -> isNatIListKind#(V)
    active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
    active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
    active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
    active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1)
    active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2)
    active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
    active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1))
    active#(isNatKind(s(V1))) -> isNatKind#(V1)
    active#(isNatKind(s(V1))) -> U81#(isNatKind(V1))
    active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
    active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2)
    active#(isNatList(take(V1,V2))) -> isNatKind#(V1)
    active#(isNatList(take(V1,V2))) -> U101#(isNatKind(V1),V1,V2)
    active#(length(cons(N,L))) -> isNatList#(L)
    active#(length(cons(N,L))) -> U111#(isNatList(L),L,N)
    active#(take(0(),IL)) -> isNatIList#(IL)
    active#(take(0(),IL)) -> U121#(isNatIList(IL),IL)
    active#(take(s(M),cons(N,IL))) -> isNatIList#(IL)
    active#(take(s(M),cons(N,IL))) -> U131#(isNatIList(IL),IL,M,N)
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(U101(X1,X2,X3)) -> active#(X1)
    active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3)
    active#(U102(X1,X2,X3)) -> active#(X1)
    active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3)
    active#(U103(X1,X2,X3)) -> active#(X1)
    active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3)
    active#(U104(X1,X2,X3)) -> active#(X1)
    active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3)
    active#(U105(X1,X2)) -> active#(X1)
    active#(U105(X1,X2)) -> U105#(active(X1),X2)
    active#(U106(X)) -> active#(X)
    active#(U106(X)) -> U106#(active(X))
    active#(U11(X1,X2)) -> active#(X1)
    active#(U11(X1,X2)) -> U11#(active(X1),X2)
    active#(U12(X1,X2)) -> active#(X1)
    active#(U12(X1,X2)) -> U12#(active(X1),X2)
    active#(U111(X1,X2,X3)) -> active#(X1)
    active#(U111(X1,X2,X3)) -> U111#(active(X1),X2,X3)
    active#(U112(X1,X2,X3)) -> active#(X1)
    active#(U112(X1,X2,X3)) -> U112#(active(X1),X2,X3)
    active#(U113(X1,X2,X3)) -> active#(X1)
    active#(U113(X1,X2,X3)) -> U113#(active(X1),X2,X3)
    active#(U114(X1,X2)) -> active#(X1)
    active#(U114(X1,X2)) -> U114#(active(X1),X2)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(length(X)) -> active#(X)
    active#(length(X)) -> length#(active(X))
    active#(U13(X)) -> active#(X)
    active#(U13(X)) -> U13#(active(X))
    active#(U121(X1,X2)) -> active#(X1)
    active#(U121(X1,X2)) -> U121#(active(X1),X2)
    active#(U122(X)) -> active#(X)
    active#(U122(X)) -> U122#(active(X))
    active#(U131(X1,X2,X3,X4)) -> active#(X1)
    active#(U131(X1,X2,X3,X4)) -> U131#(active(X1),X2,X3,X4)
    active#(U132(X1,X2,X3,X4)) -> active#(X1)
    active#(U132(X1,X2,X3,X4)) -> U132#(active(X1),X2,X3,X4)
    active#(U133(X1,X2,X3,X4)) -> active#(X1)
    active#(U133(X1,X2,X3,X4)) -> U133#(active(X1),X2,X3,X4)
    active#(U134(X1,X2,X3,X4)) -> active#(X1)
    active#(U134(X1,X2,X3,X4)) -> U134#(active(X1),X2,X3,X4)
    active#(U135(X1,X2,X3,X4)) -> active#(X1)
    active#(U135(X1,X2,X3,X4)) -> U135#(active(X1),X2,X3,X4)
    active#(U136(X1,X2,X3,X4)) -> active#(X1)
    active#(U136(X1,X2,X3,X4)) -> U136#(active(X1),X2,X3,X4)
    active#(take(X1,X2)) -> active#(X1)
    active#(take(X1,X2)) -> take#(active(X1),X2)
    active#(take(X1,X2)) -> active#(X2)
    active#(take(X1,X2)) -> take#(X1,active(X2))
    active#(U21(X1,X2)) -> active#(X1)
    active#(U21(X1,X2)) -> U21#(active(X1),X2)
    active#(U22(X1,X2)) -> active#(X1)
    active#(U22(X1,X2)) -> U22#(active(X1),X2)
    active#(U23(X)) -> active#(X)
    active#(U23(X)) -> U23#(active(X))
    active#(U31(X1,X2)) -> active#(X1)
    active#(U31(X1,X2)) -> U31#(active(X1),X2)
    active#(U32(X1,X2)) -> active#(X1)
    active#(U32(X1,X2)) -> U32#(active(X1),X2)
    active#(U33(X)) -> active#(X)
    active#(U33(X)) -> U33#(active(X))
    active#(U41(X1,X2,X3)) -> active#(X1)
    active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
    active#(U42(X1,X2,X3)) -> active#(X1)
    active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
    active#(U43(X1,X2,X3)) -> active#(X1)
    active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
    active#(U44(X1,X2,X3)) -> active#(X1)
    active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
    active#(U45(X1,X2)) -> active#(X1)
    active#(U45(X1,X2)) -> U45#(active(X1),X2)
    active#(U46(X)) -> active#(X)
    active#(U46(X)) -> U46#(active(X))
    active#(U51(X1,X2)) -> active#(X1)
    active#(U51(X1,X2)) -> U51#(active(X1),X2)
    active#(U52(X)) -> active#(X)
    active#(U52(X)) -> U52#(active(X))
    active#(U61(X1,X2)) -> active#(X1)
    active#(U61(X1,X2)) -> U61#(active(X1),X2)
    active#(U62(X)) -> active#(X)
    active#(U62(X)) -> U62#(active(X))
    active#(U71(X)) -> active#(X)
    active#(U71(X)) -> U71#(active(X))
    active#(U81(X)) -> active#(X)
    active#(U81(X)) -> U81#(active(X))
    active#(U91(X1,X2,X3)) -> active#(X1)
    active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
    active#(U92(X1,X2,X3)) -> active#(X1)
    active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
    active#(U93(X1,X2,X3)) -> active#(X1)
    active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
    active#(U94(X1,X2,X3)) -> active#(X1)
    active#(U94(X1,X2,X3)) -> U94#(active(X1),X2,X3)
    active#(U95(X1,X2)) -> active#(X1)
    active#(U95(X1,X2)) -> U95#(active(X1),X2)
    active#(U96(X)) -> active#(X)
    active#(U96(X)) -> U96#(active(X))
    cons#(mark(X1),X2) -> cons#(X1,X2)
    U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
    U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3)
    U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3)
    U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3)
    U105#(mark(X1),X2) -> U105#(X1,X2)
    U106#(mark(X)) -> U106#(X)
    U11#(mark(X1),X2) -> U11#(X1,X2)
    U12#(mark(X1),X2) -> U12#(X1,X2)
    U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3)
    U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3)
    U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3)
    U114#(mark(X1),X2) -> U114#(X1,X2)
    s#(mark(X)) -> s#(X)
    length#(mark(X)) -> length#(X)
    U13#(mark(X)) -> U13#(X)
    U121#(mark(X1),X2) -> U121#(X1,X2)
    U122#(mark(X)) -> U122#(X)
    U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4)
    U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4)
    U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4)
    U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4)
    U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4)
    U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4)
    take#(mark(X1),X2) -> take#(X1,X2)
    take#(X1,mark(X2)) -> take#(X1,X2)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U22#(mark(X1),X2) -> U22#(X1,X2)
    U23#(mark(X)) -> U23#(X)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U32#(mark(X1),X2) -> U32#(X1,X2)
    U33#(mark(X)) -> U33#(X)
    U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
    U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
    U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
    U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
    U45#(mark(X1),X2) -> U45#(X1,X2)
    U46#(mark(X)) -> U46#(X)
    U51#(mark(X1),X2) -> U51#(X1,X2)
    U52#(mark(X)) -> U52#(X)
    U61#(mark(X1),X2) -> U61#(X1,X2)
    U62#(mark(X)) -> U62#(X)
    U71#(mark(X)) -> U71#(X)
    U81#(mark(X)) -> U81#(X)
    U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
    U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
    U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
    U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3)
    U95#(mark(X1),X2) -> U95#(X1,X2)
    U96#(mark(X)) -> U96#(X)
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(U101(X1,X2,X3)) -> proper#(X3)
    proper#(U101(X1,X2,X3)) -> proper#(X2)
    proper#(U101(X1,X2,X3)) -> proper#(X1)
    proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3))
    proper#(U102(X1,X2,X3)) -> proper#(X3)
    proper#(U102(X1,X2,X3)) -> proper#(X2)
    proper#(U102(X1,X2,X3)) -> proper#(X1)
    proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3))
    proper#(isNatKind(X)) -> proper#(X)
    proper#(isNatKind(X)) -> isNatKind#(proper(X))
    proper#(U103(X1,X2,X3)) -> proper#(X3)
    proper#(U103(X1,X2,X3)) -> proper#(X2)
    proper#(U103(X1,X2,X3)) -> proper#(X1)
    proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3))
    proper#(isNatIListKind(X)) -> proper#(X)
    proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
    proper#(U104(X1,X2,X3)) -> proper#(X3)
    proper#(U104(X1,X2,X3)) -> proper#(X2)
    proper#(U104(X1,X2,X3)) -> proper#(X1)
    proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3))
    proper#(U105(X1,X2)) -> proper#(X2)
    proper#(U105(X1,X2)) -> proper#(X1)
    proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2))
    proper#(isNat(X)) -> proper#(X)
    proper#(isNat(X)) -> isNat#(proper(X))
    proper#(U106(X)) -> proper#(X)
    proper#(U106(X)) -> U106#(proper(X))
    proper#(isNatIList(X)) -> proper#(X)
    proper#(isNatIList(X)) -> isNatIList#(proper(X))
    proper#(U11(X1,X2)) -> proper#(X2)
    proper#(U11(X1,X2)) -> proper#(X1)
    proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
    proper#(U12(X1,X2)) -> proper#(X2)
    proper#(U12(X1,X2)) -> proper#(X1)
    proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
    proper#(U111(X1,X2,X3)) -> proper#(X3)
    proper#(U111(X1,X2,X3)) -> proper#(X2)
    proper#(U111(X1,X2,X3)) -> proper#(X1)
    proper#(U111(X1,X2,X3)) -> U111#(proper(X1),proper(X2),proper(X3))
    proper#(U112(X1,X2,X3)) -> proper#(X3)
    proper#(U112(X1,X2,X3)) -> proper#(X2)
    proper#(U112(X1,X2,X3)) -> proper#(X1)
    proper#(U112(X1,X2,X3)) -> U112#(proper(X1),proper(X2),proper(X3))
    proper#(U113(X1,X2,X3)) -> proper#(X3)
    proper#(U113(X1,X2,X3)) -> proper#(X2)
    proper#(U113(X1,X2,X3)) -> proper#(X1)
    proper#(U113(X1,X2,X3)) -> U113#(proper(X1),proper(X2),proper(X3))
    proper#(U114(X1,X2)) -> proper#(X2)
    proper#(U114(X1,X2)) -> proper#(X1)
    proper#(U114(X1,X2)) -> U114#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(length(X)) -> proper#(X)
    proper#(length(X)) -> length#(proper(X))
    proper#(U13(X)) -> proper#(X)
    proper#(U13(X)) -> U13#(proper(X))
    proper#(isNatList(X)) -> proper#(X)
    proper#(isNatList(X)) -> isNatList#(proper(X))
    proper#(U121(X1,X2)) -> proper#(X2)
    proper#(U121(X1,X2)) -> proper#(X1)
    proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2))
    proper#(U122(X)) -> proper#(X)
    proper#(U122(X)) -> U122#(proper(X))
    proper#(U131(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U131(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U131(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U131(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U131(X1,X2,X3,X4)) -> U131#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(U132(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U132(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U132(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U132(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U132(X1,X2,X3,X4)) -> U132#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(U133(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U133(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U133(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U133(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U133(X1,X2,X3,X4)) -> U133#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(U134(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U134(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U134(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U134(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U134(X1,X2,X3,X4)) -> U134#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(U135(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U135(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U135(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U135(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U135(X1,X2,X3,X4)) -> U135#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(U136(X1,X2,X3,X4)) -> proper#(X4)
    proper#(U136(X1,X2,X3,X4)) -> proper#(X3)
    proper#(U136(X1,X2,X3,X4)) -> proper#(X2)
    proper#(U136(X1,X2,X3,X4)) -> proper#(X1)
    proper#(U136(X1,X2,X3,X4)) -> U136#(proper(X1),proper(X2),proper(X3),proper(X4))
    proper#(take(X1,X2)) -> proper#(X2)
    proper#(take(X1,X2)) -> proper#(X1)
    proper#(take(X1,X2)) -> take#(proper(X1),proper(X2))
    proper#(U21(X1,X2)) -> proper#(X2)
    proper#(U21(X1,X2)) -> proper#(X1)
    proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
    proper#(U22(X1,X2)) -> proper#(X2)
    proper#(U22(X1,X2)) -> proper#(X1)
    proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
    proper#(U23(X)) -> proper#(X)
    proper#(U23(X)) -> U23#(proper(X))
    proper#(U31(X1,X2)) -> proper#(X2)
    proper#(U31(X1,X2)) -> proper#(X1)
    proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
    proper#(U32(X1,X2)) -> proper#(X2)
    proper#(U32(X1,X2)) -> proper#(X1)
    proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
    proper#(U33(X)) -> proper#(X)
    proper#(U33(X)) -> U33#(proper(X))
    proper#(U41(X1,X2,X3)) -> proper#(X3)
    proper#(U41(X1,X2,X3)) -> proper#(X2)
    proper#(U41(X1,X2,X3)) -> proper#(X1)
    proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
    proper#(U42(X1,X2,X3)) -> proper#(X3)
    proper#(U42(X1,X2,X3)) -> proper#(X2)
    proper#(U42(X1,X2,X3)) -> proper#(X1)
    proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
    proper#(U43(X1,X2,X3)) -> proper#(X3)
    proper#(U43(X1,X2,X3)) -> proper#(X2)
    proper#(U43(X1,X2,X3)) -> proper#(X1)
    proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
    proper#(U44(X1,X2,X3)) -> proper#(X3)
    proper#(U44(X1,X2,X3)) -> proper#(X2)
    proper#(U44(X1,X2,X3)) -> proper#(X1)
    proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
    proper#(U45(X1,X2)) -> proper#(X2)
    proper#(U45(X1,X2)) -> proper#(X1)
    proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
    proper#(U46(X)) -> proper#(X)
    proper#(U46(X)) -> U46#(proper(X))
    proper#(U51(X1,X2)) -> proper#(X2)
    proper#(U51(X1,X2)) -> proper#(X1)
    proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
    proper#(U52(X)) -> proper#(X)
    proper#(U52(X)) -> U52#(proper(X))
    proper#(U61(X1,X2)) -> proper#(X2)
    proper#(U61(X1,X2)) -> proper#(X1)
    proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2))
    proper#(U62(X)) -> proper#(X)
    proper#(U62(X)) -> U62#(proper(X))
    proper#(U71(X)) -> proper#(X)
    proper#(U71(X)) -> U71#(proper(X))
    proper#(U81(X)) -> proper#(X)
    proper#(U81(X)) -> U81#(proper(X))
    proper#(U91(X1,X2,X3)) -> proper#(X3)
    proper#(U91(X1,X2,X3)) -> proper#(X2)
    proper#(U91(X1,X2,X3)) -> proper#(X1)
    proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
    proper#(U92(X1,X2,X3)) -> proper#(X3)
    proper#(U92(X1,X2,X3)) -> proper#(X2)
    proper#(U92(X1,X2,X3)) -> proper#(X1)
    proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
    proper#(U93(X1,X2,X3)) -> proper#(X3)
    proper#(U93(X1,X2,X3)) -> proper#(X2)
    proper#(U93(X1,X2,X3)) -> proper#(X1)
    proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
    proper#(U94(X1,X2,X3)) -> proper#(X3)
    proper#(U94(X1,X2,X3)) -> proper#(X2)
    proper#(U94(X1,X2,X3)) -> proper#(X1)
    proper#(U94(X1,X2,X3)) -> U94#(proper(X1),proper(X2),proper(X3))
    proper#(U95(X1,X2)) -> proper#(X2)
    proper#(U95(X1,X2)) -> proper#(X1)
    proper#(U95(X1,X2)) -> U95#(proper(X1),proper(X2))
    proper#(U96(X)) -> proper#(X)
    proper#(U96(X)) -> U96#(proper(X))
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3)
    U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3)
    isNatKind#(ok(X)) -> isNatKind#(X)
    U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3)
    isNatIListKind#(ok(X)) -> isNatIListKind#(X)
    U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3)
    U105#(ok(X1),ok(X2)) -> U105#(X1,X2)
    isNat#(ok(X)) -> isNat#(X)
    U106#(ok(X)) -> U106#(X)
    isNatIList#(ok(X)) -> isNatIList#(X)
    U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
    U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
    U111#(ok(X1),ok(X2),ok(X3)) -> U111#(X1,X2,X3)
    U112#(ok(X1),ok(X2),ok(X3)) -> U112#(X1,X2,X3)
    U113#(ok(X1),ok(X2),ok(X3)) -> U113#(X1,X2,X3)
    U114#(ok(X1),ok(X2)) -> U114#(X1,X2)
    s#(ok(X)) -> s#(X)
    length#(ok(X)) -> length#(X)
    U13#(ok(X)) -> U13#(X)
    isNatList#(ok(X)) -> isNatList#(X)
    U121#(ok(X1),ok(X2)) -> U121#(X1,X2)
    U122#(ok(X)) -> U122#(X)
    U131#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U131#(X1,X2,X3,X4)
    U132#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U132#(X1,X2,X3,X4)
    U133#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U133#(X1,X2,X3,X4)
    U134#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U134#(X1,X2,X3,X4)
    U135#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U135#(X1,X2,X3,X4)
    U136#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U136#(X1,X2,X3,X4)
    take#(ok(X1),ok(X2)) -> take#(X1,X2)
    U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
    U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
    U23#(ok(X)) -> U23#(X)
    U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
    U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
    U33#(ok(X)) -> U33#(X)
    U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
    U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
    U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
    U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
    U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
    U46#(ok(X)) -> U46#(X)
    U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
    U52#(ok(X)) -> U52#(X)
    U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
    U62#(ok(X)) -> U62#(X)
    U71#(ok(X)) -> U71#(X)
    U81#(ok(X)) -> U81#(X)
    U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
    U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
    U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
    U94#(ok(X1),ok(X2),ok(X3)) -> U94#(X1,X2,X3)
    U95#(ok(X1),ok(X2)) -> U95#(X1,X2)
    U96#(ok(X)) -> U96#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    f120(x,y) -> x
    f120(x,y) -> y
    isNatKind(ok(X)) -> ok(isNatKind(X))
    isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
    isNat(ok(X)) -> ok(isNat(X))
    isNatIList(ok(X)) -> ok(isNatIList(X))
    length(mark(X)) -> mark(length(X))
    length(ok(X)) -> ok(length(X))
    isNatList(ok(X)) -> ok(isNatList(X))
    take(mark(X1),X2) -> mark(take(X1,X2))
    take(X1,mark(X2)) -> mark(take(X1,X2))
    take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    active(zeros()) -> mark(cons(0(),zeros()))
    active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
    active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
    active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
    active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
    active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
    active(U106(tt())) -> mark(tt())
    active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
    active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
    active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
    active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
    active(U114(tt(),L)) -> mark(s(length(L)))
    active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
    active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
    active(U122(tt())) -> mark(nil())
    active(U13(tt())) -> mark(tt())
    active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
    active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
    active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
    active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
    active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
    active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
    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(),V2)) -> mark(U62(isNatIListKind(V2)))
    active(U62(tt())) -> mark(tt())
    active(U71(tt())) -> mark(tt())
    active(U81(tt())) -> mark(tt())
    active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
    active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
    active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
    active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
    active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
    active(U96(tt())) -> mark(tt())
    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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
    active(isNatKind(0())) -> mark(tt())
    active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
    active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
    active(isNatList(nil())) -> mark(tt())
    active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
    active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
    active(length(nil())) -> mark(0())
    active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
    active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
    active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
    active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
    active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
    active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
    active(U105(X1,X2)) -> U105(active(X1),X2)
    active(U106(X)) -> U106(active(X))
    active(U11(X1,X2)) -> U11(active(X1),X2)
    active(U12(X1,X2)) -> U12(active(X1),X2)
    active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
    active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
    active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
    active(U114(X1,X2)) -> U114(active(X1),X2)
    active(s(X)) -> s(active(X))
    active(length(X)) -> length(active(X))
    active(U13(X)) -> U13(active(X))
    active(U121(X1,X2)) -> U121(active(X1),X2)
    active(U122(X)) -> U122(active(X))
    active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
    active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
    active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
    active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
    active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
    active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
    active(take(X1,X2)) -> take(active(X1),X2)
    active(take(X1,X2)) -> take(X1,active(X2))
    active(U21(X1,X2)) -> U21(active(X1),X2)
    active(U22(X1,X2)) -> U22(active(X1),X2)
    active(U23(X)) -> U23(active(X))
    active(U31(X1,X2)) -> U31(active(X1),X2)
    active(U32(X1,X2)) -> U32(active(X1),X2)
    active(U33(X)) -> U33(active(X))
    active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
    active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
    active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
    active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
    active(U45(X1,X2)) -> U45(active(X1),X2)
    active(U46(X)) -> U46(active(X))
    active(U51(X1,X2)) -> U51(active(X1),X2)
    active(U52(X)) -> U52(active(X))
    active(U61(X1,X2)) -> U61(active(X1),X2)
    active(U62(X)) -> U62(active(X))
    active(U71(X)) -> U71(active(X))
    active(U81(X)) -> U81(active(X))
    active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
    active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
    active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
    active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
    active(U95(X1,X2)) -> U95(active(X1),X2)
    active(U96(X)) -> U96(active(X))
    U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
    U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
    U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
    U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
    U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
    U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
    U105(mark(X1),X2) -> mark(U105(X1,X2))
    U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
    U106(mark(X)) -> mark(U106(X))
    U106(ok(X)) -> ok(U106(X))
    U12(mark(X1),X2) -> mark(U12(X1,X2))
    U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
    U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
    U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
    U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
    U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
    U114(mark(X1),X2) -> mark(U114(X1,X2))
    U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
    s(mark(X)) -> mark(s(X))
    s(ok(X)) -> ok(s(X))
    U13(mark(X)) -> mark(U13(X))
    U13(ok(X)) -> ok(U13(X))
    U122(mark(X)) -> mark(U122(X))
    U122(ok(X)) -> ok(U122(X))
    U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
    U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
    U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
    U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
    U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
    U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
    U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
    U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
    U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
    U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    U22(mark(X1),X2) -> mark(U22(X1,X2))
    U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
    U23(mark(X)) -> mark(U23(X))
    U23(ok(X)) -> ok(U23(X))
    U32(mark(X1),X2) -> mark(U32(X1,X2))
    U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
    U33(mark(X)) -> mark(U33(X))
    U33(ok(X)) -> ok(U33(X))
    U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
    U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
    U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
    U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
    U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
    U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
    U45(mark(X1),X2) -> mark(U45(X1,X2))
    U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
    U46(mark(X)) -> mark(U46(X))
    U46(ok(X)) -> ok(U46(X))
    U52(mark(X)) -> mark(U52(X))
    U52(ok(X)) -> ok(U52(X))
    U62(mark(X)) -> mark(U62(X))
    U62(ok(X)) -> ok(U62(X))
    U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
    U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
    U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
    U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
    U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
    U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
    U95(mark(X1),X2) -> mark(U95(X1,X2))
    U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
    U96(mark(X)) -> mark(U96(X))
    U96(ok(X)) -> ok(U96(X))
    U11(mark(X1),X2) -> mark(U11(X1,X2))
    U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
    U21(mark(X1),X2) -> mark(U21(X1,X2))
    U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
    U31(mark(X1),X2) -> mark(U31(X1,X2))
    U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
    U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
    U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
    U51(mark(X1),X2) -> mark(U51(X1,X2))
    U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
    U61(mark(X1),X2) -> mark(U61(X1,X2))
    U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
    U71(mark(X)) -> mark(U71(X))
    U71(ok(X)) -> ok(U71(X))
    U81(mark(X)) -> mark(U81(X))
    U81(ok(X)) -> ok(U81(X))
    U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
    U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
    U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
    U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
    U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
    U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
    U121(mark(X1),X2) -> mark(U121(X1,X2))
    U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
    U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
    U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
    proper(tt()) -> ok(tt())
    proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
    proper(isNatKind(X)) -> isNatKind(proper(X))
    proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
    proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
    proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
    proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
    proper(isNat(X)) -> isNat(proper(X))
    proper(U106(X)) -> U106(proper(X))
    proper(isNatIList(X)) -> isNatIList(proper(X))
    proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
    proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
    proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
    proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
    proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
    proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
    proper(s(X)) -> s(proper(X))
    proper(length(X)) -> length(proper(X))
    proper(U13(X)) -> U13(proper(X))
    proper(isNatList(X)) -> isNatList(proper(X))
    proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
    proper(U122(X)) -> U122(proper(X))
    proper(nil()) -> ok(nil())
    proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
    proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
    proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
    proper(U23(X)) -> U23(proper(X))
    proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
    proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
    proper(U33(X)) -> U33(proper(X))
    proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
    proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
    proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
    proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
    proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
    proper(U46(X)) -> U46(proper(X))
    proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
    proper(U52(X)) -> U52(proper(X))
    proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
    proper(U62(X)) -> U62(proper(X))
    proper(U71(X)) -> U71(proper(X))
    proper(U81(X)) -> U81(proper(X))
    proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
    proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
    proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
    proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
    proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
    proper(U96(X)) -> U96(proper(X))
   EDG Processor:
    DPs:
     active#(zeros()) -> cons#(0(),zeros())
     active#(U101(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2)
     active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2)
     active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2)
     active#(U104(tt(),V1,V2)) -> isNat#(V1)
     active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2)
     active#(U105(tt(),V2)) -> isNatIList#(V2)
     active#(U105(tt(),V2)) -> U106#(isNatIList(V2))
     active#(U11(tt(),V1)) -> isNatIListKind#(V1)
     active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
     active#(U111(tt(),L,N)) -> isNatIListKind#(L)
     active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N)
     active#(U112(tt(),L,N)) -> isNat#(N)
     active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N)
     active#(U113(tt(),L,N)) -> isNatKind#(N)
     active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L)
     active#(U114(tt(),L)) -> length#(L)
     active#(U114(tt(),L)) -> s#(length(L))
     active#(U12(tt(),V1)) -> isNatList#(V1)
     active#(U12(tt(),V1)) -> U13#(isNatList(V1))
     active#(U121(tt(),IL)) -> isNatIListKind#(IL)
     active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL))
     active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL)
     active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N)
     active#(U132(tt(),IL,M,N)) -> isNat#(M)
     active#(U132(tt(),IL,M,N)) -> U133#(isNat(M),IL,M,N)
     active#(U133(tt(),IL,M,N)) -> isNatKind#(M)
     active#(U133(tt(),IL,M,N)) -> U134#(isNatKind(M),IL,M,N)
     active#(U134(tt(),IL,M,N)) -> isNat#(N)
     active#(U134(tt(),IL,M,N)) -> U135#(isNat(N),IL,M,N)
     active#(U135(tt(),IL,M,N)) -> isNatKind#(N)
     active#(U135(tt(),IL,M,N)) -> U136#(isNatKind(N),IL,M,N)
     active#(U136(tt(),IL,M,N)) -> take#(M,IL)
     active#(U136(tt(),IL,M,N)) -> cons#(N,take(M,IL))
     active#(U21(tt(),V1)) -> isNatKind#(V1)
     active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
     active#(U22(tt(),V1)) -> isNat#(V1)
     active#(U22(tt(),V1)) -> U23#(isNat(V1))
     active#(U31(tt(),V)) -> isNatIListKind#(V)
     active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
     active#(U32(tt(),V)) -> isNatList#(V)
     active#(U32(tt(),V)) -> U33#(isNatList(V))
     active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
     active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
     active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
     active#(U44(tt(),V1,V2)) -> isNat#(V1)
     active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
     active#(U45(tt(),V2)) -> isNatIList#(V2)
     active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
     active#(U51(tt(),V2)) -> isNatIListKind#(V2)
     active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
     active#(U61(tt(),V2)) -> isNatIListKind#(V2)
     active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2))
     active#(U91(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2)
     active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2)
     active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2)
     active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2)
     active#(U94(tt(),V1,V2)) -> isNat#(V1)
     active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2)
     active#(U95(tt(),V2)) -> isNatList#(V2)
     active#(U95(tt(),V2)) -> U96#(isNatList(V2))
     active#(isNat(length(V1))) -> isNatIListKind#(V1)
     active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
     active#(isNat(s(V1))) -> isNatKind#(V1)
     active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
     active#(isNatIList(V)) -> isNatIListKind#(V)
     active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
     active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
     active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
     active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1)
     active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2)
     active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
     active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1))
     active#(isNatKind(s(V1))) -> isNatKind#(V1)
     active#(isNatKind(s(V1))) -> U81#(isNatKind(V1))
     active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
     active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2)
     active#(isNatList(take(V1,V2))) -> isNatKind#(V1)
     active#(isNatList(take(V1,V2))) -> U101#(isNatKind(V1),V1,V2)
     active#(length(cons(N,L))) -> isNatList#(L)
     active#(length(cons(N,L))) -> U111#(isNatList(L),L,N)
     active#(take(0(),IL)) -> isNatIList#(IL)
     active#(take(0(),IL)) -> U121#(isNatIList(IL),IL)
     active#(take(s(M),cons(N,IL))) -> isNatIList#(IL)
     active#(take(s(M),cons(N,IL))) -> U131#(isNatIList(IL),IL,M,N)
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(U101(X1,X2,X3)) -> active#(X1)
     active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3)
     active#(U102(X1,X2,X3)) -> active#(X1)
     active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3)
     active#(U103(X1,X2,X3)) -> active#(X1)
     active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3)
     active#(U104(X1,X2,X3)) -> active#(X1)
     active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3)
     active#(U105(X1,X2)) -> active#(X1)
     active#(U105(X1,X2)) -> U105#(active(X1),X2)
     active#(U106(X)) -> active#(X)
     active#(U106(X)) -> U106#(active(X))
     active#(U11(X1,X2)) -> active#(X1)
     active#(U11(X1,X2)) -> U11#(active(X1),X2)
     active#(U12(X1,X2)) -> active#(X1)
     active#(U12(X1,X2)) -> U12#(active(X1),X2)
     active#(U111(X1,X2,X3)) -> active#(X1)
     active#(U111(X1,X2,X3)) -> U111#(active(X1),X2,X3)
     active#(U112(X1,X2,X3)) -> active#(X1)
     active#(U112(X1,X2,X3)) -> U112#(active(X1),X2,X3)
     active#(U113(X1,X2,X3)) -> active#(X1)
     active#(U113(X1,X2,X3)) -> U113#(active(X1),X2,X3)
     active#(U114(X1,X2)) -> active#(X1)
     active#(U114(X1,X2)) -> U114#(active(X1),X2)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(length(X)) -> active#(X)
     active#(length(X)) -> length#(active(X))
     active#(U13(X)) -> active#(X)
     active#(U13(X)) -> U13#(active(X))
     active#(U121(X1,X2)) -> active#(X1)
     active#(U121(X1,X2)) -> U121#(active(X1),X2)
     active#(U122(X)) -> active#(X)
     active#(U122(X)) -> U122#(active(X))
     active#(U131(X1,X2,X3,X4)) -> active#(X1)
     active#(U131(X1,X2,X3,X4)) -> U131#(active(X1),X2,X3,X4)
     active#(U132(X1,X2,X3,X4)) -> active#(X1)
     active#(U132(X1,X2,X3,X4)) -> U132#(active(X1),X2,X3,X4)
     active#(U133(X1,X2,X3,X4)) -> active#(X1)
     active#(U133(X1,X2,X3,X4)) -> U133#(active(X1),X2,X3,X4)
     active#(U134(X1,X2,X3,X4)) -> active#(X1)
     active#(U134(X1,X2,X3,X4)) -> U134#(active(X1),X2,X3,X4)
     active#(U135(X1,X2,X3,X4)) -> active#(X1)
     active#(U135(X1,X2,X3,X4)) -> U135#(active(X1),X2,X3,X4)
     active#(U136(X1,X2,X3,X4)) -> active#(X1)
     active#(U136(X1,X2,X3,X4)) -> U136#(active(X1),X2,X3,X4)
     active#(take(X1,X2)) -> active#(X1)
     active#(take(X1,X2)) -> take#(active(X1),X2)
     active#(take(X1,X2)) -> active#(X2)
     active#(take(X1,X2)) -> take#(X1,active(X2))
     active#(U21(X1,X2)) -> active#(X1)
     active#(U21(X1,X2)) -> U21#(active(X1),X2)
     active#(U22(X1,X2)) -> active#(X1)
     active#(U22(X1,X2)) -> U22#(active(X1),X2)
     active#(U23(X)) -> active#(X)
     active#(U23(X)) -> U23#(active(X))
     active#(U31(X1,X2)) -> active#(X1)
     active#(U31(X1,X2)) -> U31#(active(X1),X2)
     active#(U32(X1,X2)) -> active#(X1)
     active#(U32(X1,X2)) -> U32#(active(X1),X2)
     active#(U33(X)) -> active#(X)
     active#(U33(X)) -> U33#(active(X))
     active#(U41(X1,X2,X3)) -> active#(X1)
     active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
     active#(U42(X1,X2,X3)) -> active#(X1)
     active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
     active#(U43(X1,X2,X3)) -> active#(X1)
     active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
     active#(U44(X1,X2,X3)) -> active#(X1)
     active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
     active#(U45(X1,X2)) -> active#(X1)
     active#(U45(X1,X2)) -> U45#(active(X1),X2)
     active#(U46(X)) -> active#(X)
     active#(U46(X)) -> U46#(active(X))
     active#(U51(X1,X2)) -> active#(X1)
     active#(U51(X1,X2)) -> U51#(active(X1),X2)
     active#(U52(X)) -> active#(X)
     active#(U52(X)) -> U52#(active(X))
     active#(U61(X1,X2)) -> active#(X1)
     active#(U61(X1,X2)) -> U61#(active(X1),X2)
     active#(U62(X)) -> active#(X)
     active#(U62(X)) -> U62#(active(X))
     active#(U71(X)) -> active#(X)
     active#(U71(X)) -> U71#(active(X))
     active#(U81(X)) -> active#(X)
     active#(U81(X)) -> U81#(active(X))
     active#(U91(X1,X2,X3)) -> active#(X1)
     active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
     active#(U92(X1,X2,X3)) -> active#(X1)
     active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
     active#(U93(X1,X2,X3)) -> active#(X1)
     active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
     active#(U94(X1,X2,X3)) -> active#(X1)
     active#(U94(X1,X2,X3)) -> U94#(active(X1),X2,X3)
     active#(U95(X1,X2)) -> active#(X1)
     active#(U95(X1,X2)) -> U95#(active(X1),X2)
     active#(U96(X)) -> active#(X)
     active#(U96(X)) -> U96#(active(X))
     cons#(mark(X1),X2) -> cons#(X1,X2)
     U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
     U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3)
     U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3)
     U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3)
     U105#(mark(X1),X2) -> U105#(X1,X2)
     U106#(mark(X)) -> U106#(X)
     U11#(mark(X1),X2) -> U11#(X1,X2)
     U12#(mark(X1),X2) -> U12#(X1,X2)
     U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3)
     U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3)
     U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3)
     U114#(mark(X1),X2) -> U114#(X1,X2)
     s#(mark(X)) -> s#(X)
     length#(mark(X)) -> length#(X)
     U13#(mark(X)) -> U13#(X)
     U121#(mark(X1),X2) -> U121#(X1,X2)
     U122#(mark(X)) -> U122#(X)
     U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4)
     U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4)
     U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4)
     U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4)
     U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4)
     U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4)
     take#(mark(X1),X2) -> take#(X1,X2)
     take#(X1,mark(X2)) -> take#(X1,X2)
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U22#(mark(X1),X2) -> U22#(X1,X2)
     U23#(mark(X)) -> U23#(X)
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U32#(mark(X1),X2) -> U32#(X1,X2)
     U33#(mark(X)) -> U33#(X)
     U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
     U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
     U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
     U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
     U45#(mark(X1),X2) -> U45#(X1,X2)
     U46#(mark(X)) -> U46#(X)
     U51#(mark(X1),X2) -> U51#(X1,X2)
     U52#(mark(X)) -> U52#(X)
     U61#(mark(X1),X2) -> U61#(X1,X2)
     U62#(mark(X)) -> U62#(X)
     U71#(mark(X)) -> U71#(X)
     U81#(mark(X)) -> U81#(X)
     U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
     U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
     U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
     U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3)
     U95#(mark(X1),X2) -> U95#(X1,X2)
     U96#(mark(X)) -> U96#(X)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(U101(X1,X2,X3)) -> proper#(X3)
     proper#(U101(X1,X2,X3)) -> proper#(X2)
     proper#(U101(X1,X2,X3)) -> proper#(X1)
     proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3))
     proper#(U102(X1,X2,X3)) -> proper#(X3)
     proper#(U102(X1,X2,X3)) -> proper#(X2)
     proper#(U102(X1,X2,X3)) -> proper#(X1)
     proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3))
     proper#(isNatKind(X)) -> proper#(X)
     proper#(isNatKind(X)) -> isNatKind#(proper(X))
     proper#(U103(X1,X2,X3)) -> proper#(X3)
     proper#(U103(X1,X2,X3)) -> proper#(X2)
     proper#(U103(X1,X2,X3)) -> proper#(X1)
     proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3))
     proper#(isNatIListKind(X)) -> proper#(X)
     proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
     proper#(U104(X1,X2,X3)) -> proper#(X3)
     proper#(U104(X1,X2,X3)) -> proper#(X2)
     proper#(U104(X1,X2,X3)) -> proper#(X1)
     proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3))
     proper#(U105(X1,X2)) -> proper#(X2)
     proper#(U105(X1,X2)) -> proper#(X1)
     proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2))
     proper#(isNat(X)) -> proper#(X)
     proper#(isNat(X)) -> isNat#(proper(X))
     proper#(U106(X)) -> proper#(X)
     proper#(U106(X)) -> U106#(proper(X))
     proper#(isNatIList(X)) -> proper#(X)
     proper#(isNatIList(X)) -> isNatIList#(proper(X))
     proper#(U11(X1,X2)) -> proper#(X2)
     proper#(U11(X1,X2)) -> proper#(X1)
     proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
     proper#(U12(X1,X2)) -> proper#(X2)
     proper#(U12(X1,X2)) -> proper#(X1)
     proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
     proper#(U111(X1,X2,X3)) -> proper#(X3)
     proper#(U111(X1,X2,X3)) -> proper#(X2)
     proper#(U111(X1,X2,X3)) -> proper#(X1)
     proper#(U111(X1,X2,X3)) -> U111#(proper(X1),proper(X2),proper(X3))
     proper#(U112(X1,X2,X3)) -> proper#(X3)
     proper#(U112(X1,X2,X3)) -> proper#(X2)
     proper#(U112(X1,X2,X3)) -> proper#(X1)
     proper#(U112(X1,X2,X3)) -> U112#(proper(X1),proper(X2),proper(X3))
     proper#(U113(X1,X2,X3)) -> proper#(X3)
     proper#(U113(X1,X2,X3)) -> proper#(X2)
     proper#(U113(X1,X2,X3)) -> proper#(X1)
     proper#(U113(X1,X2,X3)) -> U113#(proper(X1),proper(X2),proper(X3))
     proper#(U114(X1,X2)) -> proper#(X2)
     proper#(U114(X1,X2)) -> proper#(X1)
     proper#(U114(X1,X2)) -> U114#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(length(X)) -> proper#(X)
     proper#(length(X)) -> length#(proper(X))
     proper#(U13(X)) -> proper#(X)
     proper#(U13(X)) -> U13#(proper(X))
     proper#(isNatList(X)) -> proper#(X)
     proper#(isNatList(X)) -> isNatList#(proper(X))
     proper#(U121(X1,X2)) -> proper#(X2)
     proper#(U121(X1,X2)) -> proper#(X1)
     proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2))
     proper#(U122(X)) -> proper#(X)
     proper#(U122(X)) -> U122#(proper(X))
     proper#(U131(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U131(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U131(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U131(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U131(X1,X2,X3,X4)) -> U131#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(U132(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U132(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U132(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U132(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U132(X1,X2,X3,X4)) -> U132#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(U133(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U133(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U133(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U133(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U133(X1,X2,X3,X4)) -> U133#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(U134(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U134(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U134(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U134(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U134(X1,X2,X3,X4)) -> U134#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(U135(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U135(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U135(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U135(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U135(X1,X2,X3,X4)) -> U135#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(U136(X1,X2,X3,X4)) -> proper#(X4)
     proper#(U136(X1,X2,X3,X4)) -> proper#(X3)
     proper#(U136(X1,X2,X3,X4)) -> proper#(X2)
     proper#(U136(X1,X2,X3,X4)) -> proper#(X1)
     proper#(U136(X1,X2,X3,X4)) -> U136#(proper(X1),proper(X2),proper(X3),proper(X4))
     proper#(take(X1,X2)) -> proper#(X2)
     proper#(take(X1,X2)) -> proper#(X1)
     proper#(take(X1,X2)) -> take#(proper(X1),proper(X2))
     proper#(U21(X1,X2)) -> proper#(X2)
     proper#(U21(X1,X2)) -> proper#(X1)
     proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
     proper#(U22(X1,X2)) -> proper#(X2)
     proper#(U22(X1,X2)) -> proper#(X1)
     proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
     proper#(U23(X)) -> proper#(X)
     proper#(U23(X)) -> U23#(proper(X))
     proper#(U31(X1,X2)) -> proper#(X2)
     proper#(U31(X1,X2)) -> proper#(X1)
     proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
     proper#(U32(X1,X2)) -> proper#(X2)
     proper#(U32(X1,X2)) -> proper#(X1)
     proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
     proper#(U33(X)) -> proper#(X)
     proper#(U33(X)) -> U33#(proper(X))
     proper#(U41(X1,X2,X3)) -> proper#(X3)
     proper#(U41(X1,X2,X3)) -> proper#(X2)
     proper#(U41(X1,X2,X3)) -> proper#(X1)
     proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
     proper#(U42(X1,X2,X3)) -> proper#(X3)
     proper#(U42(X1,X2,X3)) -> proper#(X2)
     proper#(U42(X1,X2,X3)) -> proper#(X1)
     proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
     proper#(U43(X1,X2,X3)) -> proper#(X3)
     proper#(U43(X1,X2,X3)) -> proper#(X2)
     proper#(U43(X1,X2,X3)) -> proper#(X1)
     proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
     proper#(U44(X1,X2,X3)) -> proper#(X3)
     proper#(U44(X1,X2,X3)) -> proper#(X2)
     proper#(U44(X1,X2,X3)) -> proper#(X1)
     proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
     proper#(U45(X1,X2)) -> proper#(X2)
     proper#(U45(X1,X2)) -> proper#(X1)
     proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
     proper#(U46(X)) -> proper#(X)
     proper#(U46(X)) -> U46#(proper(X))
     proper#(U51(X1,X2)) -> proper#(X2)
     proper#(U51(X1,X2)) -> proper#(X1)
     proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
     proper#(U52(X)) -> proper#(X)
     proper#(U52(X)) -> U52#(proper(X))
     proper#(U61(X1,X2)) -> proper#(X2)
     proper#(U61(X1,X2)) -> proper#(X1)
     proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2))
     proper#(U62(X)) -> proper#(X)
     proper#(U62(X)) -> U62#(proper(X))
     proper#(U71(X)) -> proper#(X)
     proper#(U71(X)) -> U71#(proper(X))
     proper#(U81(X)) -> proper#(X)
     proper#(U81(X)) -> U81#(proper(X))
     proper#(U91(X1,X2,X3)) -> proper#(X3)
     proper#(U91(X1,X2,X3)) -> proper#(X2)
     proper#(U91(X1,X2,X3)) -> proper#(X1)
     proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
     proper#(U92(X1,X2,X3)) -> proper#(X3)
     proper#(U92(X1,X2,X3)) -> proper#(X2)
     proper#(U92(X1,X2,X3)) -> proper#(X1)
     proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
     proper#(U93(X1,X2,X3)) -> proper#(X3)
     proper#(U93(X1,X2,X3)) -> proper#(X2)
     proper#(U93(X1,X2,X3)) -> proper#(X1)
     proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
     proper#(U94(X1,X2,X3)) -> proper#(X3)
     proper#(U94(X1,X2,X3)) -> proper#(X2)
     proper#(U94(X1,X2,X3)) -> proper#(X1)
     proper#(U94(X1,X2,X3)) -> U94#(proper(X1),proper(X2),proper(X3))
     proper#(U95(X1,X2)) -> proper#(X2)
     proper#(U95(X1,X2)) -> proper#(X1)
     proper#(U95(X1,X2)) -> U95#(proper(X1),proper(X2))
     proper#(U96(X)) -> proper#(X)
     proper#(U96(X)) -> U96#(proper(X))
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3)
     U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3)
     isNatKind#(ok(X)) -> isNatKind#(X)
     U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3)
     isNatIListKind#(ok(X)) -> isNatIListKind#(X)
     U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3)
     U105#(ok(X1),ok(X2)) -> U105#(X1,X2)
     isNat#(ok(X)) -> isNat#(X)
     U106#(ok(X)) -> U106#(X)
     isNatIList#(ok(X)) -> isNatIList#(X)
     U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
     U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
     U111#(ok(X1),ok(X2),ok(X3)) -> U111#(X1,X2,X3)
     U112#(ok(X1),ok(X2),ok(X3)) -> U112#(X1,X2,X3)
     U113#(ok(X1),ok(X2),ok(X3)) -> U113#(X1,X2,X3)
     U114#(ok(X1),ok(X2)) -> U114#(X1,X2)
     s#(ok(X)) -> s#(X)
     length#(ok(X)) -> length#(X)
     U13#(ok(X)) -> U13#(X)
     isNatList#(ok(X)) -> isNatList#(X)
     U121#(ok(X1),ok(X2)) -> U121#(X1,X2)
     U122#(ok(X)) -> U122#(X)
     U131#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U131#(X1,X2,X3,X4)
     U132#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U132#(X1,X2,X3,X4)
     U133#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U133#(X1,X2,X3,X4)
     U134#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U134#(X1,X2,X3,X4)
     U135#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U135#(X1,X2,X3,X4)
     U136#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U136#(X1,X2,X3,X4)
     take#(ok(X1),ok(X2)) -> take#(X1,X2)
     U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
     U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
     U23#(ok(X)) -> U23#(X)
     U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
     U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
     U33#(ok(X)) -> U33#(X)
     U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
     U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
     U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
     U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
     U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
     U46#(ok(X)) -> U46#(X)
     U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
     U52#(ok(X)) -> U52#(X)
     U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
     U62#(ok(X)) -> U62#(X)
     U71#(ok(X)) -> U71#(X)
     U81#(ok(X)) -> U81#(X)
     U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
     U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
     U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
     U94#(ok(X1),ok(X2),ok(X3)) -> U94#(X1,X2,X3)
     U95#(ok(X1),ok(X2)) -> U95#(X1,X2)
     U96#(ok(X)) -> U96#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     f120(x,y) -> x
     f120(x,y) -> y
     isNatKind(ok(X)) -> ok(isNatKind(X))
     isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
     isNat(ok(X)) -> ok(isNat(X))
     isNatIList(ok(X)) -> ok(isNatIList(X))
     length(mark(X)) -> mark(length(X))
     length(ok(X)) -> ok(length(X))
     isNatList(ok(X)) -> ok(isNatList(X))
     take(mark(X1),X2) -> mark(take(X1,X2))
     take(X1,mark(X2)) -> mark(take(X1,X2))
     take(ok(X1),ok(X2)) -> ok(take(X1,X2))
     active(zeros()) -> mark(cons(0(),zeros()))
     active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
     active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
     active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
     active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
     active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
     active(U106(tt())) -> mark(tt())
     active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
     active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
     active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
     active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
     active(U114(tt(),L)) -> mark(s(length(L)))
     active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
     active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
     active(U122(tt())) -> mark(nil())
     active(U13(tt())) -> mark(tt())
     active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
     active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
     active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
     active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
     active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
     active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
     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(),V2)) -> mark(U62(isNatIListKind(V2)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt())) -> mark(tt())
     active(U81(tt())) -> mark(tt())
     active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
     active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
     active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
     active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
     active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
     active(U96(tt())) -> mark(tt())
     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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
     active(isNatKind(0())) -> mark(tt())
     active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
     active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
     active(isNatList(nil())) -> mark(tt())
     active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
     active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
     active(length(nil())) -> mark(0())
     active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
     active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
     active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
     active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
     active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
     active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
     active(U105(X1,X2)) -> U105(active(X1),X2)
     active(U106(X)) -> U106(active(X))
     active(U11(X1,X2)) -> U11(active(X1),X2)
     active(U12(X1,X2)) -> U12(active(X1),X2)
     active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
     active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
     active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
     active(U114(X1,X2)) -> U114(active(X1),X2)
     active(s(X)) -> s(active(X))
     active(length(X)) -> length(active(X))
     active(U13(X)) -> U13(active(X))
     active(U121(X1,X2)) -> U121(active(X1),X2)
     active(U122(X)) -> U122(active(X))
     active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
     active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
     active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
     active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
     active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
     active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
     active(take(X1,X2)) -> take(active(X1),X2)
     active(take(X1,X2)) -> take(X1,active(X2))
     active(U21(X1,X2)) -> U21(active(X1),X2)
     active(U22(X1,X2)) -> U22(active(X1),X2)
     active(U23(X)) -> U23(active(X))
     active(U31(X1,X2)) -> U31(active(X1),X2)
     active(U32(X1,X2)) -> U32(active(X1),X2)
     active(U33(X)) -> U33(active(X))
     active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
     active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
     active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
     active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
     active(U45(X1,X2)) -> U45(active(X1),X2)
     active(U46(X)) -> U46(active(X))
     active(U51(X1,X2)) -> U51(active(X1),X2)
     active(U52(X)) -> U52(active(X))
     active(U61(X1,X2)) -> U61(active(X1),X2)
     active(U62(X)) -> U62(active(X))
     active(U71(X)) -> U71(active(X))
     active(U81(X)) -> U81(active(X))
     active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
     active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
     active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
     active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
     active(U95(X1,X2)) -> U95(active(X1),X2)
     active(U96(X)) -> U96(active(X))
     U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
     U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
     U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
     U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
     U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
     U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
     U105(mark(X1),X2) -> mark(U105(X1,X2))
     U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
     U106(mark(X)) -> mark(U106(X))
     U106(ok(X)) -> ok(U106(X))
     U12(mark(X1),X2) -> mark(U12(X1,X2))
     U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
     U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
     U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
     U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
     U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
     U114(mark(X1),X2) -> mark(U114(X1,X2))
     U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
     s(mark(X)) -> mark(s(X))
     s(ok(X)) -> ok(s(X))
     U13(mark(X)) -> mark(U13(X))
     U13(ok(X)) -> ok(U13(X))
     U122(mark(X)) -> mark(U122(X))
     U122(ok(X)) -> ok(U122(X))
     U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
     U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
     U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
     U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
     U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
     U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
     U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
     U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
     U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
     U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     U22(mark(X1),X2) -> mark(U22(X1,X2))
     U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
     U23(mark(X)) -> mark(U23(X))
     U23(ok(X)) -> ok(U23(X))
     U32(mark(X1),X2) -> mark(U32(X1,X2))
     U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
     U33(mark(X)) -> mark(U33(X))
     U33(ok(X)) -> ok(U33(X))
     U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
     U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
     U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
     U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
     U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
     U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
     U45(mark(X1),X2) -> mark(U45(X1,X2))
     U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
     U46(mark(X)) -> mark(U46(X))
     U46(ok(X)) -> ok(U46(X))
     U52(mark(X)) -> mark(U52(X))
     U52(ok(X)) -> ok(U52(X))
     U62(mark(X)) -> mark(U62(X))
     U62(ok(X)) -> ok(U62(X))
     U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
     U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
     U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
     U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
     U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
     U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
     U95(mark(X1),X2) -> mark(U95(X1,X2))
     U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
     U96(mark(X)) -> mark(U96(X))
     U96(ok(X)) -> ok(U96(X))
     U11(mark(X1),X2) -> mark(U11(X1,X2))
     U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
     U21(mark(X1),X2) -> mark(U21(X1,X2))
     U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
     U31(mark(X1),X2) -> mark(U31(X1,X2))
     U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
     U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
     U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
     U51(mark(X1),X2) -> mark(U51(X1,X2))
     U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
     U61(mark(X1),X2) -> mark(U61(X1,X2))
     U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
     U71(mark(X)) -> mark(U71(X))
     U71(ok(X)) -> ok(U71(X))
     U81(mark(X)) -> mark(U81(X))
     U81(ok(X)) -> ok(U81(X))
     U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
     U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
     U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
     U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
     U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
     U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
     U121(mark(X1),X2) -> mark(U121(X1,X2))
     U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
     U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
     U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
     proper(tt()) -> ok(tt())
     proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
     proper(isNatKind(X)) -> isNatKind(proper(X))
     proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
     proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
     proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
     proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
     proper(isNat(X)) -> isNat(proper(X))
     proper(U106(X)) -> U106(proper(X))
     proper(isNatIList(X)) -> isNatIList(proper(X))
     proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
     proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
     proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
     proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
     proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
     proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
     proper(s(X)) -> s(proper(X))
     proper(length(X)) -> length(proper(X))
     proper(U13(X)) -> U13(proper(X))
     proper(isNatList(X)) -> isNatList(proper(X))
     proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
     proper(U122(X)) -> U122(proper(X))
     proper(nil()) -> ok(nil())
     proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
     proper(take(X1,X2)) -> take(proper(X1),proper(X2))
     proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
     proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
     proper(U23(X)) -> U23(proper(X))
     proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
     proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
     proper(U33(X)) -> U33(proper(X))
     proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
     proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
     proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
     proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
     proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
     proper(U46(X)) -> U46(proper(X))
     proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
     proper(U52(X)) -> U52(proper(X))
     proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
     proper(U62(X)) -> U62(proper(X))
     proper(U71(X)) -> U71(proper(X))
     proper(U81(X)) -> U81(proper(X))
     proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
     proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
     proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
     proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
     proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
     proper(U96(X)) -> U96(proper(X))
    graph:
     ...
    Restore Modifier:
     DPs:
      active#(zeros()) -> cons#(0(),zeros())
      active#(U101(tt(),V1,V2)) -> isNatKind#(V1)
      active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2)
      active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2)
      active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2)
      active#(U104(tt(),V1,V2)) -> isNat#(V1)
      active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2)
      active#(U105(tt(),V2)) -> isNatIList#(V2)
      active#(U105(tt(),V2)) -> U106#(isNatIList(V2))
      active#(U11(tt(),V1)) -> isNatIListKind#(V1)
      active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1)
      active#(U111(tt(),L,N)) -> isNatIListKind#(L)
      active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N)
      active#(U112(tt(),L,N)) -> isNat#(N)
      active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N)
      active#(U113(tt(),L,N)) -> isNatKind#(N)
      active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L)
      active#(U114(tt(),L)) -> length#(L)
      active#(U114(tt(),L)) -> s#(length(L))
      active#(U12(tt(),V1)) -> isNatList#(V1)
      active#(U12(tt(),V1)) -> U13#(isNatList(V1))
      active#(U121(tt(),IL)) -> isNatIListKind#(IL)
      active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL))
      active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL)
      active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N)
      active#(U132(tt(),IL,M,N)) -> isNat#(M)
      active#(U132(tt(),IL,M,N)) -> U133#(isNat(M),IL,M,N)
      active#(U133(tt(),IL,M,N)) -> isNatKind#(M)
      active#(U133(tt(),IL,M,N)) -> U134#(isNatKind(M),IL,M,N)
      active#(U134(tt(),IL,M,N)) -> isNat#(N)
      active#(U134(tt(),IL,M,N)) -> U135#(isNat(N),IL,M,N)
      active#(U135(tt(),IL,M,N)) -> isNatKind#(N)
      active#(U135(tt(),IL,M,N)) -> U136#(isNatKind(N),IL,M,N)
      active#(U136(tt(),IL,M,N)) -> take#(M,IL)
      active#(U136(tt(),IL,M,N)) -> cons#(N,take(M,IL))
      active#(U21(tt(),V1)) -> isNatKind#(V1)
      active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
      active#(U22(tt(),V1)) -> isNat#(V1)
      active#(U22(tt(),V1)) -> U23#(isNat(V1))
      active#(U31(tt(),V)) -> isNatIListKind#(V)
      active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V)
      active#(U32(tt(),V)) -> isNatList#(V)
      active#(U32(tt(),V)) -> U33#(isNatList(V))
      active#(U41(tt(),V1,V2)) -> isNatKind#(V1)
      active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2)
      active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2)
      active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2)
      active#(U44(tt(),V1,V2)) -> isNat#(V1)
      active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2)
      active#(U45(tt(),V2)) -> isNatIList#(V2)
      active#(U45(tt(),V2)) -> U46#(isNatIList(V2))
      active#(U51(tt(),V2)) -> isNatIListKind#(V2)
      active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2))
      active#(U61(tt(),V2)) -> isNatIListKind#(V2)
      active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2))
      active#(U91(tt(),V1,V2)) -> isNatKind#(V1)
      active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2)
      active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2)
      active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2)
      active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2)
      active#(U94(tt(),V1,V2)) -> isNat#(V1)
      active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2)
      active#(U95(tt(),V2)) -> isNatList#(V2)
      active#(U95(tt(),V2)) -> U96#(isNatList(V2))
      active#(isNat(length(V1))) -> isNatIListKind#(V1)
      active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1)
      active#(isNat(s(V1))) -> isNatKind#(V1)
      active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
      active#(isNatIList(V)) -> isNatIListKind#(V)
      active#(isNatIList(V)) -> U31#(isNatIListKind(V),V)
      active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1)
      active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2)
      active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1)
      active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2)
      active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1)
      active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2)
      active#(isNatKind(length(V1))) -> isNatIListKind#(V1)
      active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1))
      active#(isNatKind(s(V1))) -> isNatKind#(V1)
      active#(isNatKind(s(V1))) -> U81#(isNatKind(V1))
      active#(isNatList(cons(V1,V2))) -> isNatKind#(V1)
      active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2)
      active#(isNatList(take(V1,V2))) -> isNatKind#(V1)
      active#(isNatList(take(V1,V2))) -> U101#(isNatKind(V1),V1,V2)
      active#(length(cons(N,L))) -> isNatList#(L)
      active#(length(cons(N,L))) -> U111#(isNatList(L),L,N)
      active#(take(0(),IL)) -> isNatIList#(IL)
      active#(take(0(),IL)) -> U121#(isNatIList(IL),IL)
      active#(take(s(M),cons(N,IL))) -> isNatIList#(IL)
      active#(take(s(M),cons(N,IL))) -> U131#(isNatIList(IL),IL,M,N)
      active#(cons(X1,X2)) -> active#(X1)
      active#(cons(X1,X2)) -> cons#(active(X1),X2)
      active#(U101(X1,X2,X3)) -> active#(X1)
      active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3)
      active#(U102(X1,X2,X3)) -> active#(X1)
      active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3)
      active#(U103(X1,X2,X3)) -> active#(X1)
      active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3)
      active#(U104(X1,X2,X3)) -> active#(X1)
      active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3)
      active#(U105(X1,X2)) -> active#(X1)
      active#(U105(X1,X2)) -> U105#(active(X1),X2)
      active#(U106(X)) -> active#(X)
      active#(U106(X)) -> U106#(active(X))
      active#(U11(X1,X2)) -> active#(X1)
      active#(U11(X1,X2)) -> U11#(active(X1),X2)
      active#(U12(X1,X2)) -> active#(X1)
      active#(U12(X1,X2)) -> U12#(active(X1),X2)
      active#(U111(X1,X2,X3)) -> active#(X1)
      active#(U111(X1,X2,X3)) -> U111#(active(X1),X2,X3)
      active#(U112(X1,X2,X3)) -> active#(X1)
      active#(U112(X1,X2,X3)) -> U112#(active(X1),X2,X3)
      active#(U113(X1,X2,X3)) -> active#(X1)
      active#(U113(X1,X2,X3)) -> U113#(active(X1),X2,X3)
      active#(U114(X1,X2)) -> active#(X1)
      active#(U114(X1,X2)) -> U114#(active(X1),X2)
      active#(s(X)) -> active#(X)
      active#(s(X)) -> s#(active(X))
      active#(length(X)) -> active#(X)
      active#(length(X)) -> length#(active(X))
      active#(U13(X)) -> active#(X)
      active#(U13(X)) -> U13#(active(X))
      active#(U121(X1,X2)) -> active#(X1)
      active#(U121(X1,X2)) -> U121#(active(X1),X2)
      active#(U122(X)) -> active#(X)
      active#(U122(X)) -> U122#(active(X))
      active#(U131(X1,X2,X3,X4)) -> active#(X1)
      active#(U131(X1,X2,X3,X4)) -> U131#(active(X1),X2,X3,X4)
      active#(U132(X1,X2,X3,X4)) -> active#(X1)
      active#(U132(X1,X2,X3,X4)) -> U132#(active(X1),X2,X3,X4)
      active#(U133(X1,X2,X3,X4)) -> active#(X1)
      active#(U133(X1,X2,X3,X4)) -> U133#(active(X1),X2,X3,X4)
      active#(U134(X1,X2,X3,X4)) -> active#(X1)
      active#(U134(X1,X2,X3,X4)) -> U134#(active(X1),X2,X3,X4)
      active#(U135(X1,X2,X3,X4)) -> active#(X1)
      active#(U135(X1,X2,X3,X4)) -> U135#(active(X1),X2,X3,X4)
      active#(U136(X1,X2,X3,X4)) -> active#(X1)
      active#(U136(X1,X2,X3,X4)) -> U136#(active(X1),X2,X3,X4)
      active#(take(X1,X2)) -> active#(X1)
      active#(take(X1,X2)) -> take#(active(X1),X2)
      active#(take(X1,X2)) -> active#(X2)
      active#(take(X1,X2)) -> take#(X1,active(X2))
      active#(U21(X1,X2)) -> active#(X1)
      active#(U21(X1,X2)) -> U21#(active(X1),X2)
      active#(U22(X1,X2)) -> active#(X1)
      active#(U22(X1,X2)) -> U22#(active(X1),X2)
      active#(U23(X)) -> active#(X)
      active#(U23(X)) -> U23#(active(X))
      active#(U31(X1,X2)) -> active#(X1)
      active#(U31(X1,X2)) -> U31#(active(X1),X2)
      active#(U32(X1,X2)) -> active#(X1)
      active#(U32(X1,X2)) -> U32#(active(X1),X2)
      active#(U33(X)) -> active#(X)
      active#(U33(X)) -> U33#(active(X))
      active#(U41(X1,X2,X3)) -> active#(X1)
      active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
      active#(U42(X1,X2,X3)) -> active#(X1)
      active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
      active#(U43(X1,X2,X3)) -> active#(X1)
      active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
      active#(U44(X1,X2,X3)) -> active#(X1)
      active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
      active#(U45(X1,X2)) -> active#(X1)
      active#(U45(X1,X2)) -> U45#(active(X1),X2)
      active#(U46(X)) -> active#(X)
      active#(U46(X)) -> U46#(active(X))
      active#(U51(X1,X2)) -> active#(X1)
      active#(U51(X1,X2)) -> U51#(active(X1),X2)
      active#(U52(X)) -> active#(X)
      active#(U52(X)) -> U52#(active(X))
      active#(U61(X1,X2)) -> active#(X1)
      active#(U61(X1,X2)) -> U61#(active(X1),X2)
      active#(U62(X)) -> active#(X)
      active#(U62(X)) -> U62#(active(X))
      active#(U71(X)) -> active#(X)
      active#(U71(X)) -> U71#(active(X))
      active#(U81(X)) -> active#(X)
      active#(U81(X)) -> U81#(active(X))
      active#(U91(X1,X2,X3)) -> active#(X1)
      active#(U91(X1,X2,X3)) -> U91#(active(X1),X2,X3)
      active#(U92(X1,X2,X3)) -> active#(X1)
      active#(U92(X1,X2,X3)) -> U92#(active(X1),X2,X3)
      active#(U93(X1,X2,X3)) -> active#(X1)
      active#(U93(X1,X2,X3)) -> U93#(active(X1),X2,X3)
      active#(U94(X1,X2,X3)) -> active#(X1)
      active#(U94(X1,X2,X3)) -> U94#(active(X1),X2,X3)
      active#(U95(X1,X2)) -> active#(X1)
      active#(U95(X1,X2)) -> U95#(active(X1),X2)
      active#(U96(X)) -> active#(X)
      active#(U96(X)) -> U96#(active(X))
      cons#(mark(X1),X2) -> cons#(X1,X2)
      U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
      U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3)
      U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3)
      U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3)
      U105#(mark(X1),X2) -> U105#(X1,X2)
      U106#(mark(X)) -> U106#(X)
      U11#(mark(X1),X2) -> U11#(X1,X2)
      U12#(mark(X1),X2) -> U12#(X1,X2)
      U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3)
      U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3)
      U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3)
      U114#(mark(X1),X2) -> U114#(X1,X2)
      s#(mark(X)) -> s#(X)
      length#(mark(X)) -> length#(X)
      U13#(mark(X)) -> U13#(X)
      U121#(mark(X1),X2) -> U121#(X1,X2)
      U122#(mark(X)) -> U122#(X)
      U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4)
      U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4)
      U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4)
      U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4)
      U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4)
      U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4)
      take#(mark(X1),X2) -> take#(X1,X2)
      take#(X1,mark(X2)) -> take#(X1,X2)
      U21#(mark(X1),X2) -> U21#(X1,X2)
      U22#(mark(X1),X2) -> U22#(X1,X2)
      U23#(mark(X)) -> U23#(X)
      U31#(mark(X1),X2) -> U31#(X1,X2)
      U32#(mark(X1),X2) -> U32#(X1,X2)
      U33#(mark(X)) -> U33#(X)
      U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
      U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
      U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
      U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
      U45#(mark(X1),X2) -> U45#(X1,X2)
      U46#(mark(X)) -> U46#(X)
      U51#(mark(X1),X2) -> U51#(X1,X2)
      U52#(mark(X)) -> U52#(X)
      U61#(mark(X1),X2) -> U61#(X1,X2)
      U62#(mark(X)) -> U62#(X)
      U71#(mark(X)) -> U71#(X)
      U81#(mark(X)) -> U81#(X)
      U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
      U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
      U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
      U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3)
      U95#(mark(X1),X2) -> U95#(X1,X2)
      U96#(mark(X)) -> U96#(X)
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
      proper#(U101(X1,X2,X3)) -> proper#(X3)
      proper#(U101(X1,X2,X3)) -> proper#(X2)
      proper#(U101(X1,X2,X3)) -> proper#(X1)
      proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3))
      proper#(U102(X1,X2,X3)) -> proper#(X3)
      proper#(U102(X1,X2,X3)) -> proper#(X2)
      proper#(U102(X1,X2,X3)) -> proper#(X1)
      proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3))
      proper#(isNatKind(X)) -> proper#(X)
      proper#(isNatKind(X)) -> isNatKind#(proper(X))
      proper#(U103(X1,X2,X3)) -> proper#(X3)
      proper#(U103(X1,X2,X3)) -> proper#(X2)
      proper#(U103(X1,X2,X3)) -> proper#(X1)
      proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3))
      proper#(isNatIListKind(X)) -> proper#(X)
      proper#(isNatIListKind(X)) -> isNatIListKind#(proper(X))
      proper#(U104(X1,X2,X3)) -> proper#(X3)
      proper#(U104(X1,X2,X3)) -> proper#(X2)
      proper#(U104(X1,X2,X3)) -> proper#(X1)
      proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3))
      proper#(U105(X1,X2)) -> proper#(X2)
      proper#(U105(X1,X2)) -> proper#(X1)
      proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2))
      proper#(isNat(X)) -> proper#(X)
      proper#(isNat(X)) -> isNat#(proper(X))
      proper#(U106(X)) -> proper#(X)
      proper#(U106(X)) -> U106#(proper(X))
      proper#(isNatIList(X)) -> proper#(X)
      proper#(isNatIList(X)) -> isNatIList#(proper(X))
      proper#(U11(X1,X2)) -> proper#(X2)
      proper#(U11(X1,X2)) -> proper#(X1)
      proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
      proper#(U12(X1,X2)) -> proper#(X2)
      proper#(U12(X1,X2)) -> proper#(X1)
      proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
      proper#(U111(X1,X2,X3)) -> proper#(X3)
      proper#(U111(X1,X2,X3)) -> proper#(X2)
      proper#(U111(X1,X2,X3)) -> proper#(X1)
      proper#(U111(X1,X2,X3)) -> U111#(proper(X1),proper(X2),proper(X3))
      proper#(U112(X1,X2,X3)) -> proper#(X3)
      proper#(U112(X1,X2,X3)) -> proper#(X2)
      proper#(U112(X1,X2,X3)) -> proper#(X1)
      proper#(U112(X1,X2,X3)) -> U112#(proper(X1),proper(X2),proper(X3))
      proper#(U113(X1,X2,X3)) -> proper#(X3)
      proper#(U113(X1,X2,X3)) -> proper#(X2)
      proper#(U113(X1,X2,X3)) -> proper#(X1)
      proper#(U113(X1,X2,X3)) -> U113#(proper(X1),proper(X2),proper(X3))
      proper#(U114(X1,X2)) -> proper#(X2)
      proper#(U114(X1,X2)) -> proper#(X1)
      proper#(U114(X1,X2)) -> U114#(proper(X1),proper(X2))
      proper#(s(X)) -> proper#(X)
      proper#(s(X)) -> s#(proper(X))
      proper#(length(X)) -> proper#(X)
      proper#(length(X)) -> length#(proper(X))
      proper#(U13(X)) -> proper#(X)
      proper#(U13(X)) -> U13#(proper(X))
      proper#(isNatList(X)) -> proper#(X)
      proper#(isNatList(X)) -> isNatList#(proper(X))
      proper#(U121(X1,X2)) -> proper#(X2)
      proper#(U121(X1,X2)) -> proper#(X1)
      proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2))
      proper#(U122(X)) -> proper#(X)
      proper#(U122(X)) -> U122#(proper(X))
      proper#(U131(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U131(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U131(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U131(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U131(X1,X2,X3,X4)) -> U131#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(U132(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U132(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U132(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U132(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U132(X1,X2,X3,X4)) -> U132#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(U133(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U133(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U133(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U133(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U133(X1,X2,X3,X4)) -> U133#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(U134(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U134(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U134(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U134(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U134(X1,X2,X3,X4)) -> U134#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(U135(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U135(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U135(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U135(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U135(X1,X2,X3,X4)) -> U135#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(U136(X1,X2,X3,X4)) -> proper#(X4)
      proper#(U136(X1,X2,X3,X4)) -> proper#(X3)
      proper#(U136(X1,X2,X3,X4)) -> proper#(X2)
      proper#(U136(X1,X2,X3,X4)) -> proper#(X1)
      proper#(U136(X1,X2,X3,X4)) -> U136#(proper(X1),proper(X2),proper(X3),proper(X4))
      proper#(take(X1,X2)) -> proper#(X2)
      proper#(take(X1,X2)) -> proper#(X1)
      proper#(take(X1,X2)) -> take#(proper(X1),proper(X2))
      proper#(U21(X1,X2)) -> proper#(X2)
      proper#(U21(X1,X2)) -> proper#(X1)
      proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
      proper#(U22(X1,X2)) -> proper#(X2)
      proper#(U22(X1,X2)) -> proper#(X1)
      proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
      proper#(U23(X)) -> proper#(X)
      proper#(U23(X)) -> U23#(proper(X))
      proper#(U31(X1,X2)) -> proper#(X2)
      proper#(U31(X1,X2)) -> proper#(X1)
      proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
      proper#(U32(X1,X2)) -> proper#(X2)
      proper#(U32(X1,X2)) -> proper#(X1)
      proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
      proper#(U33(X)) -> proper#(X)
      proper#(U33(X)) -> U33#(proper(X))
      proper#(U41(X1,X2,X3)) -> proper#(X3)
      proper#(U41(X1,X2,X3)) -> proper#(X2)
      proper#(U41(X1,X2,X3)) -> proper#(X1)
      proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
      proper#(U42(X1,X2,X3)) -> proper#(X3)
      proper#(U42(X1,X2,X3)) -> proper#(X2)
      proper#(U42(X1,X2,X3)) -> proper#(X1)
      proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
      proper#(U43(X1,X2,X3)) -> proper#(X3)
      proper#(U43(X1,X2,X3)) -> proper#(X2)
      proper#(U43(X1,X2,X3)) -> proper#(X1)
      proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
      proper#(U44(X1,X2,X3)) -> proper#(X3)
      proper#(U44(X1,X2,X3)) -> proper#(X2)
      proper#(U44(X1,X2,X3)) -> proper#(X1)
      proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
      proper#(U45(X1,X2)) -> proper#(X2)
      proper#(U45(X1,X2)) -> proper#(X1)
      proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
      proper#(U46(X)) -> proper#(X)
      proper#(U46(X)) -> U46#(proper(X))
      proper#(U51(X1,X2)) -> proper#(X2)
      proper#(U51(X1,X2)) -> proper#(X1)
      proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
      proper#(U52(X)) -> proper#(X)
      proper#(U52(X)) -> U52#(proper(X))
      proper#(U61(X1,X2)) -> proper#(X2)
      proper#(U61(X1,X2)) -> proper#(X1)
      proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2))
      proper#(U62(X)) -> proper#(X)
      proper#(U62(X)) -> U62#(proper(X))
      proper#(U71(X)) -> proper#(X)
      proper#(U71(X)) -> U71#(proper(X))
      proper#(U81(X)) -> proper#(X)
      proper#(U81(X)) -> U81#(proper(X))
      proper#(U91(X1,X2,X3)) -> proper#(X3)
      proper#(U91(X1,X2,X3)) -> proper#(X2)
      proper#(U91(X1,X2,X3)) -> proper#(X1)
      proper#(U91(X1,X2,X3)) -> U91#(proper(X1),proper(X2),proper(X3))
      proper#(U92(X1,X2,X3)) -> proper#(X3)
      proper#(U92(X1,X2,X3)) -> proper#(X2)
      proper#(U92(X1,X2,X3)) -> proper#(X1)
      proper#(U92(X1,X2,X3)) -> U92#(proper(X1),proper(X2),proper(X3))
      proper#(U93(X1,X2,X3)) -> proper#(X3)
      proper#(U93(X1,X2,X3)) -> proper#(X2)
      proper#(U93(X1,X2,X3)) -> proper#(X1)
      proper#(U93(X1,X2,X3)) -> U93#(proper(X1),proper(X2),proper(X3))
      proper#(U94(X1,X2,X3)) -> proper#(X3)
      proper#(U94(X1,X2,X3)) -> proper#(X2)
      proper#(U94(X1,X2,X3)) -> proper#(X1)
      proper#(U94(X1,X2,X3)) -> U94#(proper(X1),proper(X2),proper(X3))
      proper#(U95(X1,X2)) -> proper#(X2)
      proper#(U95(X1,X2)) -> proper#(X1)
      proper#(U95(X1,X2)) -> U95#(proper(X1),proper(X2))
      proper#(U96(X)) -> proper#(X)
      proper#(U96(X)) -> U96#(proper(X))
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
      U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3)
      U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3)
      isNatKind#(ok(X)) -> isNatKind#(X)
      U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3)
      isNatIListKind#(ok(X)) -> isNatIListKind#(X)
      U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3)
      U105#(ok(X1),ok(X2)) -> U105#(X1,X2)
      isNat#(ok(X)) -> isNat#(X)
      U106#(ok(X)) -> U106#(X)
      isNatIList#(ok(X)) -> isNatIList#(X)
      U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
      U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
      U111#(ok(X1),ok(X2),ok(X3)) -> U111#(X1,X2,X3)
      U112#(ok(X1),ok(X2),ok(X3)) -> U112#(X1,X2,X3)
      U113#(ok(X1),ok(X2),ok(X3)) -> U113#(X1,X2,X3)
      U114#(ok(X1),ok(X2)) -> U114#(X1,X2)
      s#(ok(X)) -> s#(X)
      length#(ok(X)) -> length#(X)
      U13#(ok(X)) -> U13#(X)
      isNatList#(ok(X)) -> isNatList#(X)
      U121#(ok(X1),ok(X2)) -> U121#(X1,X2)
      U122#(ok(X)) -> U122#(X)
      U131#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U131#(X1,X2,X3,X4)
      U132#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U132#(X1,X2,X3,X4)
      U133#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U133#(X1,X2,X3,X4)
      U134#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U134#(X1,X2,X3,X4)
      U135#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U135#(X1,X2,X3,X4)
      U136#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U136#(X1,X2,X3,X4)
      take#(ok(X1),ok(X2)) -> take#(X1,X2)
      U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
      U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
      U23#(ok(X)) -> U23#(X)
      U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
      U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
      U33#(ok(X)) -> U33#(X)
      U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
      U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
      U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
      U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
      U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
      U46#(ok(X)) -> U46#(X)
      U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
      U52#(ok(X)) -> U52#(X)
      U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
      U62#(ok(X)) -> U62#(X)
      U71#(ok(X)) -> U71#(X)
      U81#(ok(X)) -> U81#(X)
      U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
      U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
      U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
      U94#(ok(X1),ok(X2),ok(X3)) -> U94#(X1,X2,X3)
      U95#(ok(X1),ok(X2)) -> U95#(X1,X2)
      U96#(ok(X)) -> U96#(X)
      top#(mark(X)) -> proper#(X)
      top#(mark(X)) -> top#(proper(X))
      top#(ok(X)) -> active#(X)
      top#(ok(X)) -> top#(active(X))
     TRS:
      active(zeros()) -> mark(cons(0(),zeros()))
      active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
      active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
      active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
      active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
      active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
      active(U106(tt())) -> mark(tt())
      active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
      active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
      active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
      active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
      active(U114(tt(),L)) -> mark(s(length(L)))
      active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
      active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
      active(U122(tt())) -> mark(nil())
      active(U13(tt())) -> mark(tt())
      active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
      active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
      active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
      active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
      active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
      active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
      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(),V2)) -> mark(U62(isNatIListKind(V2)))
      active(U62(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
      active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
      active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
      active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
      active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
      active(U96(tt())) -> mark(tt())
      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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
      active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
      active(isNatList(nil())) -> mark(tt())
      active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
      active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
      active(length(nil())) -> mark(0())
      active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
      active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
      active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
      active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
      active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
      active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
      active(U105(X1,X2)) -> U105(active(X1),X2)
      active(U106(X)) -> U106(active(X))
      active(U11(X1,X2)) -> U11(active(X1),X2)
      active(U12(X1,X2)) -> U12(active(X1),X2)
      active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
      active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
      active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
      active(U114(X1,X2)) -> U114(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(length(X)) -> length(active(X))
      active(U13(X)) -> U13(active(X))
      active(U121(X1,X2)) -> U121(active(X1),X2)
      active(U122(X)) -> U122(active(X))
      active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
      active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
      active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
      active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
      active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
      active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
      active(take(X1,X2)) -> take(active(X1),X2)
      active(take(X1,X2)) -> take(X1,active(X2))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X1,X2)) -> U32(active(X1),X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
      active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
      active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
      active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
      active(U45(X1,X2)) -> U45(active(X1),X2)
      active(U46(X)) -> U46(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X)) -> U52(active(X))
      active(U61(X1,X2)) -> U61(active(X1),X2)
      active(U62(X)) -> U62(active(X))
      active(U71(X)) -> U71(active(X))
      active(U81(X)) -> U81(active(X))
      active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
      active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
      active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
      active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
      active(U95(X1,X2)) -> U95(active(X1),X2)
      active(U96(X)) -> U96(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
      U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
      U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
      U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
      U105(mark(X1),X2) -> mark(U105(X1,X2))
      U106(mark(X)) -> mark(U106(X))
      U11(mark(X1),X2) -> mark(U11(X1,X2))
      U12(mark(X1),X2) -> mark(U12(X1,X2))
      U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
      U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
      U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
      U114(mark(X1),X2) -> mark(U114(X1,X2))
      s(mark(X)) -> mark(s(X))
      length(mark(X)) -> mark(length(X))
      U13(mark(X)) -> mark(U13(X))
      U121(mark(X1),X2) -> mark(U121(X1,X2))
      U122(mark(X)) -> mark(U122(X))
      U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
      U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
      U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
      U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
      U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
      U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
      take(mark(X1),X2) -> mark(take(X1,X2))
      take(X1,mark(X2)) -> mark(take(X1,X2))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X1),X2) -> mark(U32(X1,X2))
      U33(mark(X)) -> mark(U33(X))
      U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
      U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
      U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
      U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
      U45(mark(X1),X2) -> mark(U45(X1,X2))
      U46(mark(X)) -> mark(U46(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X)) -> mark(U52(X))
      U61(mark(X1),X2) -> mark(U61(X1,X2))
      U62(mark(X)) -> mark(U62(X))
      U71(mark(X)) -> mark(U71(X))
      U81(mark(X)) -> mark(U81(X))
      U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
      U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
      U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
      U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
      U95(mark(X1),X2) -> mark(U95(X1,X2))
      U96(mark(X)) -> mark(U96(X))
      proper(zeros()) -> ok(zeros())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
      proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
      proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
      proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U106(X)) -> U106(proper(X))
      proper(isNatIList(X)) -> isNatIList(proper(X))
      proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
      proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
      proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
      proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
      proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
      proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(length(X)) -> length(proper(X))
      proper(U13(X)) -> U13(proper(X))
      proper(isNatList(X)) -> isNatList(proper(X))
      proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
      proper(U122(X)) -> U122(proper(X))
      proper(nil()) -> ok(nil())
      proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
      proper(take(X1,X2)) -> take(proper(X1),proper(X2))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(U23(X)) -> U23(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
      proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
      proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
      proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
      proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
      proper(U46(X)) -> U46(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X)) -> U52(proper(X))
      proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
      proper(U62(X)) -> U62(proper(X))
      proper(U71(X)) -> U71(proper(X))
      proper(U81(X)) -> U81(proper(X))
      proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
      proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
      proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
      proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
      proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
      proper(U96(X)) -> U96(proper(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
      U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
      isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
      U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
      U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
      isNat(ok(X)) -> ok(isNat(X))
      U106(ok(X)) -> ok(U106(X))
      isNatIList(ok(X)) -> ok(isNatIList(X))
      U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
      U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
      U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
      U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
      U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
      U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
      s(ok(X)) -> ok(s(X))
      length(ok(X)) -> ok(length(X))
      U13(ok(X)) -> ok(U13(X))
      isNatList(ok(X)) -> ok(isNatList(X))
      U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
      U122(ok(X)) -> ok(U122(X))
      U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
      U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
      U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
      U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
      U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
      U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
      take(ok(X1),ok(X2)) -> ok(take(X1,X2))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      U23(ok(X)) -> ok(U23(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
      U33(ok(X)) -> ok(U33(X))
      U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
      U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
      U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
      U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
      U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
      U46(ok(X)) -> ok(U46(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X)) -> ok(U52(X))
      U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
      U62(ok(X)) -> ok(U62(X))
      U71(ok(X)) -> ok(U71(X))
      U81(ok(X)) -> ok(U81(X))
      U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
      U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
      U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
      U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
      U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
      U96(ok(X)) -> ok(U96(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     SCC Processor:
      #sccs: 57
      #rules: 273
      #arcs: 30687/224676
      DPs:
       top#(ok(X)) -> top#(active(X))
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       proper#(U96(X)) -> proper#(X)
       proper#(U95(X1,X2)) -> proper#(X1)
       proper#(U95(X1,X2)) -> proper#(X2)
       proper#(U94(X1,X2,X3)) -> proper#(X1)
       proper#(U94(X1,X2,X3)) -> proper#(X2)
       proper#(U94(X1,X2,X3)) -> proper#(X3)
       proper#(U93(X1,X2,X3)) -> proper#(X1)
       proper#(U93(X1,X2,X3)) -> proper#(X2)
       proper#(U93(X1,X2,X3)) -> proper#(X3)
       proper#(U92(X1,X2,X3)) -> proper#(X1)
       proper#(U92(X1,X2,X3)) -> proper#(X2)
       proper#(U92(X1,X2,X3)) -> proper#(X3)
       proper#(U91(X1,X2,X3)) -> proper#(X1)
       proper#(U91(X1,X2,X3)) -> proper#(X2)
       proper#(U91(X1,X2,X3)) -> proper#(X3)
       proper#(U81(X)) -> proper#(X)
       proper#(U71(X)) -> proper#(X)
       proper#(U62(X)) -> proper#(X)
       proper#(U61(X1,X2)) -> proper#(X1)
       proper#(U61(X1,X2)) -> proper#(X2)
       proper#(U52(X)) -> proper#(X)
       proper#(U51(X1,X2)) -> proper#(X1)
       proper#(U51(X1,X2)) -> proper#(X2)
       proper#(U46(X)) -> proper#(X)
       proper#(U45(X1,X2)) -> proper#(X1)
       proper#(U45(X1,X2)) -> proper#(X2)
       proper#(U44(X1,X2,X3)) -> proper#(X1)
       proper#(U44(X1,X2,X3)) -> proper#(X2)
       proper#(U44(X1,X2,X3)) -> proper#(X3)
       proper#(U43(X1,X2,X3)) -> proper#(X1)
       proper#(U43(X1,X2,X3)) -> proper#(X2)
       proper#(U43(X1,X2,X3)) -> proper#(X3)
       proper#(U42(X1,X2,X3)) -> proper#(X1)
       proper#(U42(X1,X2,X3)) -> proper#(X2)
       proper#(U42(X1,X2,X3)) -> proper#(X3)
       proper#(U41(X1,X2,X3)) -> proper#(X1)
       proper#(U41(X1,X2,X3)) -> proper#(X2)
       proper#(U41(X1,X2,X3)) -> proper#(X3)
       proper#(U33(X)) -> proper#(X)
       proper#(U32(X1,X2)) -> proper#(X1)
       proper#(U32(X1,X2)) -> proper#(X2)
       proper#(U31(X1,X2)) -> proper#(X1)
       proper#(U31(X1,X2)) -> proper#(X2)
       proper#(U23(X)) -> proper#(X)
       proper#(U22(X1,X2)) -> proper#(X1)
       proper#(U22(X1,X2)) -> proper#(X2)
       proper#(U21(X1,X2)) -> proper#(X1)
       proper#(U21(X1,X2)) -> proper#(X2)
       proper#(take(X1,X2)) -> proper#(X1)
       proper#(take(X1,X2)) -> proper#(X2)
       proper#(U136(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U136(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U136(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U136(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U135(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U135(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U135(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U135(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U134(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U134(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U134(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U134(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U133(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U133(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U133(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U133(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U132(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U132(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U132(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U132(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U131(X1,X2,X3,X4)) -> proper#(X1)
       proper#(U131(X1,X2,X3,X4)) -> proper#(X2)
       proper#(U131(X1,X2,X3,X4)) -> proper#(X3)
       proper#(U131(X1,X2,X3,X4)) -> proper#(X4)
       proper#(U122(X)) -> proper#(X)
       proper#(U121(X1,X2)) -> proper#(X1)
       proper#(U121(X1,X2)) -> proper#(X2)
       proper#(isNatList(X)) -> proper#(X)
       proper#(U13(X)) -> proper#(X)
       proper#(length(X)) -> proper#(X)
       proper#(s(X)) -> proper#(X)
       proper#(U114(X1,X2)) -> proper#(X1)
       proper#(U114(X1,X2)) -> proper#(X2)
       proper#(U113(X1,X2,X3)) -> proper#(X1)
       proper#(U113(X1,X2,X3)) -> proper#(X2)
       proper#(U113(X1,X2,X3)) -> proper#(X3)
       proper#(U112(X1,X2,X3)) -> proper#(X1)
       proper#(U112(X1,X2,X3)) -> proper#(X2)
       proper#(U112(X1,X2,X3)) -> proper#(X3)
       proper#(U111(X1,X2,X3)) -> proper#(X1)
       proper#(U111(X1,X2,X3)) -> proper#(X2)
       proper#(U111(X1,X2,X3)) -> proper#(X3)
       proper#(U12(X1,X2)) -> proper#(X1)
       proper#(U12(X1,X2)) -> proper#(X2)
       proper#(U11(X1,X2)) -> proper#(X1)
       proper#(U11(X1,X2)) -> proper#(X2)
       proper#(isNatIList(X)) -> proper#(X)
       proper#(U106(X)) -> proper#(X)
       proper#(isNat(X)) -> proper#(X)
       proper#(U105(X1,X2)) -> proper#(X1)
       proper#(U105(X1,X2)) -> proper#(X2)
       proper#(U104(X1,X2,X3)) -> proper#(X1)
       proper#(U104(X1,X2,X3)) -> proper#(X2)
       proper#(U104(X1,X2,X3)) -> proper#(X3)
       proper#(isNatIListKind(X)) -> proper#(X)
       proper#(U103(X1,X2,X3)) -> proper#(X1)
       proper#(U103(X1,X2,X3)) -> proper#(X2)
       proper#(U103(X1,X2,X3)) -> proper#(X3)
       proper#(isNatKind(X)) -> proper#(X)
       proper#(U102(X1,X2,X3)) -> proper#(X1)
       proper#(U102(X1,X2,X3)) -> proper#(X2)
       proper#(U102(X1,X2,X3)) -> proper#(X3)
       proper#(U101(X1,X2,X3)) -> proper#(X1)
       proper#(U101(X1,X2,X3)) -> proper#(X2)
       proper#(U101(X1,X2,X3)) -> proper#(X3)
       proper#(cons(X1,X2)) -> proper#(X1)
       proper#(cons(X1,X2)) -> proper#(X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       active#(U96(X)) -> active#(X)
       active#(U95(X1,X2)) -> active#(X1)
       active#(U94(X1,X2,X3)) -> active#(X1)
       active#(U93(X1,X2,X3)) -> active#(X1)
       active#(U92(X1,X2,X3)) -> active#(X1)
       active#(U91(X1,X2,X3)) -> active#(X1)
       active#(U81(X)) -> active#(X)
       active#(U71(X)) -> active#(X)
       active#(U62(X)) -> active#(X)
       active#(U61(X1,X2)) -> active#(X1)
       active#(U52(X)) -> active#(X)
       active#(U51(X1,X2)) -> active#(X1)
       active#(U46(X)) -> active#(X)
       active#(U45(X1,X2)) -> active#(X1)
       active#(U44(X1,X2,X3)) -> active#(X1)
       active#(U43(X1,X2,X3)) -> active#(X1)
       active#(U42(X1,X2,X3)) -> active#(X1)
       active#(U41(X1,X2,X3)) -> active#(X1)
       active#(U33(X)) -> active#(X)
       active#(U32(X1,X2)) -> active#(X1)
       active#(U31(X1,X2)) -> active#(X1)
       active#(U23(X)) -> active#(X)
       active#(U22(X1,X2)) -> active#(X1)
       active#(U21(X1,X2)) -> active#(X1)
       active#(take(X1,X2)) -> active#(X2)
       active#(take(X1,X2)) -> active#(X1)
       active#(U136(X1,X2,X3,X4)) -> active#(X1)
       active#(U135(X1,X2,X3,X4)) -> active#(X1)
       active#(U134(X1,X2,X3,X4)) -> active#(X1)
       active#(U133(X1,X2,X3,X4)) -> active#(X1)
       active#(U132(X1,X2,X3,X4)) -> active#(X1)
       active#(U131(X1,X2,X3,X4)) -> active#(X1)
       active#(U122(X)) -> active#(X)
       active#(U121(X1,X2)) -> active#(X1)
       active#(U13(X)) -> active#(X)
       active#(length(X)) -> active#(X)
       active#(s(X)) -> active#(X)
       active#(U114(X1,X2)) -> active#(X1)
       active#(U113(X1,X2,X3)) -> active#(X1)
       active#(U112(X1,X2,X3)) -> active#(X1)
       active#(U111(X1,X2,X3)) -> active#(X1)
       active#(U12(X1,X2)) -> active#(X1)
       active#(U11(X1,X2)) -> active#(X1)
       active#(U106(X)) -> active#(X)
       active#(U105(X1,X2)) -> active#(X1)
       active#(U104(X1,X2,X3)) -> active#(X1)
       active#(U103(X1,X2,X3)) -> active#(X1)
       active#(U102(X1,X2,X3)) -> active#(X1)
       active#(U101(X1,X2,X3)) -> active#(X1)
       active#(cons(X1,X2)) -> active#(X1)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       isNat#(ok(X)) -> isNat#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       isNatIListKind#(ok(X)) -> isNatIListKind#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       isNatKind#(ok(X)) -> isNatKind#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       isNatList#(ok(X)) -> isNatList#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       isNatIList#(ok(X)) -> isNatIList#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
       cons#(mark(X1),X2) -> cons#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3)
       U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3)
       U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3)
       U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3)
       U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U105#(ok(X1),ok(X2)) -> U105#(X1,X2)
       U105#(mark(X1),X2) -> U105#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U106#(ok(X)) -> U106#(X)
       U106#(mark(X)) -> U106#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
       U11#(mark(X1),X2) -> U11#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
       U12#(mark(X1),X2) -> U12#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U111#(ok(X1),ok(X2),ok(X3)) -> U111#(X1,X2,X3)
       U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U112#(ok(X1),ok(X2),ok(X3)) -> U112#(X1,X2,X3)
       U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U113#(ok(X1),ok(X2),ok(X3)) -> U113#(X1,X2,X3)
       U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U114#(ok(X1),ok(X2)) -> U114#(X1,X2)
       U114#(mark(X1),X2) -> U114#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       s#(ok(X)) -> s#(X)
       s#(mark(X)) -> s#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       length#(ok(X)) -> length#(X)
       length#(mark(X)) -> length#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U13#(ok(X)) -> U13#(X)
       U13#(mark(X)) -> U13#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U121#(ok(X1),ok(X2)) -> U121#(X1,X2)
       U121#(mark(X1),X2) -> U121#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U122#(ok(X)) -> U122#(X)
       U122#(mark(X)) -> U122#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U131#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U131#(X1,X2,X3,X4)
       U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U132#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U132#(X1,X2,X3,X4)
       U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U133#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U133#(X1,X2,X3,X4)
       U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U134#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U134#(X1,X2,X3,X4)
       U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U135#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U135#(X1,X2,X3,X4)
       U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U136#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U136#(X1,X2,X3,X4)
       U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       take#(ok(X1),ok(X2)) -> take#(X1,X2)
       take#(X1,mark(X2)) -> take#(X1,X2)
       take#(mark(X1),X2) -> take#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
       U21#(mark(X1),X2) -> U21#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
       U22#(mark(X1),X2) -> U22#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U23#(ok(X)) -> U23#(X)
       U23#(mark(X)) -> U23#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
       U31#(mark(X1),X2) -> U31#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
       U32#(mark(X1),X2) -> U32#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U33#(ok(X)) -> U33#(X)
       U33#(mark(X)) -> U33#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
       U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
       U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
       U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
       U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
       U45#(mark(X1),X2) -> U45#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U46#(ok(X)) -> U46#(X)
       U46#(mark(X)) -> U46#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
       U51#(mark(X1),X2) -> U51#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U52#(ok(X)) -> U52#(X)
       U52#(mark(X)) -> U52#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
       U61#(mark(X1),X2) -> U61#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U62#(ok(X)) -> U62#(X)
       U62#(mark(X)) -> U62#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U71#(ok(X)) -> U71#(X)
       U71#(mark(X)) -> U71#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U81#(ok(X)) -> U81#(X)
       U81#(mark(X)) -> U81#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U91#(ok(X1),ok(X2),ok(X3)) -> U91#(X1,X2,X3)
       U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U92#(ok(X1),ok(X2),ok(X3)) -> U92#(X1,X2,X3)
       U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U93#(ok(X1),ok(X2),ok(X3)) -> U93#(X1,X2,X3)
       U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U94#(ok(X1),ok(X2),ok(X3)) -> U94#(X1,X2,X3)
       U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U95#(ok(X1),ok(X2)) -> U95#(X1,X2)
       U95#(mark(X1),X2) -> U95#(X1,X2)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open
      
      DPs:
       U96#(ok(X)) -> U96#(X)
       U96#(mark(X)) -> U96#(X)
      TRS:
       active(zeros()) -> mark(cons(0(),zeros()))
       active(U101(tt(),V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
       active(U102(tt(),V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
       active(U103(tt(),V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
       active(U104(tt(),V1,V2)) -> mark(U105(isNat(V1),V2))
       active(U105(tt(),V2)) -> mark(U106(isNatIList(V2)))
       active(U106(tt())) -> mark(tt())
       active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1))
       active(U111(tt(),L,N)) -> mark(U112(isNatIListKind(L),L,N))
       active(U112(tt(),L,N)) -> mark(U113(isNat(N),L,N))
       active(U113(tt(),L,N)) -> mark(U114(isNatKind(N),L))
       active(U114(tt(),L)) -> mark(s(length(L)))
       active(U12(tt(),V1)) -> mark(U13(isNatList(V1)))
       active(U121(tt(),IL)) -> mark(U122(isNatIListKind(IL)))
       active(U122(tt())) -> mark(nil())
       active(U13(tt())) -> mark(tt())
       active(U131(tt(),IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
       active(U132(tt(),IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
       active(U133(tt(),IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
       active(U134(tt(),IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
       active(U135(tt(),IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
       active(U136(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
       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(),V2)) -> mark(U62(isNatIListKind(V2)))
       active(U62(tt())) -> mark(tt())
       active(U71(tt())) -> mark(tt())
       active(U81(tt())) -> mark(tt())
       active(U91(tt(),V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
       active(U92(tt(),V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
       active(U93(tt(),V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
       active(U94(tt(),V1,V2)) -> mark(U95(isNat(V1),V2))
       active(U95(tt(),V2)) -> mark(U96(isNatList(V2)))
       active(U96(tt())) -> mark(tt())
       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(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
       active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
       active(isNatList(nil())) -> mark(tt())
       active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
       active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
       active(length(nil())) -> mark(0())
       active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
       active(take(0(),IL)) -> mark(U121(isNatIList(IL),IL))
       active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
       active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
       active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
       active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
       active(U105(X1,X2)) -> U105(active(X1),X2)
       active(U106(X)) -> U106(active(X))
       active(U11(X1,X2)) -> U11(active(X1),X2)
       active(U12(X1,X2)) -> U12(active(X1),X2)
       active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
       active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
       active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
       active(U114(X1,X2)) -> U114(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(length(X)) -> length(active(X))
       active(U13(X)) -> U13(active(X))
       active(U121(X1,X2)) -> U121(active(X1),X2)
       active(U122(X)) -> U122(active(X))
       active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
       active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
       active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
       active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
       active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
       active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
       active(take(X1,X2)) -> take(active(X1),X2)
       active(take(X1,X2)) -> take(X1,active(X2))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X1,X2)) -> U32(active(X1),X2)
       active(U33(X)) -> U33(active(X))
       active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
       active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
       active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
       active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
       active(U45(X1,X2)) -> U45(active(X1),X2)
       active(U46(X)) -> U46(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X)) -> U52(active(X))
       active(U61(X1,X2)) -> U61(active(X1),X2)
       active(U62(X)) -> U62(active(X))
       active(U71(X)) -> U71(active(X))
       active(U81(X)) -> U81(active(X))
       active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
       active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
       active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
       active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
       active(U95(X1,X2)) -> U95(active(X1),X2)
       active(U96(X)) -> U96(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
       U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
       U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
       U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
       U105(mark(X1),X2) -> mark(U105(X1,X2))
       U106(mark(X)) -> mark(U106(X))
       U11(mark(X1),X2) -> mark(U11(X1,X2))
       U12(mark(X1),X2) -> mark(U12(X1,X2))
       U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
       U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
       U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
       U114(mark(X1),X2) -> mark(U114(X1,X2))
       s(mark(X)) -> mark(s(X))
       length(mark(X)) -> mark(length(X))
       U13(mark(X)) -> mark(U13(X))
       U121(mark(X1),X2) -> mark(U121(X1,X2))
       U122(mark(X)) -> mark(U122(X))
       U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
       U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
       U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
       U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
       U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
       U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
       take(mark(X1),X2) -> mark(take(X1,X2))
       take(X1,mark(X2)) -> mark(take(X1,X2))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X1),X2) -> mark(U32(X1,X2))
       U33(mark(X)) -> mark(U33(X))
       U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
       U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
       U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
       U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
       U45(mark(X1),X2) -> mark(U45(X1,X2))
       U46(mark(X)) -> mark(U46(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X)) -> mark(U52(X))
       U61(mark(X1),X2) -> mark(U61(X1,X2))
       U62(mark(X)) -> mark(U62(X))
       U71(mark(X)) -> mark(U71(X))
       U81(mark(X)) -> mark(U81(X))
       U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
       U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
       U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
       U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
       U95(mark(X1),X2) -> mark(U95(X1,X2))
       U96(mark(X)) -> mark(U96(X))
       proper(zeros()) -> ok(zeros())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(0()) -> ok(0())
       proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
       proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
       proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
       proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U106(X)) -> U106(proper(X))
       proper(isNatIList(X)) -> isNatIList(proper(X))
       proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
       proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
       proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
       proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
       proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
       proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
       proper(s(X)) -> s(proper(X))
       proper(length(X)) -> length(proper(X))
       proper(U13(X)) -> U13(proper(X))
       proper(isNatList(X)) -> isNatList(proper(X))
       proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
       proper(U122(X)) -> U122(proper(X))
       proper(nil()) -> ok(nil())
       proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
       proper(take(X1,X2)) -> take(proper(X1),proper(X2))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
       proper(U33(X)) -> U33(proper(X))
       proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
       proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
       proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
       proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
       proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
       proper(U46(X)) -> U46(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X)) -> U52(proper(X))
       proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
       proper(U62(X)) -> U62(proper(X))
       proper(U71(X)) -> U71(proper(X))
       proper(U81(X)) -> U81(proper(X))
       proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
       proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
       proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
       proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
       proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
       proper(U96(X)) -> U96(proper(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
       U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
       isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
       U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
       U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U106(ok(X)) -> ok(U106(X))
       isNatIList(ok(X)) -> ok(isNatIList(X))
       U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
       U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
       U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
       U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
       U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
       U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
       s(ok(X)) -> ok(s(X))
       length(ok(X)) -> ok(length(X))
       U13(ok(X)) -> ok(U13(X))
       isNatList(ok(X)) -> ok(isNatList(X))
       U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
       U122(ok(X)) -> ok(U122(X))
       U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
       U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
       U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
       U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
       U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
       U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
       take(ok(X1),ok(X2)) -> ok(take(X1,X2))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
       U33(ok(X)) -> ok(U33(X))
       U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
       U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
       U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
       U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
       U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
       U46(ok(X)) -> ok(U46(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X)) -> ok(U52(X))
       U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
       U62(ok(X)) -> ok(U62(X))
       U71(ok(X)) -> ok(U71(X))
       U81(ok(X)) -> ok(U81(X))
       U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
       U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
       U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
       U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
       U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
       U96(ok(X)) -> ok(U96(X))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
      Open